FROM -THE -LIBRARY- OF 
 WILLIAM -A HILLEBRAND 
 
 ENGINEERING LIBRARY 
 
STANDARD TABLE 
 
 OF 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 AND 
 
 THEIR DERIVATIVES 
 
Standard Table 
 
 OF 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 AND 
 
 Their Derivatives 
 
 WITH 
 
 Explanatory Text on Electrochemical Calculations 
 
 Solutions of Typical Practical Examples and 
 
 Introductory Notes on Electrochemistry 
 
 BY 
 
 CARL HERING, M.E., D.Sc. 
 
 Past President American Electrochemical Society and American 
 Institute of Electrical Engineers. Author of 
 "Conversion Tables" 
 
 AND 
 
 FREDERICK H. GETMAN, Ph.D. 
 
 Research Chemist 
 Formerly Associate Professor of Chemistry in Bryn Mater College 
 
 NEW YORK 
 
 D. VAN NOSTRAND COMPANY 
 
 25 PARK PLACE 
 
 1917 
 
\>v 
 
 .COPYRIGHT, IQI?, BY 
 
 NOSTRAND COMPANY 
 
 LIBRARY 
 
 THE-PLIMPTON-PRESS 
 NORWOOD-MAS S-U-S'A 
 
PREFACE 
 
 The chief purpose of this publication is to serve as 
 a reference book on account of the tables and other 
 data given in it, and not as a treatise on electro- 
 chemistry in general; sufficient explanatory text has 
 however been added to enable the data to be used 
 for most purposes without the need of a further 
 treatise on the subject. To make the data available 
 also to the student, electroplater, engineer, and 
 others who may not have made a special study of 
 chemistry and electrochemistry, the descriptive text 
 has been given in elementary and easily understood 
 terms. 
 
 In Electrochemical Industries (later Metallurgical & 
 Chemical Engineering) for January, 1903, one of the 
 present authors, Carl Hering, published a very 
 complete table of electrochemical equivalents calcu- 
 lated from the then best fundamental values. Since 
 then a more accurate value of the fundamental 
 electrochemical constant, based on silver, has been 
 adopted internationally and quite a number of the 
 atomic weights have been changed. The table in 
 the present book has therefore been entirely recalcu- 
 lated by its author from the latest and best inter- 
 nationally adopted fundamental values, including the 
 atomic weights for 1917. It has also been enlarged 
 to include all the elements and practically all of 
 their valences. The equivalents are given in terms 
 of various units, including in each case their re- 
 ciprocals. 
 
 995706 
 
vi PREFACE 
 
 The methods of making electrochemical calcula- 
 tions involving these equivalents are described by 
 means of a number of typical practical examples 
 accompanied by explanatory notes. A brief descrip- 
 tion of some of the elementary principles of chem- 
 istry involved in such calculations, has been added. 
 
 Some of the conceptions and simplified methods 
 of calculation described in the text may differ from 
 those more generally taught or found in textbooks; 
 they are offered here merely as suggestions which 
 lead to the same result as the older and more com- 
 plicated ones; the latter are also described as al- 
 ternatives to be used by those who prefer them. 
 
 The rapid developments of recent years in the 
 physical conceptions of electrochemical phenomena 
 made it desirable to include an introductory descrip- 
 tion of them in a section on the Electronic Theory. 
 This, and a section on Electrolysis which includes a 
 brief explanation of the dissociation theory, have 
 been prepared by the other author, Frederick H. 
 Getman. 
 
 The authors acknowledge their indebtedness to 
 Dr. J. W. Richards for revising and bringing up to 
 date his table of the valences which the elements 
 have in their more usual combinations. Also to the 
 Bureau of Standards for most of the fundamental 
 constants and for valuable advice and assistance. 
 
 CARL HERING 
 FREDERICK H. GETMAN 
 
 Philadelphia, Pa., and Stamford, Conn., 
 June, 1917. 
 
CONTENTS 
 
 Preface v 
 
 Introduction ix 
 
 PART I 
 
 Section I. Fundamental Laws 1 
 
 Section IE. Fundamental Data and Description of the 
 
 Tables 7 
 
 Section HI. Table I. Electrochemical Equivalents by 
 
 Weight 12 
 
 Table n. Grams per Ampere-hour in the 
 
 Order of Magnitude 21 
 
 Table III. Electrophysical Equivalents by 
 
 Volume 23 
 
 Table IV. Valences of the Elements in 
 
 Their Combinations 24 
 
 Section IV. Calculations Involving Electrochemical 
 
 Equivalents. Examples 28 
 
 PART H 
 
 Section V. Electrolysis. Theory of Electrolytic Dissoci- 
 ation. Faraday's Law. Coulometers ... 63 
 Section VI. The Electronic Theory 73 
 
 Appendix I. Valence 91 
 
 Appendix n. Elementary Principles of Chemical Reac- 
 tions and Calculations .*.... 112 
 
 Appendix m. Conversion Factors Used in Electrochemical 
 
 Calculations 120 
 
 Appendix IV. Glossary of Terms 123 
 
 Index 125 
 
 Vll 
 
INTRODUCTION 
 
 The chief purpose of the present book is to pro- 
 vide a table of constants, based on the latest and 
 best fundamental values, for making calculations of 
 the amounts of substances electrolytically deposited, 
 dissolved, or otherwise chemically changed, by an 
 electric current, and to explain by means of a series 
 of typical practical examples and descriptive text, 
 how such calculations are made. This forms Part I. 
 
 In many of the simplest kinds of calculations in- 
 volving merely the quantities of metal deposited or 
 dissolved, or the quantities of gases evolved by a 
 given current, or the reverse, the calculations by 
 means of the constants in the table are so extremely 
 simple, consisting merely of a multiplication, that no 
 further knowledge of chemistry or the laws of elec- 
 trolysis is required, all the involved parts of the 
 complete calculations having been made in the 
 preparation of the table. 
 
 Many of these calculations being greatly simplified 
 by considering the chemical valence as a separate 
 factor, as distinguished from using chemical equiva- 
 lents, a description of the significance which the 
 valences have in electrochemistry is given in Ap- 
 pendix I; the application of valences to such calcu- 
 lations is described in the examples. The older 
 methods are also described for the benefit of those 
 who do not understand or do not agree with the 
 suggested conception of the meaning and application 
 of valence to electrochemical calculations which is 
 
X INTRODUCTION 
 
 believed to be in agreement with the modern and 
 generally accepted electronic theory. 
 
 The physical conception of electrochemical phe- 
 nomena has been greatly developed in recent years, 
 and altho this does not change the simplest ways of 
 making the calculations by the use of this table, yet 
 it is of interest and of use. This has been briefly 
 summarized in Part II, which includes also a brief 
 treatise on electrolysis as based on the modern 
 dissociation theory. 
 
 The elementary principles of chemistry involved 
 in the usual calculations are briefly summarized in 
 Appendix II; for the more involved cases a fur- 
 ther knowledge of chemistry and electrochemistry is 
 necessary. 
 
 A list of the principal conversion factors l used in 
 such calculations is given in Appendix III. 
 
 In place of a glossary of the terms used in this 
 book, the places in the text where they have been 
 defined and used are given in Appendix IV. 
 
 1 Taken from Bering's Conversion Tables. 
 
PART I 
 
 - * j * j * * 
 Section I 
 
 FUNDAMENTAL LAWS 
 
 The simplest and most basic law of electrolysis 
 refers to the elements when they are in their gaseous 
 state, or in the state of vapor. When in this state 
 it is true alike for every element that to set free a 
 liter of this gas or vapor requires.. the same constant 
 amount of electricity in coulombs or ampere-hours 
 when there is one atom to the molecule and when 
 the change of valence is unity. For those elements 
 in which there are two or more atoms to the molecule 
 it will require two or more times this constant quan- 
 tity of electricity, in direct proportion; and for any 
 other change of valence the constant must also be 
 increased in direct proportion. This law applies 
 strictly to perfect or ideal gases only, and it may be 
 true that some of the gaseous elements deviate 
 slightly from this perfect state; the latter may be 
 due to a lack of precision in our knowledge of the 
 physical constants of the elements in their gaseous 
 form. But the deviations do not seem to be greater 
 than fractions of one percent and they may therefore 
 be neglected in most cases. 
 
 From the latest and best fundamental physical 
 constants, which are given in Section n, this funda- 
 mental constant for perfect gases is 4,309.7 coulombs, 
 
 1 
 
2 ELECTROCHEMICAL EQUIVALENTS 
 
 or 1.1971 ampere-hours, per liter of gas or vapor, 
 at 0C. and 760 mm. atmospheric pressure ; or exactly 
 1 ampere-hour per liter at a temperature of 53.82 C. 
 The fifth place of figures is uncertain. This constant 
 applies directly to a monatomic element (meaning 
 oris/ fcayiiig ; only one atom to the molecule) like 
 sodium vapor for instance, when the change of 
 valence is unity; for a diatomic element (two atoms 
 to the molecule) like hydrogen, and when the change 
 of valence is unity, this constant must be multiplied 
 by 2; for a diatomic element like oxygen, and when 
 the change of valence is 2 (the element is then called 
 bivalent or di-valent) the constant must be multiplied 
 by 2 x2; etc. 
 
 As this constant is the same for all the elements 
 and is independent of then* atomic weights or vapor 
 densities, this relation between the amount of gas 
 or vapor and the amount of electricity required to 
 set it free is the simplest and most direct one, and 
 may therefore be said to be the most fundamental 
 one. It may be said to be the physical relation as 
 distinguished from the chemical relation more com- 
 monly used. It may be deduced by combining the 
 generally accepted law of Faraday with that of Avo- 
 gadro, which latter states that one gram molecule 
 of every element occupies the same volume when it 
 is in its state of gas or vapor, when the temperatures 
 and pressures are the same. 
 
 When the amounts of electrolytic gases of any of 
 the elements are desired in terms of their volume, as 
 distinguished from then* weight, this relation is also 
 the simplest and most direct one to use for making 
 the calculations; and as it happens that all the six 
 gaseous elements which might be evolved electrolyti- 
 cally are diatomic at ordinary temperatures, doubling 
 
FUNDAMENTAL LAWS 3 
 
 this constant will make it apply to all of them for 
 each unit change of valence. Derivatives of this 
 constant, for convenience in calculations concerning 
 these six elements, are given in Table HI. 
 
 But hi most cases the elements concerned in 
 electrolytic calculations are not in their gaseous 
 state and sometimes they merely undergo a chemical 
 change and are not set free or dissolved. This 
 simple physical relation is then not the most con- 
 venient one to use. Moreover to specify a quantity 
 of a substance in terms of its weight (or mass) 
 instead of its volume, is often the most rational 
 way, and may simplify other subsequent calculations; 
 for gases furthermore the quantity is then independ- 
 ent of the otherwise disturbing effect of the tempera- 
 ture and pressure. 
 
 When the weights of the quantities are concerned 
 the simplest relation, deduced from Faraday's law, 
 is that every gram ion involved in an electrolytic 
 change, no matter of which element, requires the 
 same number of coulombs or ampere-hours of 
 electricity, per unit change of valence; if the change 
 of valence is two, three, etc., the amount of electricity 
 is two, three, etc., times as great. 
 
 From the latest and best fundamental physical 
 constants given in Section II, this constant is 96,494 
 coulombs or 26.804 ampere-hours per gram ion. 
 This is called a "faraday," a name which has not 
 yet been formally adopted but is sanctioned by good 
 usage and has been generally accepted. For many 
 calculations however this constant is a very incon- 
 venient and awkward one to use; the following 
 derivatives of it will often be found more convenient. 
 Table I is based on this constant. 
 
 The quantity of electricity required to electrolyze 
 
4 ELECTROCHEMICAL EQUIVALENTS 
 
 a given quantity of any element by weight, and for 
 each unit change of valence, is equal to : 
 
 96.494 -T- atomic weight, in coulombs per milligram ; 
 26.804 -=- atomic weight, in ampere-hours per gram; 
 12,158. -T- atomic weight, in ampere-hours per pound. 
 
 The reciprocals of these standard values are : 
 
 Atomic weight x 0.010363, in milligrams per coulomb; 
 Atomic weight x 0.037308, in grams per ampere-hour; 
 Atomic weight x 0.082250, in pounds per 1000 ampere-hours. 
 
 The physical meaning of these constants is that 
 they would be the actual values for a hypothetical 
 element having an' atomic weight of exactly unity. 
 As the atomic weight of hydrogen is 1.008 they 
 represent that element to within a little less 
 than 1%. 
 
 These constants are for a change of valence of 
 unity; when it is other than unity those of the 
 first group must be multiplied by the change of 
 valence, or those of the second group (the recipro- 
 cals) divided by it. 
 
 The term "change of valence " is used here instead 
 of the shorter one "valence" used in most books, 
 because the latter term by itself may sometimes lead 
 to very incorrect results; it is not always the valence 
 which an element has in a chemical compound which 
 governs the electrolytic quantities involved, but it is 
 always the change of valence during electrolysis 
 which is the true governing factor, that is, it is 
 always the difference between the valences before 
 and after electrolysis. Faraday's law stated in terms 
 of valence, as it usually is, fails to apply in some 
 cases, but when stated in terms of the change of 
 valence it becomes a universal law. 
 
FUNDAMENTAL LAWS 5 
 
 The valence of any element in its free, uncombined 
 state must be considered to be zero, because the 
 term valence, in Faraday's law at least, must be 
 interpreted to mean the number of bonds per atom 
 which hold it in combination with another element, 
 hence when the element is no longer combined these 
 bonds of course no longer exist. Therefore when an 
 element has been set free by electrolysis it means 
 that it has changed its valence from what it had in 
 the compound to zero; in that specific case therefore, 
 and only in that case, is the "valence" numerically 
 equal to the "change of valence," and it is only this 
 particular case and not the more general one, that 
 the textbooks can refer to when they give Faraday's 
 law in terms of "valence" instead of more broadly 
 and more correctly in terms of the "change of 
 valence." For further explanations see the examples 
 in Section IV and Appendix I on Valence. 
 
 It follows from the above that the same current 
 will electrolyze chemically equivalent quantities per 
 minute. For some cases this is a convenient way of 
 stating Faraday's law; the valence then does not 
 enter into the calculation as it is already embodied 
 in the chemically equivalent quantities. This is 
 illustrated in the examples, Section IV. 
 
 Another fundamental law of electrolysfs is that at 
 the cathode there will always appear that kind of a 
 chemical reaction which is called a reduction, which 
 always involves a reduction of the valence, while at 
 the anode there will always appear the opposite or re- 
 versed kind called oxidation, or better, adduction, 
 which always involves an increase of valence. When 
 chemical reductions and adductions or oxidations are 
 thus interpreted in terms of changes of valence, for 
 simplifying conceptions and calculations, it becomes 
 
6 ELECTROCHEMICAL EQUIVALENTS 
 
 necessary to couple with the valence the algebraic 
 signs + or - which it must have in order to cor- 
 respond with the direction of the current which 
 produces the reaction. For further explanation see 
 Appendix I on Valence. 
 
Section n 
 
 FUNDAMENTAL DATA AND DESCRIPTION 
 OF THE TABLES 
 
 The fundamental constants on which the values 
 in this table are based are the electrochemical 
 equivalent of silver, 0.001 118 00 gram per coulomb, 
 which has been accepted internationally, and the 
 atomic weight of silver 107.88 which is the inter- 
 nationally accepted value for 1917. Both have been 
 accepted by the Bureau of Standards. 
 
 Theur quotient gives the resulting value 96493.7 
 coulombs per univalent gram ion (log = 4.984 4991) 
 for the electrochemical constant called the faraday; 
 for most purposes this is more conveniently rounded 
 off to 96 500, the error being less than 1/100 of 1 %. 
 The equivalent of the former is 26.803 8 ampere- 
 hours (log = 1.428 1966), conveniently rounded off 
 to 26.8 (error about 1.5 hundredths of 1%). On the 
 above basis the faraday necessarily becomes a de- 
 rived quantity and is therefore not the fundamental 
 constant. 
 
 The atomic weights of all the elements are the 
 international values for 1917, based on oxygen = 16, 
 but as the electrochemical equivalents are absolute 
 and not relative, they would of course be the same 
 for atomic weights based on hydrogen = 1. These 
 atomic weights were obtained directly from Dr. 
 F. W. Clarke, Chairman of the International Com- 
 mittee. The table includes the constants for all the 
 elements excepting only the six noble gases which 
 enter into no combinations. 
 
 7 
 
8 ELECTROCHEMICAL EQUIVALENTS 
 
 Altho most of the atomic weights are not known to 
 more than four places of figures, the constants in 
 the table have been carried out uniformly to five 
 places in order that when more accurate atomic 
 weights become known the constants can be corrected 
 by proportion. In order that all calculations may be 
 made by a multiplication, the reciprocals of all the 
 values have also been given, thereby eliminating all 
 calculations by division. The constants are given in 
 terms of the three most commonly used compound 
 units, milligrams per coulomb, grams per ampere- 
 hour and pounds per 1000 ampere-hours. 
 
 The different valences for which the constants are 
 given in Table I are believed to include most of the 
 cases occurring in practice, either as valences or as 
 changes of valences. In some cases the constants 
 for a valence 1 have been included even tho that 
 valence may not occur in practice, in order to facilitate 
 calculating the constants for other valences or changes 
 of valence than those given, by a mere multiplication 
 or division by the new valences; to avoid confusion 
 these values are italicized hi Table I. Near the end 
 of this table it is shown how to calculate the constants 
 for any other valences; thus if n is the constant 
 given in any of the columns for a valence v, then for 
 any other valence x multiply the constant n by v/x 
 or by x/v as stated in that column. For the valences 
 which the elements have in their various compounds 
 see Table IV. 
 
 The last line of values gives the general formulas 
 and constants for calculating any of the values in the 
 table for any atomic weight y and any valence *, 
 based on the internationally accepted fundamental 
 electrochemical equivalent as given above. 
 
 Table II gives the constants of column 7 of Table I, 
 
DESCRIPTION OF TABLES 9 
 
 arranged in the order of the magnitude of the electro- 
 chemical equivalents of the elements. For other 
 valences than those given in the table there would of 
 course be additional values hi this supplementary 
 table. The values given in italics in Table I have 
 been omitted in Table II. 
 
 The constants in Table I are hi terms of the weights, 
 but when the volumes are desired of those elements 
 which are gases, the calculations of the amounts set 
 free by electrolysis are still further simplified by using 
 the constants in Table III; it being then a physical 
 as distinguished from a chemical relation, the con- 
 stants become the same for all the gaseous elements, 
 as they no longer involve the atomic weights; this 
 follows from a combination of the laws of Faraday and 
 Avogadro. This relation is accurately true only for 
 perfect gases; slight deviations may therefore arise 
 in practice. The additional basic constant involved 
 in the determinations of the conversion factors in this 
 Table III is the constant of Avogadro's law, namely 
 22.390 liters, for the volume of a gram molecule of 
 any of the elements in their gaseous state, at C and 
 760 mm. This constant is here deduced from the 
 weight of a liter of oxygen 1.4292 grams 1 and its 
 molecular weight 32, by dividing the latter by the 
 former. The other basic factor is that in these six 
 gaseous elements the molecules consist of two atoms, 
 that is, they are diatomic. 
 
 The application of the constants in Tables I and 
 EH to the solution of practical problems is described 
 by typical examples given hi Section IV. 
 
 1 This value is the one used in the well known Landolt- 
 Boernstein tables as the basis for calculating the densities of 
 
TABLES 
 
 OF 
 
 ELECTROCHEMICAL 
 
 AND 
 
 ELECTROPHYSICAL EQUIVALENTS 
 
 AND 
 
 THEIR DERIVATIVES 
 
12 ELECTROCHEMICAL EQUIVALENTS 
 
 
 
 
 
 
 
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 TABLES 13 
 
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14 ELECTROCHEMICAL EQUIVALENTS 
 
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TABLES 
 
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16 ELECTROCHEMICAL EQUIVALENTS 
 
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 ELECTROCHEMICAL EQUIVALENTS 
 
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TABLES 
 
 19 
 
 TH CO TP TH Ci Ci CO O iO TH CO N. IO O 00 CO *> CN CD iH LQ CO 
 P ^ ,_, t- CN CO f <=> <=> TH CO CO Ti C> TH TH CN CN CO 
 
 T-i CN o ci od ci cd Tj c i- <> CN TJ< 
 o oo c- o 10 c- o TH oo TH so co co 
 
 o oo 
 
 TH CO 
 
 10 CN TH CN CN CN -^ O TH CN CO 
 
 CO t- O t~ t> O 00 O O 
 
 t- ^*i oeo oo o HO o >*t- 
 
 ^ CO t~O l> vH 00 Tti 00 ^CO 
 
 t- CO t-0 t- CO OO-^ O> IO 
 
 co 
 
 OO 
 
 O 
 
 O> 
 
 rH ^< cd id T}< ^ ^<c o 
 
 co nJ oo co 
 
 VOCO 
 ^tH 
 
 cOTHCOCD 
 lO TH CO rH 
 
 OOTH tO rH^I iH t- THC 
 
 (N TtH tD O COO) CO t~ iO O CN ^ Ci 00 CXI t- >"( CO lO CO t- 
 
 ^CqtNj 10 iHCO TlJ rj| ^*|O4 CN *^tNOt-;CO *JCOT1JIOCO 
 
 o d T-l o oo o o oo cs o o o o o o o o o o o 
 
 00 C5 t~- TH CO CD 0> TH O Tj ^O CO iH t- -^ 
 T-Jf; O O0 TH O T-| -^ OOTpb-COTH 
 T-i O TH t^C4 <N (N (N TH O VO CO TH i-i T-i 
 
 CO ^- CO 00 CO O) O 00 tO TH ^ "^ 00 t^ C9 CO ^O tO O to CO CO 
 
 TH (N -^ TH t^ TH CO TH CNIO CN <9 V H V <Sl rH CN CN CO Tj< 
 
 10 q 10 oq ^I'^J o t^ ^J ? . ^x .*^ 1 ^ ^^^J .^!^ 
 
 TH CO Tj< TH O TH TH TH TH CO 00 <SrHCJC4CO O* T-i TH CN C CO 
 
 COCOCNtO TH TH CO C- CO <N CO (N t- TH O T* TH CO 
 
 CO CO CN C1 TH t- TH O O IO CO O^<b*COCO 'O 00 TH b- -^ 
 
 OOO O> T}< TJ4 CN CN tOt- Tj* SO CO CO iH t^ =C CN C^ CO TH 
 
 CO CO CN ^ TH O CO OO TH CO CN ^ tO t^* 00 TH VO CN TH O> TH 
 
 OCOCN to T-jt- eq to oco T-J c>o>^coco >>ooo^j^j 
 
 OOO O CN O O O OO O * O O O O (^OOOO 
 
 CM ^ CO CO iHCO Tj CO 
 
 ^ CO r^ IO CO 
 
 CN q 
 
 O Tji 
 IpQ 
 
 ^ 10 t> 
 
 CN 00 CO 
 
 CN 
 
 I 
 
 B 
 
 II 
 
 s I 
 
20 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 t* TH IQ C^ Ol C^ O5 t* . ^^ 
 
 cotdcoc<ic>T-iTHco ^ 2 ~t; 
 r>iHioo> TH T-I t- eoCxiS^ 
 
 -Ht-O>THO?THCOIO rtNX 
 
 O5 O> rj< CO >O CO OO CO^>C4>> 
 OCOOCOt-TfCOOO dC^v 
 
 (NtHTHOTlicQNT-i ^S' 
 
 QC 
 
 O O O iH 
 
 CO Tt^ 00 *^H CO x ^^ ^ 
 
 Q>OCOtCOtOOTHT)< ^CO^ 
 
 o\O)co^cotHT-ic4co CqX 
 *ioooc> oi i-i T-I o 
 
 COtOTHCOCqOiCN ^Tj*^ 
 
 * C CO > 
 
 o> 
 
 CO IO t- O T-4 CO 
 
 ^St-OOCOTHtOiHCOCO ^COX 
 
 ^5CMiHT-lt- CO Tj( t- t-\CO^, 
 
 ^cqiHT-jTHtococooq flqX 
 cjooo'd o o o d 
 
 ^COTtlO CO CO C* rJI>X 
 
 CO 
 
 t- CO <O 
 
 s 
 
 11 ,1 
 
 SF 3* M a 
 
 >H >H N N 
 
 04 j 3 g ^ 
 
 ^> 5 g gjj 
 
 P 6 M ^ 
 
 I fill 
 Illll 
 
 o o 
 
 O 
 
 .I 
 
 It'll 
 
Table H 
 
 GRAMS PER AMPERE-HOUR 
 or Kilograms per 1000 Ampere-hours (Column 7 of Table I). 
 
 IN ORDER OF MAGNITUDE 
 (Values which are in italics in Table I have been omitted here.) 
 
 
 val. 
 
 
 
 val. 
 
 
 Hydrogen 
 
 1 
 
 0.037607 
 
 Scandium 
 
 3 
 
 0.54843 
 
 Boron 
 
 5 
 
 0.082078 
 
 Arsenic 
 
 5 
 
 0.55932 
 
 Nitrogen 
 
 5 
 
 0.10454 
 
 Bromine 
 
 5 
 
 0.59633 
 
 Carbon 
 
 4 
 
 0.11197 
 
 Molybdenum 
 
 6 
 
 0.59693 
 
 Boron 
 
 3 
 
 0.13680 
 
 Sulfur 
 
 2 
 
 0.59805 
 
 Oxygen 
 
 4 
 
 0.14923 
 
 Ruthenium 
 
 6 
 
 0.63237 
 
 Glucinum 
 
 2 
 
 0.16975 
 
 Vanadium 
 
 3 
 
 0.63424 
 
 Nitrogen 
 
 3 
 
 0.17423 
 
 Chromium 
 
 3 
 
 0.64667 
 
 Chlorine 
 
 7 
 
 0.18899 
 
 Germanium 
 
 4 
 
 0.67621 
 
 Sulfur 
 
 6 
 
 0.19935 
 
 Iodine 
 
 7 
 
 0.67645 
 
 Carbon 
 
 2 
 
 0.22394 
 
 Manganese 
 
 3 
 
 0.68311 
 
 Phosphorus 
 
 5 
 
 0.23161 
 
 Iron 
 
 3 
 
 0.69443 
 
 Manganese 
 
 8 
 
 0.25617 
 
 Columbium 
 
 5 
 
 0.69766 
 
 Lithium 
 
 1 
 
 0.25892 
 
 Fluorine 
 
 1 
 
 0.70885 
 
 Silicon 
 
 4 
 
 0.26395 
 
 Molybdenum 
 
 5 
 
 0.71632 
 
 Chlorine 
 
 5 
 
 0.26459 
 
 Nickel 
 
 3 
 
 0.72975 
 
 Manganese 
 
 7 
 
 0.29276 
 
 Cobalt 
 
 3 
 
 0.73335 
 
 Oxygen 
 
 2 
 
 0.29847 
 
 Selenium 
 
 4 
 
 0.73870 
 
 Sulfur 
 
 4 
 
 0.29903 
 
 Calcium 
 
 2 
 
 0.74747 
 
 Chromium 
 
 6 
 
 0.32334 
 
 Tellurium 
 
 6 
 
 0.79280 
 
 Aluminum 
 
 3 
 
 0.33702 
 
 Zirconium 
 
 4 
 
 0.84503 
 
 Manganese 
 
 6 
 
 0.34156 
 
 Sodium 
 
 1 
 
 0.85809 
 
 Vanadium 
 
 5 
 
 0.38054 
 
 Gallium 
 
 3 
 
 0.86928 
 
 Phosphorus 
 
 3 
 
 0.38601 
 
 Osmium - 
 
 8 
 
 0.89027 
 
 Arsenic 
 
 7 
 
 0.39952 
 
 Molybdenum 
 
 4 
 
 0.89540 
 
 Bromine 
 
 7 
 
 0.42595 
 
 Antimony 
 
 5 
 
 0.89689 
 
 Chlorine 
 
 3 
 
 0.44098 
 
 Arsenic 
 
 3 
 
 0.93221 
 
 Titanium 
 
 4 
 
 0.44863 
 
 Iodine 
 
 5 
 
 0.94703 
 
 Magnesium 
 
 2 
 
 0.45367 
 
 Ruthenium 
 
 4 
 
 0.94856 
 
 Ruthenium 
 
 8 
 
 0.47428 
 
 Vanadium 
 
 2 
 
 0.95136 
 
 Vanadium 
 
 4 
 
 0.47568 
 
 Chromium 
 
 2 
 
 0.97001 
 
 Selenium 
 
 6 
 
 0.49247 
 
 Bromine 
 
 3 
 
 0.99389 
 
 Manganese 
 
 4 
 
 0.51234 
 
 Palladium 
 
 4 
 
 0.99520 
 
 21 
 
22 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 
 val. 
 
 
 
 val. 
 
 
 Manganese 
 
 2 
 
 1.0247 
 
 Samarium 
 
 3 
 
 1.8704 
 
 Iron 
 
 2 
 
 1.0416 
 
 Europium 
 
 3 
 
 1.8903 
 
 Nickel 
 
 2 
 
 1.0946 
 
 Lead 
 
 4 
 
 1.9326 
 
 Cobalt 
 
 2 
 
 1.1000 
 
 Gadolinium 
 
 3 
 
 1.9562 
 
 Yttrium 
 
 3 
 
 1.1031 
 
 Terbium 
 
 3 
 
 1.9798 
 
 Tin 
 
 4 
 
 1.1071 
 
 Palladium 
 
 2 
 
 1.9904 
 
 Uranium 
 
 8 
 
 1.1109 
 
 Dysprosium 
 
 3 
 
 2.0209 
 
 Tungsten 
 
 6 
 
 1.1441 
 
 Holmium 
 
 3 
 
 2.0333 
 
 Copper 
 
 2 
 
 1.1858 
 
 Erbium 
 
 3 
 
 2.0855 
 
 Osmium 
 
 6 
 
 1.1870 
 
 Thulium 
 
 3 
 
 2.0955 
 
 Tellurium 
 
 4 
 
 1.1892 
 
 Cadmium 
 
 2 
 
 2.0967 
 
 Molybdenum 
 
 3 
 
 1.1939 
 
 Indium 
 
 2 
 
 2.1415 
 
 Platinum 
 
 6 
 
 1.2138 
 
 Ytterbium 
 
 3 
 
 2.1577 
 
 Zinc 
 
 2 
 
 1.2194 
 
 Thorium 
 
 4 
 
 2.1676 
 
 Rhodium 
 
 3 
 
 1.2797 
 
 Lutecium 
 
 3 
 
 2.1763 
 
 Gallium 
 
 2 
 
 1.3039 
 
 Tin 
 
 2 
 
 2.2142 
 
 Cerium 
 
 4 
 
 1.3081 
 
 Uranium 
 
 4 
 
 2.2217 
 
 Chlorine 
 
 1 
 
 1.3229 
 
 Copper 
 
 1 
 
 2.3717 
 
 Tantalum 
 
 5 
 
 1.3543 
 
 Tellurium 
 
 2 
 
 2.3784 
 
 Tungsten 
 
 5 
 
 1.3729 
 
 Gold 
 
 3 
 
 2.4524 
 
 Indium 
 
 3 
 
 1.4277 
 
 Thallium 
 
 3 
 
 2.5370 
 
 Potassium 
 
 1 
 
 1.4588 
 
 Barium 
 
 2 
 
 2.5625 
 
 Selenium 
 
 2 
 
 1.4774 
 
 Bismuth 
 
 3 
 
 2.5867 
 
 Uranium 
 
 6 
 
 1.4811 
 
 Uranium 
 
 3 
 
 2.9623 
 
 Antimony 
 
 3 
 
 1.4948 
 
 Bromine 
 
 1 
 
 2.9817 
 
 Bismuth 
 
 5 
 
 1.5520 
 
 Rubidium 
 
 1 
 
 3.1880 
 
 Iodine 
 
 3 
 
 1.5784 
 
 Tungsten 
 
 2 
 
 3.4323 
 
 Strontium 
 
 2 
 
 1.6347 
 
 Platinum 
 
 2 
 
 3.6413 
 
 Tungsten 
 
 4 
 
 1.7162 
 
 Mercury 
 
 2 
 
 3.7420 
 
 Lanthanum 
 
 3 
 
 1.7286 
 
 Lead 
 
 2 
 
 3.8651 
 
 Cerium 
 
 3 
 
 1.7442 
 
 Silver 
 
 1 
 
 4.0248 
 
 Praseodymium 
 
 3 
 
 1.7522 
 
 Radium 
 
 2 
 
 4.2158 
 
 Uranium 
 
 5 
 
 1.7774 
 
 Iodine 
 
 1 
 
 4.7351 
 
 Molybdenum 
 
 2 
 
 1.7908 
 
 Caesium 
 
 1 
 
 4.9549 
 
 Neodymium 
 
 3 
 
 1.7945 
 
 Gold 
 
 1 
 
 7.3572 
 
 Iridium 
 
 4 
 
 1.8011 
 
 Mercury 
 
 1 
 
 7.4840 
 
 Platinum 
 
 4 
 
 1.8206 
 
 Thallium 
 
 1 
 
 7.6109 
 
Table m 
 
 ELECTROPHYSICAL EQUIVALENTS OF GASES 
 BY VOLUME 
 
 The following constants, which are independent of the atomic 
 weights or vapor densities, apply to all the six elements, BRO- 
 MINE, CHLORINE, FLUORINE, HYDROGEN, NITROGEN, 
 and OXYGEN, which in their free state are normally gases, 
 and all of which are diatomic. They are here assumed to 
 have the properties of a perfect or ideal gas. The constants 
 are for a unit change of. valence, hence for any other change 
 of valence (for oxygen it is generally 2) the constants of the 
 first group must be multiplied by it and those of the second 
 group divided by it. 
 
 The volumes of the gases are for C and 760 mm, 
 
 8.6193 coulombs per cubic centimeter ; 
 2.3943 ampere-hours per liter ; 
 67.798 ampere-hours per cubic foot 
 
 The reciprocals are : 
 
 0.11602 cubic centimeter per coulomb ; 
 0.41767 liter per ampere-hour: 
 14.750 cubic feet per 1000 ampere-hours. 
 
 23 
 
Table IV 
 
 VALENCES OF THE ELEMENTS IN THEIR 
 COMBINATIONS 
 
 Prepared by Prof. Jos. W. Richards 
 
 The following are the practical or actual valences irrespective 
 of any interpretation involving structural formulas. There are 
 additional valences which occur more rarely, and still others 
 about which there may be some doubt. By the word " salts " 
 is meant oxides, sulfides, sulfates, chlorides, chlorates, etc. 
 
 NAMES VALENCES 
 
 Aluminum Salts + III; aluminates + III. 
 
 Antimony Antimonous salts + III ; antimonic salts + V ; 
 
 antimonites + III ; antimonates + V ; anti- 
 
 monides - III, sometimes - I and - II. 
 
 Argon Non-valent ; forms no known combinations. 
 
 Arsenic Arsenious salts + III ; arsenic salts + V ; arse- 
 
 nites + III ; arsenates + V ; arsenides - III, 
 
 sometimes - I and - n. 
 
 Barium Salts + II ; peroxide + IV. 
 
 Bismuth Bismuthous salts + III ; bismuthic salts and 
 
 bismuthates + V. 
 
 Boron Salts + III ; borates + III ; perborates + V. 
 
 Bromine Bromides - I; hypo-bromites + I; bromites 
 
 + III ; bromates + V ; .perbromates + VII. 
 
 Cadmium Salts + H. 
 
 Caesium Salts + I. 
 
 Calcium Salts + H. 
 
 Carbon Carbonates + IV ; salts usually + IV ; in CO 
 
 + II ; hydrocarbons, free valences - I to - IV. 
 
 Cerium Cerous salts + III ; eerie salts + IV. 
 
 Chlorine Chlorides - I ; hypochlorites + I ; chlorites 
 
 + III; chlorates + V; perchlorates + VII; in 
 
 chlorine oxides + 1, + III, -f IV, + V, + VII. 
 24 
 
TABLES 
 
 25 
 
 Chromium Chromous salts + n ; chromic salts + HI ; tri- 
 
 * oxide + VI ; chromites -f ni ; chromates or 
 
 di-chromates + VI. 
 
 Cobalt Cobaltous salts + H ; cobaltic salts + HI. 
 
 Columbium CbO + H ; CbO 2 + IV ; columbic salts and 
 
 columbates +V. 
 
 Copper Cuprous salts + I ; cupric salts + n. 
 
 Dysprosium .... Salts + III. 
 
 Erbium Salts + m. 
 
 Europium Salts -f HI. 
 
 Fluorine Fluorides - I ; all compounds - I. 
 
 Gadolinium Salts + in. 
 
 Gallium Salts + HI. 
 
 Germanium .... Germanous salts + n ; germanic salts + IV ; 
 
 germanites + n ; germanates + IV. 
 
 Glucinum Salts + n. 
 
 Gold Aurous salts + 1 ; auric salts + HI ; aurates 
 
 + m. 
 
 Helium Non-valent; forms no known combinations. 
 
 Holmium Salts + HI. 
 
 Hydrogen + I ; in peroxide + H. 
 
 Indium Salts + m. 
 
 Iodine . . Iodides - I ; hypo-iodites + I ; iodites + in ; 
 
 iodates + V ; per-iodates + VH ; iodic oxide 
 
 + V. 
 
 Indium Iridous salts + HI ; iridic salts + IV. 
 
 Iron Ferrous .salts + H; ferric salts + HI; ferrites 
 
 + HI ; ferrates + VI. 
 
 Krypton Non-valent ; forms no known combinations. 
 
 Lanthanum Salts + HI. 
 
 Lead Usual salts or plumbic salts + H ; di-oxide or 
 
 peroxide and plumbates + IV ; sub-oxide + I. 
 
 Lithium Salts + L 
 
 Lutecium Salts + HI. 
 
 Magnesium . . . Salts + H. 
 
 Manganese .... Manganous salts + H ; manganic salts + HI ; 
 
 di-oxide or peroxide + IV ; manganates + VI ; 
 
 permanganates -f VH. 
 
 Mercury Mercurous salts + I ; mercuric salts -f H. 
 
 Molybdenum . . Molybdous salts + H ; molybdic salts -f HI ; di- 
 oxide + IV ; tri-oxide and molybdates + VI. 
 Neodymium . . . Salts + HI. 
 
26 ELECTROCHEMICAL EQUIVALENTS 
 
 Neon Non-valent ; forms no known combinations. 
 
 Nickel Nickelous salts + II ; nickelic salts + III. 
 
 Niton Non-valent; forms no known combinations. 
 
 Nitrogen Ammonia and ammonium salts (NH 4 salts) 
 
 - Ill ; most organic nitrogen compounds 
 
 - Ill ; nitrous oxide + I ; nitric oxide + II ; 
 sesqui-oxide and nitrites + III ; di-oxide (per- 
 oxide) + IV ; nitric anhydride and nitrates 
 + V. (In ammonium nitrite and nitrate the 
 N in the NH 4 radical is - III and in the acid 
 radical + III or + V.) 
 
 Osmium Osmous salts + II ; osmic salts + IV ; sesqui- 
 oxide + III ; tri-oxide and osmates + VI ; 
 peroxide and perosmates + VIII. 
 
 Oxygen Oxides, salts, etc. - II. 
 
 Palladium Palladous salts + II ; palladic salts + IV. 
 
 Phosphorus .... Phosphorous salts and phosphites + III ; phos- 
 phoric salts and phosphates + V ; phosphides 
 
 - Ill ; hypophosphites + I ; hypophosphates 
 + IV. 
 
 Platinum Platinous salts and platinites + II; platinic 
 
 salts and platinates + IV. 
 
 Potassium Salts + I. 
 
 Praseodymium . . Salts + III. 
 
 Radium Salts + II. 
 
 Rhodium Rhodous salts + II ; rhodic salts + III ; 
 
 dioxide + IV. 
 
 Rubidium Salts + I. 
 
 Ruthenium Ruthenous salts + II ; ruthenic salts + III ; 
 
 ruthenic anhydride and ruthenates + VI ; 
 
 per-ruthenic anhydride + VIII. 
 
 Samarium Salts + III. 
 
 Scandium Salts + III. 
 
 Selenium Selenites + IV ; selenates + VI ; selenides - II. 
 
 Silicon Silicides - IV; salts, oxide and silicates + IV. 
 
 Silver Salts + I. 
 
 Sodium . Salts + I. 
 
 Strontium Salts + II. 
 
 Sulfur Sulfides - II; di-sulfides - I; SO 2 and sulfites 
 
 + IV; SO 3 and sulfates + VI; hyposulfites 
 
 (thio-sulfates) +11; S 2 O 3 +III; S 2 O 7 and 
 
 per-sulfates + VII. 
 
TABLES 27 
 
 Tantalum Salts and tantalates + V. 
 
 Tellurium Tellurides - n ; di-tellurides -I ; tellurous 
 
 salts + n ; telluric salts and tellurites + IV ; 
 
 TeO 8 and tellurates + VL 
 
 terbium Salts + HI. 
 
 Thallium Thallous salts + 1; thallic salts + ffl. 
 
 Thorium Salts + IV. 
 
 Thulium Salts + HL 
 
 Tin Stannous salts and stannites + H ; stannic salts 
 
 and stannates + IV. 
 Titanium Titanous salts and titanites + ffl; titanic salts 
 
 and titanates + IV. 
 Tungsten WO +H; WO 2 and WCU +IV; WCU +V; 
 
 tungstic oxide and tungstates + VL 
 Uranium Uranous salts + IV ; uranic salts and uranates 
 
 + VI; oxides +m, +IV, +VI, +VHI; 
 
 chloride +V. 
 Vanadium Vanadates + V; vanadous salts + HI; VO 
 
 + H; V0 2 +IV. 
 
 Xenon Non-valent ; forms no known combinations. 
 
 Ytterbium Salts + m. 
 
 Yttrium Salts + HI. 
 
 Zinc Salts +H. 
 
 Zirconium. . . . Salts and zirconates + IV. 
 
Section IV 
 
 CALCULATIONS INVOLVING ELECTROCHEMICAL 
 EQUIVALENTS. EXAMPLES 
 
 There are in general three ways of making calcula- 
 tions which are based on Faraday's law and there- 
 fore involve electrochemical equivalents, that is, 
 calculations of the quantities of the materials by 
 weight which are deposited, dissolved, or otherwise 
 chemically changed when an electric current is passed 
 thru an electrolyte. The simplest cases are so easy 
 to calculate with the aid of the accompanying table 
 that very little and in some cases no knowledge of 
 chemistry is required ; even in some of these simplest 
 ones, however, it is essential to know what the so- 
 called "valence" is of the chemical element in the 
 problem; whenever it is unity it can be neglected; 
 those who do not know how to determine it had 
 better consult a chemist ; an explanation of the 
 meaning of this term is given in Appendix I. In the 
 more involved cases a knowledge of chemistry is 
 required for making the calculations ; some of the 
 elementary principles of chemistry are given in Ap- 
 pendix II. 
 
 The first and simplest method of making such 
 calculations is to use the figures given in Table I, 
 which includes all the elements and practically all the 
 valences occurring in practice ; all that is necessary 
 then is to multiply the proper figure from the table 
 (being careful about the valence) by the quantity of 
 
 28 
 
EXAMPLES 29 
 
 material or current and the time stated hi the par- 
 ticular problem ; the table saves the most tedious 
 parts of the complete calculations, as they have 
 already been made in calculating the values given in 
 it ; the table is a convenience but not a necessity, as 
 the calculations could all be made without it, tho they 
 are then more laborious and sometimes far more so. 
 
 The second method is based on the single electro- 
 chemical constant called a "faraday" which is the 
 same for all the elements.- It is the electric charge 
 carried by a gram ion when the valence is unity. No 
 table is then required, but the calculations are often 
 quite lengthy, tedious, and confusing. It is then 
 necessary to know the value of the faraday ; its best 
 known value at the present time is very nearly 96,500 
 coulombs or about 26.80 ampere-hours (more ac- 
 curately 96,493.7 and 26.8038). As before, it must be 
 known what the valence is in the particular problem. 
 For valences 2, 3, 4, etc. (whether positive or nega- 
 tive), the charges are 2, 3, 4, etc. faradays. 
 
 When the elements are set free in the form of 
 gases or vapors, and when the amounts are desired 
 hi terms of their volumes instead of their weights, 
 there exists a still simpler constant than the faraday, 
 because the amount of electricity required to set free 
 a liter of the vapor of any element is always the same 
 per unit atom in the molecule and per unit change of 
 valence. This constant for and 760 mm. is 4309.7 
 coulombs or 1.1971 ampere-hours per liter. This 
 need then merely be multiplied by the number of 
 atoms in a molecule of the gas or vapor, called its 
 atomicity (and apparently always a simple whole 
 number), and by the change of valence (also generally 
 a simple whole number) to give the result directly. 
 For the atomicity of an element works on chemistry 
 
30 ELECTROCHEMICAL EQUIVALENTS 
 
 should be consulted. The change of valence must be 
 determined hi each particular case ; hi all ordinary 
 cases that of hydrogen is 1 and of oxygen 2. For the 
 six gaseous elements, the atomicity of all of which at 
 ordinary temperatures is 2, this constant and its 
 derivations are given hi Table III. As the calcula- 
 tions are then so simple and direct no further explana- 
 tions are necessary (see Example 2 below). 
 
 The third general method of making electrochemical 
 calculations is first to make the electrochemical part 
 of it for some other convenient element or radical, 
 like hydrogen, oxygen, zinc, SO 4 , or some element in 
 the particular reaction for which the calculation is 
 simple and surely correct, and then by a purely 
 chemical calculation determine what the chemical 
 equivalent of this amount of the intermediary element 
 is hi terms of the one for which the figures are de- 
 sired. When the valences of the two are the same, 
 then* chemical equivalent weights are in proportion to 
 their atomic weights ; when the valences are different 
 reduce the relative weights to unity valence by 
 dividing the atomic weights by the respective valences. 
 This methods always requires some knowledge of 
 chemistry and sometimes considerable. In some of 
 the more involved, complicated, or obscure cases this 
 is the safest and surest method, as it is less liable to 
 be confusing. It is always more lengthy and tedious 
 than the first method, and sometimes much more so. 
 If hydrogen is always used as this intermediary (be- 
 cause its atomic weight is practically unity) the table 
 is rendered unnecessary except for the values for 
 hydrogen. 
 
 With these brief statements about the three 
 methods they are best explained hi detail by the 
 following set of examples and the remarks accom- 
 
EXAMPLES 31 
 
 panying them. These examples have been chosen to 
 be characteristic of the more usual typical cases and 
 include also a few of the unusual ones. 
 
 Example I. Simplest case. Valence may be neglected. 
 How much silver will be deposited per hour by 
 10 amperes? The valence of silver being always 
 unity can be neglected. For silver, column 7 of the 
 table states that one ampere-hour will deposit 4.025 
 grams, hence 10 amperes will deposit 40.25 grams per 
 hour (one troy ounce is equal to 20 pennyweight or 
 to 31.104 grams). 
 
 To calculate this by the second method, without 
 the table, one must know that every gram ion of the 
 silver (or of any other element whose valence is 
 unity) carries a charge of one "faraday" which is 
 equal to about 96,500 (accurately 96,493.7) coulombs 
 of electricity (a coulomb is equal to an ampere flowing 
 for one second). In cases occurring in practice it is 
 often more convenient to use its equivalent 26.8038 
 ampere-hours. A gram ion of silver is as many grams 
 as are expressed by its atomic weight, hence for silver 
 the weight of a gram ion is 107.88 grams. 10 amperes 
 for one hour are equal to 10 x 3600 seconds = 36,000 
 coulombs (or ampere-seconds). Dividing this by the 
 faraday, 96,500 coulombs gives 0.373 gram ions, and 
 as a gram ion of silver weighs 107.88 grams, the 
 desired result is 0.373 x 107.88 = 40.25 grams, as 
 before. Or the faraday may in this case be more 
 conveniently taken as 26.8 ampere-hours, then 10 
 ampere-hours divided by 26.8 equals 0.373 gram ions, 
 as before. The use of the table saves these some- 
 what lengthy computations and the errors arising in 
 multiplying when one should have divided, or the 
 reverse, as the problems are often the reverse of the 
 present one. 
 
32 ELECTROCHEMICAL EQUIVALENTS 
 
 In the third method of making this calculation, 
 which may be resorted to by those who are not used 
 to the conception of valences, or hi some complicated 
 or involved cases, select some other convenient inter- 
 mediary element, like hydrogen for instance, for the 
 electrochemical part of the calculation, using the 
 values for that element in the table, and then by a 
 purely chemical calculation determine the chemically 
 equivalent weights of that intermediary element and 
 of the original one ; the electrochemical equivalents 
 will then be hi the proportion of these weights. 
 
 In many cases hydrogen is selected as this inter- 
 mediary element, chiefly because its atomic weight is 
 practically unity, hence the corresponding weights of 
 all the other elements are equal to then* atomic 
 weights which must however be divided by the 
 valence which they have hi that particular problem 
 when it is not unity. Another reason for selecting 
 hydrogen is that the whole table is then reduced to 
 the few figures for hydrogen alone. Hence selecting 
 hydrogen hi the present problem, find from the table 
 how much hydrogen will be set free in one hour by 
 the 10 amperes; the table gives 0.03761 grams for 
 one ampere, hence multiplying by 10 gives 0.3761 
 grams. 
 
 To find the chemically equivalent weights of silver 
 and hydrogen, it is hi this case sufficient (because 
 both have a valence of unity) to use their atomic 
 weights 107.88 and 1.008; for most purposes it is 
 accurate enough to assume that of hydrogen to be 
 unity. The valence of silver and hydrogen are both 
 unity and may therefore here be neglected ; if instead 
 of silver it were zinc, for instance, whose valence is 
 always 2, the atomic weight of zinc, 65.37, would have 
 to be divided by this valence 2 to get the chemically 
 
EXAMPLES 33 
 
 equivalent weights, which would then be 32.69 and 
 1.008. 
 
 Having found the chemically equivalent weight of 
 silver to be 107.88 + 1.008 = 107.02 times that of 
 hydrogen, multiply the above 0.3761 grams of hydro- 
 gen by 107.02, giving as before 40.25 grams of silver 
 per hour, for 10 amperes. 
 
 While this method is a somewhat involved one for 
 such a simple case as the present one, it is explained 
 here because it is often a safe method to resort to 
 (even if only as a check) in the more complicated and 
 involved cases like those in which there is no deposit 
 or merely a change of valence, as is the case for 
 instance with depolarizers, or when the valence is not 
 known or is obscured ; and in some of these more 
 involved cases it may be more convenient to use some 
 other element which is actually involved in the par- 
 ticular reaction, instead of hydrogen ; these cases will 
 be described below in other examples. 
 
 Example 2. Gas. How many amperes will it take to 
 generate a cubic foot of hydrogen per hour? A liter 
 of hydrogen at 0C. and 760 mm. weighs 0.09004 
 grams, hence a cubic foot will weigh 0.09004 x 28.32 
 = 2.55 grams. The valence of hydrogen, being unity, 
 can be neglected. From Table I, column 8, it takes 
 26.59 ampere-hours to generate one gram; hence 
 2.55 grams will require 26.59 x 2.55 = 67.8 ampere- 
 hours ; therefore it will take 67.8 amperes to generate 
 one cubic foot of hydrogen per hour. 
 
 Hydrogen being a gas and as the amount is here 
 required in terms of volume and not of weight, this 
 same result can be obtained directly from Table m. 
 
 Example 3. Anode. Valence 2. How long will 10 
 pounds of copper anodes last in a copper plating or 
 electrotyping bath in which the average current is 50 
 
34 ELECTROCHEMICAL EQUIVALENTS 
 
 amperes, the solution being a cupric salt, like sulfate 
 of copper? The valence of copper in a cupric salt is 
 2, hence from the table, column 10, one pound of 
 copper at this valence will be consumed by 382.5 
 ampere-hours, which at 50 amperes means a little 
 over 76 hours. 
 
 In making this calculation by means of the unit 
 faraday, it must be remembered that the copper in 
 this case has a valence of 2, hence each gram ion of 
 63.57 grams now carries a charge of 2 faradays or 
 193,000 coulombs. 50 amperes equal 180,000 cou- 
 lombs per hour, which divided into 193,000 gives 
 1.072 gram ions of 63.57 grams, making 68.15 grams 
 or 0.150 Ibs., hence 10 Ibs. will last 76 hours, as 
 before. 
 
 In making the calculation by the other method 
 based on hydrogen as an intermediary element it 
 must not be forgotten that the equivalent weight of 
 copper is now the atomic weight divided by 2, because 
 the valence now is 2. 
 
 Example 4. Primary lattery. How many pounds 
 of zinc will be consumed per hour (not including local 
 action) in a battery of primary cells generating 1 
 kilowatt, the available voltage being 1.7 per cell? 
 Zinc always has the same valence, 2 ; when the 
 figures in the table are used this valence has already 
 been included in them and therefore the valence may 
 be ignored in the subsequent calculations. For ziric, 
 column 9 gives the constant 2.688 and states that 
 when divided by the volts this is equal to the pounds 
 per kilowatt-hour. Dividing 2.688 by 1.7 gives 1.58 
 pounds per hour for one kilowatt. The zinc con- 
 sumption will of course be the same for a single large 
 cell as for a battery of cells, and is independent of 
 whether the cells are connected in series or in parallel. 
 
EXAMPLES 35 
 
 To calculate this zinc consumption from the unit 
 "faraday," that is, without the table, the valence 2 
 must be taken into account. This unit is the charge 
 carried by a monovalent gram ion, that is, it is for a 
 valence 1. For any other valence this constant must 
 be multiplied by the valence ; hence for zinc it is 
 96,500 x 2 = 193,000 coulombs. One kilowatt at 1.7 
 volts means 588 amperes which for one hour is equal 
 to 3600 x 588 = 2,116,800 coulombs ; dividing by 2 
 faradays or 193,000 coulombs, gives 10.96 gram ions 
 of zinc, and as one gram ion is numerically equal to 
 the atomic weight, hence is 65.37 grams, this equals 
 10.96 x 65.37 = 716.0 grams ; multiplying by 0.002205 
 gives 1.58 pounds, as before. This example again 
 shows how much calculation is saved by using the 
 table. 
 
 Single valence. The above examples show how to 
 use the table when the chemical element is set free or 
 dissolved and has only a single valence, in which 
 cases there can be no question as to what the valence 
 is. The table is used in the same way with those 
 elements which have several valences, as stated in 
 column 4 ; it is then of course of the utmost import- 
 ance to know which of its valences is the one involved 
 in the particular problem ; the importance of this is 
 shown in the next paragraph. 
 
 Several valences. When copper, for instance, is 
 deposited from the ordinary copper sulfate, CuSO 4 
 (cupric sulfate), its valence is 2, as the copper then 
 is the chemical equivalent of two atoms of hydrogen 
 in the corresponding hydrogen compound H 2 SO 4 
 (sulfuric acid). Hence with that electrolyte the 
 constants in the table for the valence 2 must be used. 
 If however it is deposited from the cuprous sulfate 
 Cu 2 SO 4 , the copper is the direct equivalent of the 
 
36 ELECTROCHEMICAL EQUIVALENTS 
 
 hydrogen, hence its valence then is 1. As will be 
 seen from the table, the same current then deposits 
 twice as much copper, hence the importance of using 
 the constants for the correct valence. 
 
 When the table is not used, or only indirectly, the 
 changes necessary in the calculations when the val- 
 ence is anything else than unity, have already been 
 described above hi examples 1, 3, and 4. 
 
 Change of valence. The above cases are the more 
 usual ones in which some chemical element like a 
 metal or gas is set free or dissolved at the electrodes. 
 In some other cases however the element is neither 
 set free nor dissolved ; in these the current merely 
 changes the valence of the element from one value to 
 another. This is the case for instance in many of 
 the so-called depolarizers of batteries, like in the 
 manganese of the peroxide in the usual dry cell, the 
 lead of the positive plate of the lead storage battery, 
 the chromium or nitrogen of the corresponding acids 
 in the Grove or the Bunsen cells. Also in such reac- 
 tions as the changing of ferrous into ferric salts, 
 cuprous to cupric salts, etc., or the reverse. 
 
 In all such cases the simplest rule is to find out 
 what the valences are before and after the passage 
 of the current, the difference between them will then 
 be the change of valence, and it is this difference 
 which must be used in column 4 of the table to find 
 the corresponding electrochemical equivalents. The 
 function of the current may be said to be the changing 
 of the valence of an element ; and for a unit amount 
 of any given element a certain definite amount of 
 electricity is required to change the valence by one 
 unit, no matter whether that valence was high or low ; 
 for instance, it takes just as much electricity to 
 reduce a gram of copper from a cupric (valence 2) to 
 
EXAMPLES 37 
 
 a cuprous (valence 1) salt, in which operation the 
 change of valence is 1, as it does to deposit a gram 
 of the metal from the cuprous salt in which the change 
 of valence is also 1 ; after metals or other elements 
 have been set free as such, their valence is zero, as 
 they are then no longer in combination with other 
 elements and therefore then have no existing bonds ; 
 hence depositing a free element is really also a case 
 of change of valence (see Appendix I). 
 
 In subtracting one valence from another the differ- 
 ence may have the negative sign, as in subtracting 3 
 from 2 ; the sign of this difference need not be con- 
 sidered as it signifies merely the direction of the 
 current but not the amount; hence all the valences 
 in the table apply equally well to the negative as to 
 the positive values. These features of valences are 
 described more fully in Appendix I. 
 
 Example 5. Depolarizer. Change of valence. How 
 much peroxide of manganese is required as a de- 
 polarizer in a dry cell for a discharge of 100 ampere- 
 hours? In this reaction 2 MnO 2 is reduced to Mn 2 O 3 , 
 the remaining atom of oxygen being that which per- 
 forms the operation of depolarizing by combining with 
 the ion which would otherwise tend to be set free 
 there and cause polarization. 
 
 The valence of the manganese in the original ma- 
 terial is 4 (as oxygen here has a valence of 2) , while 
 in the resulting product it is 3 (the oxygen now having 
 6 bonds, each of the two manganese atoms must 
 have 3), hence the difference or change of valence is 
 1. From the table, column 9 for manganese, valence 
 1, 4.518 pounds of the element manganese are re- 
 quired for 1000 ampere-hours, hence 0.4518 Ib. for 
 100 ampere-hours. This is for the element man- 
 ganese ; the corresponding amount of the peroxide is 
 
38 ELECTROCHEMICAL EQUIVALENTS 
 
 then determined as usual by the well known chemical 
 calculations ; thus the molecular weight (or more 
 correctly the formula weight) of the peroxide MnO 2 
 is 54.93 + (16 x 2) = 86.93, and that of manganese 
 alone is 54.93 ; hence 0.4518 Ib. of Mn x 86.93 ^ 
 54.93 = .715 or about 3/4 Ib. of the peroxide. 
 
 The same result may be obtained without involving 
 the change of valences, but it will be found to be far 
 more cumbersome. In that case write out the com- 
 plete chemical equation of the reaction involving the 
 zinc, the manganese oxides, and the ammonium 
 chloride. Then calculate the amount of zinc con- 
 sumed by the 100 ampere-hours, as described above, 
 using the constants in the table, and then from the 
 equation by purely chemical calculations, determine 
 the amount of the peroxide corresponding to that 
 amount of zinc. 
 
 Subscripts may be ignored. After having determined 
 the valence involved in a reaction, the subscripts in 
 the chemical formulas of compounds can be ignored 
 entirely in these electrochemical calculations. For a 
 given valence of an element an ampere-hour corre- 
 sponds to a fixed and definite amount of the element 
 and is entirely independent of any arbitrary chemical 
 formula. 
 
 Thus from cuprous chloride CuCl the amount of 
 chlorine involved by one ampere-hour is exactly the 
 same as in cupric chloride CuCl 2 , namely 1.323 grams, 
 altho the subscript is twice as great in the second 
 case ; the valence of the chlorine is the same in 
 both, namely 1. For the copper the subscripts are 
 the same in both (unity), yet the amount of copper 
 deposited per ampere from CuCl is twice as great as 
 from CuCl 2 because the valence is half as great. 
 The subscripts are important for determining the 
 
EXAMPLES 39 
 
 valences, but beyond that they should be ignored in 
 such calculations, as they may cause confusion. For 
 the indirect method of calculation in which the whole 
 chemical equation must be written out, the subscripts 
 are of course important for balancing the equation 
 and must be considered in the purely chemical part 
 of the calculation. 
 
 Coefficients may be ignored. What was said above 
 about subscripts is equally applicable to the coeffi- 
 cients in chemical formulas; they moreover are not 
 even necessary to determine the valence. This is 
 illustrated by the following example. 
 
 Example 6. Ignoring .coefficients. How much nitric 
 acid will be required in a Bunsen cell for 100 ampere- 
 hours, assuming that the nitric acid HNO 3 is all 
 reduced to nitric oxide NO? 
 
 The chemical formula for this reaction is 
 
 3 Zn + 3 H 2 SO4.+ 2 HNO 3 = 3 ZnSO 4 + 2 NO 
 + 4H 2 O 
 
 which it will be seen contains numerous coefficients. 
 In the simplest and most direct form of calculation 
 based on the change of valence, all that is necessary 
 to know is that the valence of the nitrogen in the 
 nitric acid is 5 and in the nitric oxide it is 2, hence the 
 change of valence is 3 ; all these coefficients may 
 therefore be neglected, and in fact need not even be 
 known. From the table the constant for nitrogen 
 for a change of valence of 3 is 0.3841 pounds per 1000 
 ampere-hours; for 100 ampere-hours it is therefore 
 0.0384 Ib. From this the amount of the acid is cal- 
 culated by the usual chemical method; thus the 
 atomic weight of N = 14.01, and the molecular weight 
 of HNO 3 = 1.008 + 14.01 + 48. = 63.02 ; therefore 
 0.0384 Ib. x 63.02 - 14.01 = .173 Ib. of nitric acid ; 
 
40 ELECTROCHEMICAL EQUIVALENTS 
 
 this of course refers only to the nitric acid itself and 
 does not include the water in which the commercial 
 acid is dissolved. 
 
 If however the calculation is made in the longer 
 indirect way, that is, by first determining electro- 
 chemically the amount of zinc corresponding to the 
 100 ampere-hours, and then chemically the amount of 
 nitric acid corresponding to this amount of zinc, - 
 the coefficients of course enter into the calculation, 
 tho only in the purely chemical part of it. Thus from 
 the table 100 ampere-hours corresponds to .269 Ib. of 
 zinc, no matter what the coefficient of the zinc is in 
 this formula. From the equation 3 Zn corresponds to 
 2 HNO 3 , hence the amounts of zinc and nitric acid 
 are in the proportion of the weights of these two 
 quantities. The atomic weight of zinc is 65.37 and 
 the molecular weight (or formula weight) of nitric 
 acid is 63.02 (see above) ; hence .269 Ib. x (2 x 63.2) 
 *- (3 x 65.37) = .173 Ib. of nitric acid, as before. 
 
 Intermediate reactions may be ignored. The reaction 
 in example 6 involves an intermediate reaction also; 
 the zinc is dissolved in the sulfuric acid in which it 
 replaces the hydrogen, and this hydrogen then reduces 
 the nitric acid ; this at least may serve as a simple 
 explanation of the reaction. In the direct method 
 of calculation based on the change of valence all 
 such intermediate reactions may be ignored, while 
 in the' chemical part of the indirect method they may 
 sometimes have to be known hi order to write 
 out the chemical equation. The amount of nitrogen 
 oxidized or reduced by one ampere-hour, involving 
 a given change of its valence, is a fixed and definite 
 quantity, and is entirely independent of any other 
 reactions which may be occurring at the same time, 
 except of course if they are resultant reactions of 
 
EXAMPLES 41 
 
 a purely chemical kind, often termed secondary re- 
 actions. 
 
 Invoked reactions. The above examples illustrate 
 the simplest kinds of cases involving calculations of 
 electrochemical equivalents. The following examples 
 will serve to illustrate some of the less simple cases 
 which involve features that are different from those in 
 the more usual ones and which might sometimes give 
 rise to confusion. 
 
 Example 7. Nothing set free or dissolved at one of the 
 electrodes. If the cathode is in copper sulfate and 
 the platinum anode is in ferrous sulfate, copper will 
 be deposited on the cathode as usual; but at the 
 platinum anode the corresponding SO 4 ion will not 
 set free oxygen as is more usual, but will oxidize the 
 ferrous sulfate into the ferric, hence nothing will be 
 set free or dissolved there. The iron solution acts as 
 a depolarizer at the anode by combining with the 
 SO 4 , thereby preventing it from forming a film of 
 oxygen gas over the anode. 
 
 However the somewhat unusual fact that nothing 
 is set free or dissolved at the anode involves no 
 difficulties in the electrochemical calculation for that 
 electrode when based on the change of valence, and 
 need lead to no confusion. The iron salt has been 
 changed at that electrode from ferrous to ferric, 
 which is a true electrochemical reaction ; it means 
 that its valence has been changed from 2 to 3, hence 
 by 1 unit ; the amount of iron so changed per ampere- 
 hour is therefore found directly from the table, 
 column 7, for valence 1, namely 2.083 grams per 
 ampere-hour. The amounts of the sulfates cor- 
 responding to this amount of the iron, are then 
 readily determined from the purely chemical calcula- 
 tions. 
 
42 ELECTROCHEMICAL EQUIVALENTS 
 
 The equation of this reaction is 
 
 CuSO 4 + 2 FeSO 4 = Cu + Fe 2 (SO 4 ) 3 
 
 The valence of the radical SO 4 is 2, as it combines 
 with 2 hydrogen atoms in H 2 SO 4 ; from its valence 
 the valences of the iron in these ferrous and ferric 
 salts are evident from their formulas, 2 in the first 
 and (3 x 2) -T- 2 = 3 in the second. 
 
 The amount of iron salts could be determined also 
 without considering the valences by finding first how 
 much copper will be deposited by a given current and 
 then by a purely chemical calculation, using the 
 above equation, determine the corresponding amounts 
 of the iron salts. 
 
 Example 8. Nothing set free or dissolved at either 
 electrode. If a platinum cathode is in a solution of 
 ferric sulfate, and a platinum anode is in a solution 
 of ferrous sulfate (the latter like in example 7), then 
 at the cathode the ferric sulfate will be reduced to 
 the ferrous, while at the anode the ferrous will be 
 oxidized or adduced to the ferric ; hence nothing will 
 be set free or dissolved at either electrode. The 
 SO 4 ions will go from the cathode to the anode. 
 
 The reaction is 
 
 Fe 2 (SO 4 ) 3 (at cathode) + 2 FeSO 4 (at anode) = 
 2 FeSO 4 (at cathode) + Fe 2 (SO 4 ) 3 (at anode). 
 
 The valence of the iron in the ferric state is 3 and 
 'in the ferrous 2, hence there is a change of 1, and 
 this change is the same hi amount at each electrode, 
 tho of opposite sign, which merely signifies the rela- 
 tively reverse direction of the current. The electro- 
 chemical equivalent is therefore found directly from 
 the table to be 2.083 grams of iron per ampere-hour ; 
 this applies to either electrode. 
 
EXAMPLES 43 
 
 This is a case in which the method of calculation 
 based on the change of valence is far simpler than 
 with the older methods, as there is now nothing 
 tangible set free or dissolved at either electrode 
 which could be used as a basis, as was the case in 
 all of the other examples. The iron cannot now be 
 used as a basis because it is not deposited and has a 
 different valence at each electrode ; to use either of 
 these valences would give a totally wrong result. 
 
 A possible way of making this calculation without 
 considering the change of valence, would be to use 
 the radical SO 4 as a basis, as this is in effect trans- 
 ferred from one electrode to the other just as the 
 metal is hi electroplating, and its valence is the same, 
 namely 2, in both of the salts, hence can be neg- 
 lected ; having the same valence its electrochemical 
 equivalent at each electrode is the same per ampere- 
 hour. 
 
 Its electrochemical equivalent is not given hi the 
 table because it is not an element, but it can readily 
 be determined from any of the sulfates, such as 
 FeSO 4 . Thus the iron in this sulfate has a valence 
 of 2, hence its electrochemical equivalent from the 
 table is 1.042 grams per ampere-hour. As every 
 atom of iron corresponds to one molecule of SO 4 the 
 amount of the latter in grams per ampere-hours will 
 be in the proportion of then* atomic weights. That of 
 iron is 55.84 and that of SO 4 is 32.06 + (16 x 4) = 
 96.06. Hence 1.042 grams x 96.06 *- 55.84 = 1.79 
 grams of SO 4 per ampere-hour. 
 
 At the anode one SO 4 combines with two FeSO 4 to 
 form one Fe 2 (SO 4 ) 3 ; hence 2 Fe (atomic weight 
 2 x 55.84 = 111.68) corresponds to one of SO 4 (atomic 
 weight 96.06). As there are 1.79 grams of SO 4 per 
 ampere-hour, there will be 1,79 x 111.68 -=- 96.1 = 
 
44 ELECTROCHEMICAL EQUIVALENTS 
 
 2.083 grams of iron involved at each electrode per 
 ampere-hour, the same as was found above by a far 
 simpler calculation. A similar calculation made for 
 the cathode reaction will give the same result except 
 that what is a gain of SO 4 at one is a loss at the 
 other. 
 
 It will be noticed that the end results are chemically 
 the same as those at the start, hence nothing has been 
 accomplished other than changing the positions of the 
 two solutions, which should be separated by a porous 
 cup. It is analogous to electroplating in which the 
 end results are also chemically the same, the metal 
 being merely transferred from the anode to the 
 cathode. 
 
 It is assumed of course that this reaction is not 
 carried out faster than the solutions in contact with 
 the electrodes can be replaced by diffusion, otherwise 
 some other reactions will take place, like the deposi- 
 tion of iron or the evolution of oxygen. As this 
 reaction involves no resultant chemical change it 
 should require no more voltage than that necessary 
 to overcome the resistance ; hence using a voltage 
 too low to set free iron or oxygen, ought to prevent 
 these other reactions from taking place. 
 
 Example 9. The same as Example 8 but involving in 
 addition a purely chemical reaction. The platinum 
 anode is again hi a solution of ferrous sulfate, but 
 the cathode now is in a solution of chromic and 
 sulfuric acid. Again nothing will be set free or 
 dissolved at either electrode. The complete equation 
 
 is 
 
 2 H 2 CrO 4 + 6 H 2 SO 4 + 6 FeSO 4 = 
 
 Cr 2 (S0 4 ) 3 + 8 H 2 + 3 Fe 2 (SO 4 ) 3 
 
 The chromic acid will be reduced at the cathode 
 which would form a precipitate but this is dissolved 
 
EXAMPLES 45 
 
 in the sulfuric acid forming chromium sulfate. 
 The chromium at the cathode has changed its valence 
 from 6 to 3, hence the difference is 3 ; its amount can 
 therefore be found directly from the table. At the 
 anode the change of valence of the iron is 1, namely 
 from 2 in the ferrous to 3 in the ferric state ; hence 
 its amount can also be found directly from the table. 
 
 The sulfuric acid however has a double function, 
 half of it being electrolyzed to give the SO 4 to the 
 ferrous sulfate at the anode, the hydrogen from it 
 going to fdrm water, while the other half acts purely 
 chemically to dissolve the reduced chromic acid, 
 forming chromium sulfate and water. The latter 
 half must therefore not be included in the electro- 
 chemical calculations, but must be added to that 
 required electrochemically in order to get the total 
 acid for the complete reaction. In such complicated 
 reactions it is safest to use the chromium or the iron 
 in the electrochemical calculations and then calculate 
 the amount of sulfuric acid by purely chemical 
 means from the above equation. 
 
 The metals in solution at the anode and cathode 
 being different (iron and chromium), the calculations 
 might again be made as suggested in the previous 
 example 8, by using SO 4 as a basis, as it is this that 
 may be said to be what is transferred from one 
 electrode to the other. 
 
 It may be of interest to note here that this reaction 
 forms an odd kind of storage battery, in which only 
 the two liquids enter into the reaction and carry the 
 energy, the plates themselves remaining completely 
 unchanged. The fresh liquids could be supplied to 
 the battery as the source of the energy, and the ex- 
 hausted liquids only (and not the whole battery) 
 would be taken to a power station and recharged by 
 
46 ELECTROCHEMICAL EQUIVALENTS 
 
 means of a current. One of the objections to it is 
 that it is a two fluid battery, hence requires porous 
 partitions to keep the liquids separated, and that they 
 will nevertheless gradually contaminate each other. 
 
 Example 10. Nothing is set free or dissolved at one of 
 the electrodes, and the current appears to do double duty 
 on the same electrolyte. If the electrodes are both plati- 
 num and there is only a single solution of cuprous 
 chloride, CuCl, copper will be deposited at the 
 cathode with a valence of 1, while at the anode 
 the chlorine will raise (oxidize, or better, adduce) 
 the cuprous to cupric chloride, CuCl 2 , hence nothing 
 will be set free or dissolved at the anode. The 
 chemical equation is 
 
 2 CuCl = Cu + CuCl 2 
 
 The amount of copper deposited per ampere-hour 
 is readily calculated from the table, remembering that 
 the valence now is 1 and not 2 as is more usual; 
 that is, there will be twice as much deposited per 
 ampere-hour as from the more usual copper solutions. 
 But the facts that nothing is set free or dissolved at 
 the anode and that the amount of cuprous chloride 
 which is changed to cupric is double that correspond- 
 ing to the copper deposited, may give rise to some 
 confusion. 
 
 The chlorine which had been combined with the 
 copper which is deposited on the cathode, tends to be 
 set free at the anode, but it there combines with 
 some of the cuprous chloride, CuCl, to form the cupric, 
 CuCl 2 . The fact that one molecule of the cuprous 
 chloride is completely decomposed at the cathode, 
 while at the same time another molecule of it is 
 raised to the cupric salt at the anode by the same 
 current, explains why twice as much of the original 
 Solution is changed when compared with that which 
 
EXAMPLES 47 
 
 corresponds to the amount of deposited copper. The 
 above chemical equation also shows that in this 
 reaction one part of metallic, free copper corresponds 
 to two parts of the original solution. 
 
 To have calculated the amount of cuprous salt 
 which has been acted upon per ampere-hour, from 
 the amount of chlorine arriving at the anode, or 
 from the amount of copper deposited, would have led 
 to entirely wrong results ; it is necessary in such 
 cases to consider the actions at both electrodes, and 
 in this particular case the current does a double duty, 
 as the same current changes two molecules of the 
 same compound, one at each electrode. Removing 
 some of the copper (chemically) from cuprous chloride 
 or adding some chlorine to it (chemically) both pro- 
 duce the same effect, namely changing some of it to 
 the cupric chloride ; hence in that sense it might be 
 said that the chemical changes of the solution are in 
 this case alike at both electrodes. 
 
 Example 1 1. Exhaustion of the same electrolyte at both 
 electrodes. How many ampere-hours will it require 
 to extract all of the lead from a solution of nitrate 
 of lead Pb(NO 3 ) 2 containing 100 grams of lead, 
 when electrolyzed between two platinum electrodes? 
 In this case the lead will be deposited from the 
 solution at both electrodes, it. being reduced at the 
 cathode where it be will deposited as metallic lead, 
 and it will be oxidized or adduced at the anode 
 where it will be deposited as peroxide of lead. The 
 residual solution will be nitric acid, and it is here 
 assumed that this will not redissolve the lead on the 
 cathode by local action. 
 
 The equation is 
 
 2 Pb(N0 3 ) 2 + H 2 = Pb + 4 HNO 3 + PbO 2 
 
48 ELECTROCHEMICAL EQUIVALENTS 
 
 The valence of the lead in the nitrate is 2, in the 
 peroxide it is 4, and hi the form of metallic lead it is 
 0. Hence the change of valence at each electrode 
 is 2 ; being the same at both, the amount of lead 
 deposited on each electrode will be the same, hence 
 50 grams. From the table 1 gram at valence 2 will 
 require 0.2587 ampere-hours, hence 50 grams at each 
 electrode will require 50 x .2587 = 12.94 ampere- 
 hours. 
 
 Or it may be calculated without involving the 
 changes of valence by finding the lead deposited as 
 such at the cathode and then by purely chemical 
 calculations finding the corresponding amount at the 
 anode ; the equation shows these two to be the same. 
 
 Example 12. Change of valence involving different 
 signs. Negative Valences. How much sulfur would 
 be involved per ampere-hour hi the oxidation or 
 adduction of hydrogen sulfide, H 2 S, into sulfuric 
 acid, H 2 SO 4 , if it were done electrolytically? The 
 equation is 
 
 H 2 S + 4 H 2 O = 4 H 2 + H 2 SO 4 
 
 In all the previous examples illustrating the more 
 usual cases involving a change of valence, the two 
 valences of the elements had the same sign before 
 and after the electrolysis, and then* signs need there- 
 fore not be considered. But in some cases like the 
 present, the sign of the valence changes and therefore 
 becomes very important. 
 
 In every compound the bonds representing the 
 valences must always add up to zero. Those of 
 hydrogen are always + and those of oxygen nearly 
 always . In H 2 S the sulfur must therefore have 
 two negative bonds, hence a valence of - 2 to balance 
 the two positive bonds of the H 2 . But in H 2 SO 4 the 
 sulfur has 6 positive bonds (the oxygen having 8 
 
EXAMPLES 49 
 
 negative ones, two of which combine with the hydro- 
 gen), hence has a valence of + 6. 
 
 The change of valence being the algebraic difference 
 is therefore in this reaction equal to the difference 
 between - 2 and + 6 which is 8 (the sign of this 
 difference is no longer of importance as it merely 
 refers to the direction of the current). In the table 
 the highest valence given is 6 ; the figure for valence 
 1 is 1.196 grams per ampere-hour, hence for a valence 
 of 8 it will be one-eighth of this, namely 0.150 grams 
 of sulfur, as the same current now has to neutralize 
 8 times as many bonds per gram. This is a very small 
 amount of sulfur for that amount of electricity, 
 hence this reaction would take much current or a 
 long time. This example is described as a simple 
 hypothetical case to show how to make the calcula- 
 tions when there is a change of sign of the val- 
 ence ; as the sulfur would have to pass thru the 
 state of zero valence which means that it is then in 
 its free state, some free sulfur is likely to form in the 
 solution. In practice it is simpler to burn the H 2 S 
 in the air to a low oxide and then oxidize a solution 
 of this to a higher oxide by electrolysis. 
 
 This calculation could be made also without con- 
 sidering this change of valence, by determining from 
 the table the amount of hydrogen liberated per 
 ampere-hour (disregarding the coefficient and sub- 
 script) and then by a purely chemical calculation (hi 
 which the coefficients and subscripts must be con- 
 sidered) find the corresponding amount of sulfur 
 from the above equation. Thus, from the table, 
 0.03761 gram of hydrogen is liberated per ampere- 
 hour. From the second half of the equation, for 
 every 8 atoms of hydrogen liberated there will be one 
 of sulfur; from their atomic weights the respective 
 
50 ELECTROCHEMICAL EQUIVALENTS 
 
 weights will therefore be as 8 x 1.008 is to 32.06. 
 Hence 0.03761 gram of hydrogen per ampere-hour in 
 this case corresponds to 0.03761 x 32.06 -f- 8.064 = 
 0.150 grams of sulfur per ampere-hour, the same as 
 before. 
 
 Example 13. A similar case. When nitric acid is 
 reduced to ammonia there is a similar change of sign 
 of the valence, but hi this case it is a change from 
 + to as it is a reduction, while in the previous 
 case it was a change from -- to +, as it was an 
 adduction or a so-called oxidation. The valence of the 
 nitrogen in the acid HNO 3 is + 5 (+1 + 5-6 = 0), 
 and in the ammonia NH 3 it is 3 (-3+3 = 0), 
 hence the change is then* algebraic difference, 8. 
 
 The calculation may be made without involving 
 these valences by starting with the amount of oxygen 
 which would have to be set free, and then determin- 
 ing the nitric acid involved by a purely chemical 
 calculation. In these indirect calculations the element 
 which is set free, as distinguished from merely being 
 changed, is always a good basis for starting such 
 calculations, as was also shown in other Examples. 
 
 Example 14. Partial change of valence. How much 
 nitric acid is required per ampere-hour when used as 
 a depolarizer in a Bunsen cell, assuming the nitric 
 acid to be changed into ammonium nitrate? The 
 equation is 
 
 4 Zn + 4 H 2 SO 4 + 2 HNO 3 = 
 4 ZnSO 4 + NH 4 NO 3 + 3 H 2 O 
 
 In the nitric acid the valence of the nitrogen is 
 + 5( + l + 5-6 = 0), and in the first part (NH 4 ) of 
 the ammonium nitrate, it is - 3 (- 3 + 4 + 5 - 6 = 0), 
 hence the change of valence is 8. But part of the 
 nitrogen of the original nitric acid does not change 
 its valence, remaining as NO 3 ; this part is therefore 
 
EXAMPLES 51 
 
 not involved in the electrochemical part of the reac- 
 tion. The original acid does a double duty; the 
 equation shows that half of the nitrogen is electro- 
 chemically converted into ammonia and the other half 
 remains as NO 3 . The former is calculated electro- 
 chemically for a change of valence of 8, which is then 
 doubled to get the total. 
 
 This may also be calculated by the indirect method 
 without involving these changes of valence. The zinc 
 may then be used as the basis for the electrochemical 
 part of the calculation, the corresponding nitric acid 
 being then determined from it by a purely chemical 
 calculation. In such rare and involved cases as this 
 one the indirect method, tho longer, will no doubt be 
 the safest one to use by those not accustomed to the 
 more convenient conception of changes of valences 
 and negative valences. 
 
PART II 
 
 Section V 
 
 ELECTROLYSIS 
 
 Theory of Electrolytic Dissociation, Faraday's Law, 
 Coulometers 
 
 Introductory. Conductors of electricity may be 
 divided into two classes as follows: (1) conductors 
 of the first class which experience a rise of tempera- 
 ture due to the passage of the electric current but do 
 not undergo any chemical change and, (2) conductors 
 of the second class, in which the passage of the 
 electric current is invariably accompanied by chemical 
 decomposition. To the first class belong the metals 
 and their alloys and a few non-metallic elements 
 such as carbon. To the conductors of the second 
 class, termed electrolytes, belong solutions of acids 
 bases, and salts, either fused or in solution. Elec- 
 trolytes are always necessarily compounds and never 
 simple elements. Mercury, for example, is a liquid 
 conductor but it is not electrolyzable. While under 
 ordinary conditions pure water is a non-conductor, it 
 is interesting to note that it becomes a good con- 
 ductor of electricity when an acid, a base, or a salt is 
 dissolved in it. Although salts are non-conductors at 
 ordinary temperatures, they conduct readily, with 
 simultaneous decomposition, when heated above their 
 melting points. Fused salts form practically the only 
 exception to the rule that pure chemical compounds 
 
 53 
 
54 ELECTROCHEMICAL EQUIVALENTS 
 
 are non-conductors of electricity. Practically all 
 organic compounds, with the exception of organic 
 acids, bases, and salts, when dissolved in water are 
 non-conductors. Such non-conducting substances, 
 among which alcohol, ether, starch, and sugar may 
 be mentioned as typical examples, are called non- 
 electrolytes. It should be borne in mind that the 
 property of electrical conductance is not confined to 
 aqueous solutions alone. The decomposition of an 
 electrolyte resulting from the passage of an electric 
 current thru its solution is known as electrolysis. 
 
 To Faraday we owe, not only our knowledge of the 
 fundamental law of electrolysis, but also the precise 
 definition of certain terms used in connection with 
 electrolytic phenomena. In his "Experimental Re- 
 searches" 1 we find the following definitions: "In 
 place of the term pole, I propose using that of electrode, 
 and I mean thereby that substance, or rather surface, 
 whether of air, water, metal, or any other body, which 
 bounds the extent of the decomposing matter in the di- 
 rection of the electric current. The surfaces at which, 
 according to common phraseology, the electric current 
 enters and leaves a decomposing body, are most impor- 
 tant places of action, and require to be distinguished 
 apart from the poles, with which they are mostly, 
 and the electrodes, with which they are always, in 
 contact. 
 
 . . . The anode is therefore that surface at which 
 the electric current . . . enters : ... it is where 
 oxygen, chlorine, acids, etc., are evolved. . . . The 
 cathode is that surface at which the current leaves the 
 decomposing body, ... the combustible bodies, 
 
 1 "Experimental Researches in Electricity," by Michael 
 Faraday. Everyman's Library, Vol. 576, pp. 112-114. 
 
ELECTROLYSIS 
 
 55 
 
 metals, alkalies, and bases are evolved there. . . . 
 Finally I require a term to express those bodies which 
 can pass to the electrodes, or, as they are usually 
 called, the poles. ... I propose to distinguish such 
 bodies by calling those anions which go to the anode 
 of the decomposing body; and those passing to the 
 cathode, cations; and when I have occasion to speak 
 of these together, I shall call them ions. Thus, the 
 chloride of lead is an electrolyte, and when electrolysed 
 evolves the two ions chlorine and lead, the former 
 being an an ion, and the latter a cation." 
 
 The different parts of an electrolytic cell are shown 
 in the accompanying diagram, (Fig. 1). It is impor- 
 tant to note that, contrary to common usage, it is the 
 surfaces of the plates rather _ _ 
 
 than the plates themselves, 
 which constitute the elec- 
 trodes of the cell. In bat- 
 teries the cathode is gen- 
 erally called the positive 
 pole because the current 
 
 enters the outside circuit 
 
 , . . 
 from this pole ; and the 
 
 lr f 
 
 electrolytic cell showing parts. 
 
 anode (usually zinc) is then called the negative pole. 
 This is reversed in electrolytic baths. Hence the 
 terms positive and negative poles are ambiguous, 
 while the terms anode and cathode are not. The 
 cations move with the current through the electrolytic 
 cell toward the cathode or negative plate and are 
 positively charged, while the anions migrate in the 
 reverse direction toward the anode or positive plate 
 and are negatively charged. In practice it is a matter 
 of great importance to recognize that electrolytic 
 changes occur only in the molecular layer next to the 
 electrodes. Thus, hi the electrolysis of a solution of 
 
56 ELECTROCHEMICAL EQUIVALENTS 
 
 copper sulfate, when the thin layer of solution next 
 the cathode is exhausted of copper, hydrogen will be 
 evolved, unless the solution is vigorously stirred or 
 the cathode is rotated. 
 
 Electrolytic Phenomena. The products obtained at 
 the two electrodes of an electrolytic cell are always 
 different and may be collected in various ways de- 
 pending upon theur nature. When gases are formed 
 they may be collected in appropriate tubes. When 
 insoluble solids are formed they generally adhere to 
 the electrode surface or fall to the bottom of the cell 
 as a precipitate. When soluble substances are 
 produced it is customary to surround one of the 
 electrodes with a porous cup, or to interpose some 
 sort of porous diaphragm between the electrodes, 
 which will minimize the diffusion of the product of 
 electrolysis from the vicinity of the electrode at 
 which it is formed. When a current of electricity is 
 passed between two platinum plates immersed in a 
 solution of silver nitrate, metallic silver is deposited 
 at the cathode while oxygen together with nitric acid 
 is set free at the anode. The two ions, Ag and NO' 3 , 
 are discharged at the cathode and anode respectively : 
 the NO 3 radical is then assumed to react with the 
 water to produce nitric acid and oxygen as indicated 
 by the equation 
 
 2 NO 3 + H 2 = 2 HNO 3 + O 
 
 The interaction of the NO 3 ion and the water hi 
 which the electrolyte was dissolved is known as 
 secondary action. 1 
 
 1 While the above explanation of secondary action is not in 
 accord with the generally accepted theory of LeBlanc, Zeit. 
 Phys. Chem. 11, 805 (1893), based on the primary decomposi- 
 tion of water, for all practical purposes it may be assumed to be 
 correct. 
 
ELECTROLYSIS 57 
 
 When a current of electricity is passed between 
 platinum plates immersed in a solution of potassium 
 nitrate, hydrogen is liberated at the cathode and 
 oxygen at the anode. An examination of the solution 
 in the neighborhood of the electrodes reveals the 
 presence of potassium hydroxide at the cathode and 
 nitric acid at the anode. In this case the two ions, 
 K and NO ' 3 , are discharged at then- respective elec- 
 trodes and then a secondary reaction may be assumed 
 to take place between each discharged ion and the 
 water, as shown by the following equations 
 
 K + H 2 O = KOH + H (reaction at cathode 1 ) 
 
 2 NO 3 + H 2 O = 2 HNO 3 + O (reaction at anode 1 ) 
 
 If, hi this experiment, the negative terminal of plati- 
 num is replaced by a cup of mercury, a portion of the 
 potassium will be dissolved, forming an amalgam, thus 
 confirming the primary separation of metallic potas- 
 sium at the cathode. The reactions taking place at 
 the electrodes during electrolysis are opposite in 
 character ; oxidation invariably occurs at the anode while 
 reduction invariably occurs at the cathode. These facts 
 are of extreme practical importance and are often 
 either overlooked or are insufficiently emphasized 
 in introductory textbooks of electrochemistry. The 
 anode and cathode reactions accompanying the elec- 
 trolysis of potassium nitrate, as given above, may be 
 cited as illustrations of this generalization. 
 
 Theory of Electrolytic Dissociation. When an elec- 
 trolyte is dissolved in water, all of the properties of 
 the solution indicate that a larger number of dissolved 
 units are present than in a solution of a non-elec- 
 
 1 More properly these equations should be written ionically, 
 thus; K + H.OH = K + OH' + H 
 
 2NO 3 + H.OH = 2H + 
 
58 ELECTROCHEMICAL EQUIVALENTS 
 
 trolyte of the same concentration. Since electrolytes 
 are believed to conduct the electric current by virtue 
 of particles, called ions, formed from the molecules of 
 the electrolyte, it is assumed that these ions together 
 with the undissociated molecules are responsible for 
 the abnormal behavior of electrolytic solutions. This 
 hypothesis, put forward by Arrhenius in 1887, is known 
 as the theory of electrolytic dissociation. The fundamental 
 assumptions involved in this theory are as follows : 
 
 (a) When the molecules of an electrolyte are dis- 
 solved in water some of them undergo dissociation 
 into ions. Thus, potassium chloride (KC1) disso- 
 ciates into the ions K and Cl'. 
 
 (b) The extent to which the molecules dissociate is 
 dependent upon the dilution of the solution ; the more 
 dilute the solution, the greater is the degree of 
 dissociation. 
 
 (c) Each ion is highly charged with electricity. It 
 is this electrical charge which differentiates an ion 
 from the corresponding atom, the usual chemical 
 properties of an element being greatly modified by the 
 presence of an electrical charge. Thus, atomic 
 potassium reacts violently with water to form hy- 
 drogen and potassium hydroxide, whereas ionic 
 potassium is wholly without action on water. 
 
 (d) The ions resulting from the dissociation of an 
 electrolyte are of two kinds. One kind of ion carries 
 a positive charge, and the other carries a negative 
 charge. Since the solution, as a whole, is electrically 
 neutral, it follows that the sum of the positive and 
 negative charges must be equal. The character of 
 the charge carried by an ion may be indicated by 
 writing the usual plus or minus signs over the symbols 
 of the ions or preferably by the use of a dot () for a 
 positive charge and of a dash(') for a negative charge. 
 
ELECTROLYSIS 59 
 
 Thus, the electrolytic dissociation of potassium chloride 
 into positively charged potassium and negatively 
 charged chlorine ions may be represented by the equation 
 
 KC1 = K + Ci 
 
 or KC1 = K + Cl' 
 
 Molecules which undergo dissociation into two ions 
 are known as binary electrolytes, while those which 
 yield on dissociation three or four ions are called 
 ternary or quaternary electrolytes respectively. The 
 following equations are examples of the dissociation 
 of ternary and quaternary electrolytes 
 
 K 2 S0 4 = 2 K + S0" 4 , 
 
 BaCl 2 = Ba + 2 Cl', 
 
 AlCla = Al + 3 Cl'. 
 
 (e) The properties of a solution of an electrolyte 
 are dependent upon both the ions and the undisso- 
 ciated molecules. The ions are in general more 
 active chemically than the molecules from which they 
 are derived and consequently the influence of the 
 ions is predominant in deterrnining the properties of 
 a solution of an electrolyte. 
 
 The theory of electrolytic dissociation, while not 
 free from defects, has proven to be a generalization of 
 great value in the development of the science of 
 electrochemistry. All of the changes which occur 
 during electrolysis can be satisfactorily explained by 
 means of this theory. 1 
 
 1 The reader who desires further information concerning the 
 theory of electrolytic dissociation is referred to the following 
 books where a clear exposition of the theory together with 
 some of its applications will be found : 
 
 " Theory of Electrolytic Dissociation " Jones (Macmillan 
 Co.) ; " The Theory of Electrolytic Dissociation " Talbot 
 and Blanchard (Macmillan Co.). 
 
 "The Nature of Solution "Jones (D.Van Nostrand Co.). 
 
60 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 Migration of the 
 local phenomenon 
 
 ~ 
 
 Copper Sulphate 
 + Agar Agar 
 
 Ions. That electrolysis is not a 
 taking place in the immediate 
 neighborhood of the elec- 
 trodes, but involves an 
 actual migration of the ions 
 of the electrolyte, may be 
 shown by a variety of ex- 
 periments of which the fol- 
 lowing is one of the most 
 striking. The lower part 
 of the U-tube shown in 
 Fig. 2 is charged with a 
 
 Fig. 2. Diagram of an exper- dilute solution of copper 
 U1UStrate migration sulfate containing about 5 
 per cent of agar agar and 
 is then allowed to stand until the solution has set to 
 a jelly. Dilute solutions of copper sulfate may be shown 
 to be completely dissociated into ions as indicated by 
 the equation 
 
 CuSO 4 = Cu + SO" 4 
 
 Since pure, anhydrous copper sulfate is known to 
 be colorless, and since sodium sulfate, potassium 
 sulfate, and sulfuric acid, all of which substances 
 contain the SO" 4 ion, are colorless, it follows that the 
 blue color of a dilute solution of copper sulfate must 
 be ascribed to the Cii ion alone. This conclusion is 
 confirmed by the fact that dilute solutions of all 
 cupric salts have the same color. 
 
 When the solution in the U-tube has solidified, the 
 position of the surface of the jelly hi each arm of the 
 U-tube is marked by means of strips of gummed 
 paper pasted on the outside of the tube. Then some 
 colorless electrolyte, such as a solution of potassium 
 nitrate to which agar agar has been added, is intro- 
 duced into each arm of the U-tube. After the agar 
 
ELECTROLYSIS 61 
 
 agar has set to a jelly, a few cubic centimeters of the 
 potassium nitrate solution containing no agar agar is 
 added to each arm of the tube and two platinum 
 plates introduced as shown in the diagram. The 
 tube is now immersed in ice-water to prevent the 
 softening of the jelly by the heat developed by the 
 passage of the electric current. On applying a current 
 of 110 volts with a 16 candle-power lamp included 
 in the circuit, the blue solution which owes its color 
 to the presence of Cu ions will be seen to move 
 toward the cathode, ascending on the left-hand side 
 and descending on the right-hand side of the U-tube. 
 While solutions containing SO"* ions are colorless, it 
 is reasonable to infer that these ions migrate in the 
 opposite direction. In fact the experiment may be so 
 modified as to reveal the actual movement of the 
 SO " 4 ions toward the anode. The agar agar which is 
 added to prevent the transference of water with the 
 current, has been shown to increase the resistance of 
 the solution relatively little. 
 
 By slight modifications of the above experiment, the 
 actual speeds of the ions under a definite potential 
 gradient have been accurately determined. The ac- 
 companying table gives the speeds of some of the more 
 common ions in centimeters per second when measured 
 in dilute aqueous solution at 18C. under a potential 
 difference of 1 volt between plates 1 centimeter apart. 
 Cations Speed, cm./ sea. An ions Speed, cm./ sec. 
 H 0.003294 OH' 0.001802 
 
 Li 0.000346 Cl' 0.000677 
 
 Na 0.000450 NO' 3 0.000640 
 
 K 0.000669 C1O' 3 0.000570 
 
 NH 4 0.000667 
 Ag 0.000559 
 
 Cu 0.000444 
 
62 ELECTROCHEMICAL EQUIVALENTS 
 
 It will be observed that the two fastest moving ions 
 are the H ion and the OH' ion, the former having a 
 speed nearly twice that of the latter. 
 
 It has been shown that the speeds of the ions are 
 specific properties, being uninfluenced by the presence 
 of other ions hi the same solution. It has also been 
 shown that an increase in the difference of potential 
 between the plates of an electrolytic cell causes 
 proportional increase in the speed with which the 
 ions move. Notwithstanding the fact that the ions 
 move so slowly under a fall of potential of 1 volt per 
 centimeter, it may be shown that enormous forces are 
 involved in imparting to the ions speeds of the order 
 of magnitude of those given in the above table. It 
 has been calculated, for example, that a force equal 
 to a weight of 299,000,000 kilograms is necessary to 
 impart to the H ion a speed of 0.003294 cm. per sec. 
 at 18C. The magnitude of this force is to be as- 
 cribed to the extremely small mass and the relatively 
 large surface of the H ion. 
 
 Faraday s Law. The quantitative relation between 
 the amount of electricity passing thru a solution of 
 an electrolyte and the resulting chemical action was 
 discovered by Faraday about 1835. In his. experi- 
 ments Faraday varied the size and nature of the 
 electrode surfaces, the concentration of the elec- 
 trolyte, and the amount of current passing thru 
 the solutions in a given time. In all cases he found 
 that the same current produced the same amount of 
 chemical decomposition, or in other words, for the 
 same electrolyte the amount of chemical decomposition is 
 directly proportional to the amount of electricity which is 
 passed thru the solution of the electrolyte. When solu- 
 tions of different electrolytes were subjected to the 
 action of the same current by placing them in series 
 
ELECTROLYSIS 
 
 63 
 
 in the circuit, Faraday found that the masses of the prod- 
 ucts of electrolysis were directly proportional to their chemi- 
 cal equivalents. By the term " chemical equivalent " is 
 meant the ratio of the formula-weight of a substance 
 to its valence. Thus, the formula weight of silver 
 is 107.88 and its valence is 1, hence its chemical 
 equivalent is 107.88 ; similarly, the formula-weight, 
 of the SO " 4 ion is 96.06 and its valence is 2, therefore 
 its chemical equivalent is 48.03. 
 
 The foregoing statements of the results of Faraday's 
 experiments may be combined in a single generaliza- 
 tion as follows : When the same quantity of electricity is 
 passed thru one or more solutions of the same or different 
 electrolytes, the masses of the substances which separate at the 
 electrodes are directly proportional to their chemical equivalents, 
 and are independent of the concentration and temperature of 
 the solutions, the extent of the electrode surfaces, and all other 
 circumstances. This generalization is known as Faraday's 
 Law and may be regarded as the fundamental law of 
 electrochemical science. 
 
 The meaning of the law may be illustrated by the 
 following experiment : If solutions of hydrochloric 
 
 fMWH 
 
 HCl H 2 SO< KCl 'CuSfk AuCh F*Cl z 
 Fig. 3. Diagram of an experiment illustrating Faraday's law. 
 
 acid (HCl), sulfuric acid (H 2 SO 4 ), potassium chloride 
 (KCl), cupric sulfate (CuSO 4 ), auric chloride (AuCls), 
 ferrous chloride (FeCl 2 ), and ferric chloride (FeCla) 
 are placed in different cells, as shown in Fig. 3, and 
 are then subjected to the action of the same quantity 
 
64 ELECTROCHEMICAL EQUIVALENTS 
 
 of electricity by connecting them in series with a 
 battery of storage cells, it will be found that when 
 1.008 grams of hydrogen is liberated from each of 
 the two acids. 35.45 grams of chlorine will be set free 
 from each of the chloride solutions, 96.06/2 = 48.03 
 grams of SO 4 will be set free from the sulfuric acid 
 and cupric sulfate, while the amounts of the metals 
 deposited at the cathode surfaces of the respective 
 cells will be 39.10 grams of potassium, 63.57/2 = 31.7 
 grams of copper, 197.2/3 = 65.7 grams of gold, 55.84/2 
 = 27.92 grams of ferrous iron, and 55.84/3 = 18.61 
 grams of ferric iron. 
 
 The foregoing experiment illustrates the fact that 
 the quantity of substance set free by a given quantity 
 of electricity increases inversely as its valence in the 
 solution employed ; thus, 27.92 grams of ferrous iron 
 is liberated by the same current which deposits 18.61 
 grams of ferric iron. This point is of importance in 
 connection with the economic use of electricity in all 
 electrolytic processes. The validity of Faraday's law 
 has been tested by numerous experiments carried 
 out with the utmost care. It has been found to hold, 
 not only for all solvents, but also for fused elec- 
 trolytes as well. 
 
 The Electrochemical Constant. Since the same quantity 
 of electricity positive or negative is always 
 carried by a univalent ion, this quantity may be 
 considered as the unit of ionic charge. A bivalent 
 ion will thus carry two unit charges and an n-valent 
 ion will' carry n unit charges. In other words, we 
 may think of valence as representing the number of 
 unit charges of electricity which are associated with 
 the respective ions. According to this view Faraday's 
 law may be stated as follows : Chemically equivalent 
 masses of matter possess the same capacity for electricity. 
 
ELECTROLYSIS 65 
 
 The precise measurement of this fundamental quantity 
 of electricity is obviously a matter of great scientific 
 and practical importance. It can be determined by 
 passing a known quantity of electricity thru a solu- 
 tion of an electrolyte and weighing the metal deposited 
 at the cathode surface or measuring the volume of 
 gas set free. 
 
 The most satisfactory results have been obtained 
 when a neutral solution of silver nitrate is used, 
 containing about 15 parts of the salt to 100 parts of 
 water, and with a current density of about 0.01 
 ampere per square centimeter. The silver is de- 
 posited on a platinum dish the inner surface of which 
 serves as the cathode, while a silver plate, wrapped 
 hi filter paper to retain any particles of silver which 
 may be detached by the current, constitutes the 
 anode surface. 
 
 The unit of quantity of electricity is the coulomb. 
 This may be defined as the quantity of electricity 
 which has passed through a circuit when a current of 
 1 ampere has been flowing constantly for 1 second. 
 The mass of a substance in grams deposited by 1 
 coulomb of electricity is commonly called the elec- 
 trochemical equivalent, of the substance. 
 
 The accepted value of the electrochemical equiva- 
 lent of silver is 0.00111800 gram per coulomb. It is 
 evident, therefore, that 107.88 + 0.00111800 = 96493.7 
 coulombs of electricity will be required to deposit the 
 equivalent weight of silver in grams. 
 
 Since electrochemical equivalents are proportional 
 to chemical equivalents (Faraday's law), it is evident 
 that 96493.7 coulombs of electricity will be required to liberate 
 the equivalent weight of any ion. This number, 96493.7 
 coulombs, represents the fundamental electrochemical 
 unit, and is called the electrochemical constant or tbefaraday. 
 
66 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 Coulomders. (Voltameters.) As has been shown, the 
 quantity of electricity passing through any electric 
 circuit can be ascertained by determining the amount 
 of chemical change produced at an electrode surface. 
 An electrolytic cell, so arranged as to measure the 
 quantity of electricity which has passed through it by 
 the amount of chemical action it produces, is called a 
 coulometer or a voltameter, the former term being 
 preferable. There are three general types of coulom- 
 eter in use, viz., (1) weight coulometers, (2) volume 
 coulometers, and (3) titration coulometers. These 
 will be considered very briefly in the subsequent 
 paragraphs. 
 
 Weight Coulometers. (a) The Silver Coulometer. In 
 the weight coulometer, as the name implies, the 
 quantity of electricity is determined by measuring the 
 gain in weight of the cathode plate due to the deposi- 
 tion of metal from the 
 electrolyte. The most 
 accurate of all coulom-' 
 eters is the silver 
 coulometer. This in- 
 strument has already 
 been mentioned in con- 
 nection with the deter- 
 mination of the electro- 
 chemical constant (p. 
 65). The silver cou- 
 lometer used and rec- 
 ommended by Richards 
 Fig. 4. Simple silver coulometer. , TT . , , . 
 
 and Heimrod 1 is shown 
 
 in Fig. 4. It consists of a large platinum crucible E, the 
 
 inner surface of which constitutes the cathode, a piece 
 
 of pure silver C, which forms the anode surface, a 
 
 1 Zeit. phys. Chem. 41, 302. (1902). 
 
ELECTROLYSIS 67 
 
 porous cup D, to retain any particles of silver which 
 may be detached mechanically by the current, and 
 the glass insulating supports A and B. The electro- 
 lyte consists of a neutral solution of silver nitrate, 
 prepared by dissolving 20 to 40 grams of pure silver 
 nitrate in 100 grams of distilled water. By weighing 
 the platinum crucible before and after the passage of 
 the current, the amount of electricity which has 
 flowed through the coulometer may be computed from 
 the electrochemical equivalent of silver, 0.00111800 
 gram per coulomb. The mean error of a single de- 
 termination is about 0.03 per cent for a deposit 
 weighing not less than 500 milligrams. The current 
 density must not exceed 0.2 ampere per square centi- 
 meter of anode surface or 0.02 ampere per square 
 centimeter of cathode surface. Care should be taken 
 to insure the removal of the last traces of silver 
 nitrate solution before weighing the crucible. This is 
 accomplished by washing with distilled water until 
 the washings give no turbidity with a solution of hy- 
 drochloric acid. The crucible is then dried in an air 
 bath and weighed. The solution of silver nitrate 
 may be used repeatedly until a deposit corresponding 
 to 3 grams of silver per 100 cc. of solution has been 
 reached. 
 
 A simple and inexpensive form of silver coulometer 
 has recently been designed by the United States 
 Bureau of Standards 1 for general use. The following 
 description of the apparatus is taken verbatim from 
 the official publication. 
 
 "The anode was made in the form of a large ring 
 set in a glass dish containing the electrolyte. This 
 silver ring was made large to minimize the difficulties 
 
 1 Bull. Bureau of Standards. Vol. 10. p. 529. 
 
68 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 with the anode slime. The cathode was a small 
 platinum ring resting in a shallow glass dish sub- 
 merged in the electrolyte and so arranged that the 
 whole might be lifted out together. As this platinum 
 
 ring weighed only 
 10.5 g., the largest 
 item of expense was 
 reduced to about one- 
 tenth that of the large 
 size standards." 
 It is not intended 
 that this form should 
 be used in any work 
 requiring the highest 
 precision, but it has 
 been shown that it 
 may be relied on 
 
 of 1 per cent. The 
 arrangement of the parts is shown hi the accompany- 
 ing drawing (Fig. 5). 
 
 (b) The Copper Coulometer. In this instrument the 
 anode surface usually consists of two sheets of pure 
 copper with a thin sheet of platinum or copper be- 
 tween them serving as the cathode surface. The 
 electrolytic solution recommended by Oettel l for the 
 copper coulometer has the following composition : 
 
 Crystallized Cupric Sulfate 15 grams 
 
 Cone. Sulfuric Acid (Sp. Gr. 1.84) 5 grams 
 
 Alcohol 95 per cent 5 c. c. 
 
 Distilled Water 100 c. c. 
 
 When the current density is so adjusted that it does 
 
 not exceed 0.015 ampere per square centimeter of 
 
 1 Chem. Zeit. 77, 543 (1893). 
 
ELECTROLYSIS 
 
 69 
 
 cathode surface, it is claimed by Oettel that the 
 copper coulometer will give results which agree 
 perfectly with those obtained with the silver coulom- 
 eter. It has been shown, however, that there are 
 several inherent defects in the copper coulometer 
 which render it a less trustworthy instrument than 
 the silver coulometer. Thus, the copper deposited 
 at the cathode surface dissolves slightly in acid 
 cupric sulfate forming a cuprous salt, thereby 
 diminishing the weight of the cathode plate. If a 
 neutral solution of cupric sulfate be used, there is 
 too great a gain in the weight of the cathode plate 
 owing to the deposition of cuprous oxide resulting 
 from the hydrolysis of cuprous sulfate. As the 
 temperature rises the proportion of cuprous ions to 
 cupric ions increases, causing too great an increase in 
 the weight of the deposit. To reduce errors due to 
 oxidation it is often recommended that a slow current 
 of carbon dioxide 
 be bubbled through 
 the solution. The 
 mean error of a 
 single determina- 
 tion with the cop- 
 per coulometer is 
 about 0.2 per cent. 
 The advantages of 
 the copper coulom- 
 eter over the sil- 
 ver coulometer are 
 
 Fig. 6. Copper coulometer. 
 
 that it is cheap and that the copper deposit is more 
 adhesive than the silver deposit. A satisfactory form 
 of copper coulometer is shown hi Fig. 6. 
 
 Volume Coulometers. The best known coulometer 
 of this type is the so-called water-coulometer. In 
 
70 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 this instrument the total volume of electrolytic gases, 
 or the volume of either one or the other of the con- 
 stituent gases of water, is measured. The form of 
 
 water-coulometer devised 
 by F. Kohlrausch 1 is 
 shown in Fig. 7. A glass 
 tube graduated into 1/10 
 cc. serves to measure the 
 volume of the gases 
 evolved by the passage of 
 the current thru water 
 which has been made 
 conducting by the addi- 
 tion of sulfuric acid. 
 The graduated tube is 
 fitted into a shallow glass 
 reservoir of about 500 
 
 Fig. 7. Volume ^ometero7 cc - capacity by means of 
 Kohlrausch. a ground joint. Thru 
 
 two tubulures, fitted with 
 
 rubber stoppers, electrical connection is established 
 with two platinum plates. A small thermometer is 
 sealed into the upper part of the graduated tube to 
 enable the experimenter to determine the temperature 
 of the gas. Kohlrausch recommends that a solution 
 of sulfuric acid, sp. gr. 1.14, be used to fill the tube 
 and the reservoir. When the electric current to be 
 measured is passed thru the solution, the uncor- 
 rected volume of the resulting mixture of hydrogen 
 and oxygen is read directly on the graduated tube. 
 By means of suitable tables the reduction of the 
 volume of the gas to standard conditions may be 
 readily performed, and, knowing that 1 coulomb of 
 electricity liberates 0.17403 cc. of hydrogen and oxygen 
 1 Elektrotech. Zeit. 6, 190. (1885). 
 
ELECTROLYSIS 
 
 71 
 
 in molecular proportions at and 760 mm. pressure, 
 the quantity of electricity whicji has passed thru 
 the circuit can be easily computed. The convenience 
 in reading the volume of gas corresponding to the 
 current which passes thru the coulometer is offset 
 by the disadvantage that a comparatively high voltage 
 is required. Furthermore, the water coulometer is 
 not adapted to the measurement of large quantities of 
 electricity. 
 
 Titration Coulomders. In the measurement of 
 small quantities of electricity the titration coulometer 
 is often useful. 1 The apparatus is + 
 
 shown in Fig. 8. The vertical 
 glass tube, fitted at its lower end 
 with a glass stop-cock, is filled up 
 to the dotted line with a concen- 
 trated solution of potassium iodide 
 acidified with hydrochloric acid. 
 A dilute solution of hydrochloric 
 acid is then added by means of a 
 funnel or pipette, care being taken 
 to avoid mixing with the more 
 dense solution. The anode plate 
 consists of a spiral of platinum 
 wire while a piece of platinum foil 
 serves as the cathode plate. When 
 a current of electricity passes 
 thru the solution, iodine is lib- 
 erated at the anode, 1 equivalent 
 or 126.92 grams of iodine corre- 
 sponding to 96500 coulombs of 
 electricity. The amount of iodine 
 
 Fig. 8. Titration 
 coulometer. 
 
 1 See Danneel, Zeit. Elektrochem. 4, 154 (1898). See also 
 Washburn and Bates, Jour. Am. Chem. Soc., 34, 1341 (1912). 
 
72 ELECTROCHEMICAL EQUIVALENTS 
 
 set free is determined by withdrawing the lower layer 
 of the solution by means of the stop-cock and titrating 
 with a standard solution of sodium thiosulfate accord- 
 ing to the well-known procedure of volumetric 
 analysis. 
 
Section VI 
 
 THE ELECTRONIC THEORY 
 
 Electric Discharge in High Vacua. The recent ad- 
 vance in our knowledge of the nature of electricity 
 and of the constitution of matter is due hi large 
 measure to the pioneer work of Sir William Crookes 
 on the phenomena of electric discharge hi high vacua. 
 In a paper communicated to the Royal Society hi 
 1879, Crookes showed that when an electric dis- 
 charge is passed through a highly exhausted glass 
 tube, rays are shot off from the cathode. These 
 "cathode rays," as they are called, are capable of 
 exciting fluorescence where they impinge upon the 
 walls of the tube ; a vivid green fluorescence being 
 developed in soda glass, and a blue fluorescence in 
 potash glass. 
 
 The rays travel hi a rectilinear path and may be 
 brought to a focus by means of a concave cathode. 
 When various minerals are placed at the focus within 
 the exhausted tube they are rendered fluorescent, 
 while a piece of platinum foil can be rendered in- 
 candescent by prolonged bombardment by the rays. 
 
 It was Crookes' view that the rays consist of a 
 stream of electrified molecules of the residual gas. 
 In order to test the correctness of this hypothesis he 
 caused the rays, after leaving the cathode, to pass 
 thru two parallel slits cut hi an aluminum dia- 
 phragm, thus giving two parallel streams of cathode 
 rays. By means of a phosphorescent screen placed 
 
 73 
 
74 ELECTROCHEMICAL EQUIVALENTS 
 
 within the tube in such a position as to be grazed by 
 the rays, then: path could be easily traced. It was 
 found that the two streams of cathode rays diverged ; 
 that is, they behaved like two adjacent streams of 
 similarly electrified bodies. From these experiments, 
 Crookes was led to consider these rays as made up of 
 "a fourth or radiant state of matter." Later experi- 
 ments by Perrin and Sir J. J. Thomson, in which the 
 rays were subjected to the action of both magnetic 
 and electrostatic fields, have proved the rays to 
 consist of negatively charged particles. 
 
 Velocity of the Cathode Particle. The velocity of the 
 cathode particle was determined by Thomson in the 
 following manner : The amount of magnetic de- 
 flection produced by subjecting the cathode stream 
 to the action of a magnetic field is proportional to 
 the velocity, v, with which the particles are moving, 
 to the intensity of the magnetic field, H, and also to 
 the magnitude of the charge, e, resident upon each 
 particle. The corresponding deflection produced by 
 an electric field is proportional to the intensity of the 
 field, X, and to the charge, e, on each particle. 
 Thomson devised an experiment in which the cathode 
 stream could be subjected to the simultaneous action 
 of both magnetic and electrostatic forces, but so 
 arranged that the effect of one field could be exactly 
 counterbalanced by that of the other, thus causing 
 the cathode stream to pursue an undeviated, recti- 
 linear path. A suitable phosphorescent screen served 
 to detect any deviation from the normal path of the 
 particles when uninfluenced by either magnetic or 
 electric forces. 
 
 When the magnetic and electric forces are thus 
 balanced, we have 
 
 Hev = Xe 
 
ELECTRONIC THEORY 75 
 
 v =i 
 
 By means of this equation, the velocity of the cathode 
 particle may be calculated, and it was found that hi a 
 highly exhausted tube this velocity may be as high as 
 60,000 miles per second, or nearly one-third of the 
 velocity of light. 
 
 Ratio of Charge to Mass. Thomson next directed 
 his attention to the determination of the ratio which 
 the electric charge carried by a cathode particle bears 
 to its mass. He showed that this ratio can be found 
 by subjecting the rays to the action of an electro- 
 static field alone. Under these conditions the cathode 
 particles are deflected from then* rectilinear path hi 
 exactly the same way that a rifle-bullet is deflected 
 from a horizontal path and constrained to fall to the 
 earth at a continually accelerated rate under the 
 influence of the attraction of gravitation. 
 
 In the case of a cathode particle, its acceleration 
 will be directly proportional to the strength of the 
 field, X, to its charge, e, and inversely proportional to 
 its mass, m. Or, expressing these facts hi mathe- 
 matical language, we have 
 
 Acceleration = 
 m 
 
 The science of Mechanics teaches, that the distance 
 thru which a body will fall freely under the in- 
 fluence of gravity hi a tune t, is 1/2 gt 2 , where g is the 
 acceleration due to gravity. Similarly, the deflection 
 of the cathode stream under the influence of the 
 electrostatic field, X, as shown by the displacement 
 of the luminous spot on the phosphorescent screen, 
 will be 
 
76 ELECTROCHEMICAL EQUIVALENTS 
 
 m 
 
 Since t = 1/v, where t, 1, and v denote time, distance, 
 and velocity respectively, we may replace t 2 in the 
 above expression for displacement by ! 2 /v 2 , when we 
 have 
 
 d- 1 XeP 
 ~*' rn^ 
 
 or 
 
 e = 2d v 2 
 
 m X I 2 
 
 In this last equation all of the terms on the right- 
 hand side of the equality sign are susceptible of direct 
 measurement. 
 
 Thomson found that the ratio e/m is the same for 
 all cathode rays provided they are not moving with 
 velocities of the same order of magnitude as the veloc- 
 ity of light. He also found that the ratio is indepen- 
 dent of the nature of the residual gas in the tube 
 and likewise of the chemical nature of the electrodes. 
 The value of e/m, expressed hi electrostatic units, is 
 5.1 x 10 17 . The largest value of e/m hitherto known 
 was that for the hydrogen ion in electrolysis, where 
 the ratio of charge to mass, expressed in electrostatic 
 units, is 3 x 10 14 . Therefore, for the cathode par- 
 ticle, the ratio is 1700 times greater than the cor- 
 responding ratio for the hydrogen ion in electrolysis. 
 It is evident that this may be due to the charge 
 being 1700 tunes greater than the charge on the 
 hydrogen ion in electrolysis (the mass of the ion and 
 that of the cathode particle being assumed equal), or, 
 to the mass of the cathode particle being only 1/1700 
 of the mass of that of the hydrogen ion (the charges 
 being assumed the same). 
 
ELECTRONIC THEORY 77 
 
 Magnitude of the Charge, e. It is a familiar fact 
 that fogs are due to the condensation of water vapor 
 on dust particles in the atmosphere, each particle of 
 dust acting as the nucleus around which a droplet of 
 water can form. On cooling a mass of air which has 
 been completely freed from dust, no fog will be 
 formed because there are no nuclei upon which water 
 vapor can condense. Air in this condition is said to be 
 "supersaturated," i.e., it holds more than the normal 
 amount of moisture for that particular temperature. 
 If a little dust be introduced into supersaturated air, 
 an immediate condensation to fog occurs. It has 
 been shown by C. T. R. Wilson that if a vessel be 
 filled with air from which all dust particles have been 
 removed by filtration through cotton-wool, it is possi- 
 ble to cool it to such an extent that it will hold in 
 suspension fully eight times the amount of water 
 vapor it should normally contain. On further cooling, 
 the moisture precipitates in the form of rain. 
 
 Wilson also discovered that cathode particles serve 
 as nuclei for the condensation of moisture from super- 
 saturated air, and that condensation occurs at a 
 temperature corresponding to a fourfold saturation. 
 By enclosing a mass of dust-free air in a glass 
 chamber closed by a piston* the desired degree of 
 supersaturation can be obtained by withdrawing the 
 piston, thus expanding the air and lowering its temper- 
 ature. If cathode rays are then permitted to enter 
 the chamber, a fog immediately results, and by 
 proper adjustment of the expansion, it is possible to 
 estimate the actual weight of water condensed. 
 
 Having determined the total weight of condensed 
 moisture, it is evident that a knowledge of the average 
 volume of a single drop would make possible the 
 calculation of the total number of drops, and, on the 
 
78 ELECTROCHEMICAL EQUIVALENTS 
 
 reasonable assumption that each drop is associated 
 with but one cathode particle, the number of such 
 particles would be known. The volume of a single 
 drop can be computed by means of a formula derived 
 by Sir George Stokes for the velocity of fall of a 
 minute spherical body in terms of its radius, r, and 
 the viscosity, ??, of the medium in which it falls. 
 Stokes' formula is 
 
 where u denotes the velocity of fall of the body and 
 g is the acceleration due to gravity. By noting the 
 velocity with which the fog settles in the expansion 
 chamber, the value of r in the foregoing formula may 
 be calculated. 
 
 Having calculated the total number of cathode 
 particles, by dividing the total weight of water con- 
 densed by the volume of a single drop, 4/3 * r 3 , it only 
 remains to measure the total quantity of electricity 
 on the precipitated water vapor in order to ascertain 
 the charge on each particle. The charge on a single 
 cathode particle was thus found to be 3.1 x 1(H 
 electrostatic units. Recent improvements in Wilson's 
 method have enabled Millikan 1 to determine the 
 value of e with extreme accuracy. Millikan assigns 
 to e the value 4.4775 x KH electrostatic units, the 
 error not exceeding 1 part in 1000. 
 
 These cathode particles were at first called cor- 
 puscles but they are now commonly known as elec- 
 trons. The electron appears to be nothing but an 
 isolated charge of negative electricity. All electrons 
 are alike, being entirely independent of the particular 
 
 1 Millikan, Phil. Mag. IV, 19, 209 (1910) ; Phys. Rev. 32, 349 
 (1911) ; Trans. Am. Electrochem. Soc., 21, 185, (1912). 
 
ELECTRONIC THEORY 79 
 
 atom from which they may have escaped. This leads 
 to the view that electricity, like matter, is made up of 
 discrete particles analogous to atoms. An electron 
 may be defined as a minute particle having an ap- 
 parent mass of about 1/1700 that of the atom of hydro- 
 gen and carrying a negative charge of electricity 
 equal to 4.4775 x 10~ 10 electrostatic units. 
 
 Other Sources of Electrons. Cathode rays are not 
 the only source of electrons. Electrons are given out 
 by radio-active substances, by metals, and by some 
 amalgams when heated or exposed to light, especially 
 to ultra-violet light, and also by gas flames charged 
 with the vapors of salts. Whatever the source from 
 which the electrons may be derived, the value of the 
 ratio, e/m, remains constant. The constancy of this 
 ratio led Sir J. J. Thomson to say that the electron 
 is to be regarded "as one of the bricks of which 
 atoms are built up." 
 
 Structure of the Atom. According to Thomson, the 
 atom of any element is assumed to consist of an as- 
 semblage of negatively charged particles or electrons, 
 held together by a positively charged nucleus, the 
 amount of positive electricity being equivalent to the 
 total negative charge of the electrons. At the present 
 time little definite information exists as to this positive 
 nucleus, beyond the fact that carriers of positive 
 electricity possess masses which are comparable with 
 the mass of the atom of hydrogen. A small number 
 of electrons near the surface or outer shell of the 
 atom are believed to possess a greater degree of 
 freedom and to be less firmly held than those nearer 
 the positive nucleus. These electrons are known as 
 the valence electrons, since their number determines 
 the maximum valence of the atom. 
 
 While further discussion of atomic structure lies 
 
80 ELECTROCHEMICAL EQUIVALENTS 
 
 beyond the scope of this book yet mention should be 
 made of the recent theory of Nicholson. 1 According 
 to Nicholson the positive residue of the atom exists 
 hi the form of separate masses, each of uniform 
 density and having diameters which are relatively 
 small in comparison with the diameters of the elec- 
 trons. Nicholson says, "In a complex atom, built up 
 of simpler systems, the assemblage of positive charges 
 is hi many respects similar to the assemblage of 
 electrons which revolve around them, and it is not 
 unlikely that many of the positive charges would also 
 revolve. But they are not all of the same size, 
 although the difference hi size is not great. Then* 
 mass is so great that a disturbance which could expel 
 one of them from an atom would also expel many of 
 the attendant electrons, and it would be impossible 
 to isolate a positive charge." 
 
 The Electron and the Chemical Elements. While the 
 hypothetical atom of Thomson undoubtedly bears but 
 a remote resemblance to the real atom, and while as 
 Thomson has pointed out, there are many imperfec- 
 tions in his theory, it nevertheless sheds a most 
 interesting light on the mutual relationships of the 
 chemical elements and then* differences in valence or 
 combining power. 
 
 Thomson has calculated the possible distribution of 
 negative electric charges within a sphere of positive 
 electricity of uniform density. When the presence of 
 only one electron is assumed, it necessarily goes to 
 the center of the sphere. Where a larger number are 
 assumed to be present the calculation has been 
 confined to those cases hi which the electrons lie in a 
 plane passing thru the center of the sphere. The 
 
 1 Nicholson, Phil. Mag. IV, 22, 864 (1911). 
 
ELECTRONIC THEORY 81 
 
 maximum number of electrons which can be in equi- 
 librium in a single ring is 5. In order to increase the 
 number of electrons in a ring it is necessary to place 
 some of them within the ring. Thus, though a ring 
 containing 6 equally spaced electrons is unstable 
 alone, it immediately acquires stability if 1 electron 
 is placed at the center of the ring. A system involv- 
 ing a greater number of electrons will arrange itself 
 in a series of concentric rings, the number of electrons 
 in successive rings decreasing as the center is ap- 
 proached. The accompanying table shows the num- 
 bers of electrons from 1 to 69, arranged in rings, the 
 first line showing the numbers which may fall into 
 one ring, the second line the numbers which may give 
 rise to two rings, the third line those which form three 
 rings, and so on. 
 
 NUMBERS OF ELECTRONS IN CONCENTRIC RINGS 
 12345 
 
 5 6 7 8 8 8 9 10 10 10 11 
 11112333455 
 
 11 11 11 12 12 12 13 13 13 13 13 14 14 15 15 
 5 6 7 7 8 8 8 8 9 10 10 10 10 10 11 
 11111233334455 '5 
 
 15 15 15 16 16 16 16 16 16 16 17 17 17 17 17 17 17 
 
 11 11 11 11 12 12 12 13 13 13 13 13 13 14 14 15 15 
 
 5 6 7 7 7 8 8 8 8 9 9 10 10 10 10 10 11 
 
 11111122333344555 
 
 17 18 18 18 18 18 19 19 19 19 20 20 20 20 20 20 20 20 20 21 21 
 
 15 15 15 15 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 
 
 11 11 11 11 11 12 12 12 12 13 13 13 13 13 13 13 14 14 15 15 15 
 
 5 5 6 7 7 7 7 8 8 8 8 8 9 9 10 10 10 10 10 10 11 
 
 111111112223333445555 
 
 It will be observed that the numbers in the same 
 vertical columns of the table are repeated in each 
 series, the number of electrons in the outer ring 
 forming the top line. For example, in the first 
 
82 ELECTROCHEMICAL EQUIVALENTS 
 
 column of the first series, we find the numbers 5, 1 ; 
 in the next series we find the numbers 11, 5, 1 ; in 
 the next series we find the numbers 15, 11, 5, 1 ; and 
 in the last series we find the numbers 17, 15, 11, 5, 1. 
 
 The bearing of this table on the natural grouping of 
 the chemical elements may be illustrated by consider- 
 ing the properties of all configurations having 20 
 electrons in the outer ring. The smallest number of 
 electrons in a system having 20 electrons in the outer 
 ring is 59. In this case the number of electrons 
 within is only just sufficient to impart stability to the 
 ring, any slight disturbance being able to cause the 
 loss of 1 electron. Should this occur the residue 
 would acquire a positive charge and the resulting 
 atom, containing 58 electrons, would resemble in its 
 properties a univalent positive element. When we 
 pass from 59 to 60 electrons, the outer ring acquires 
 greater stability owing to the presence of an additional 
 electron within the system. Similarly, the system 
 containing 61 electrons is even more stable than that 
 containing 60 electrons. The stability continues to 
 increase until the number of electrons in the atom 
 reaches 67, when the addition of another electron 
 destroys the stability of the system, since it enters 
 the outer ring, thus increasing the number of elec- 
 trons to 21, and producing a configuration favoring the 
 detachment of an electron, as in the case of the 
 system containing 59 electrons. 
 
 It will be observed that the change from 59 to 67 
 electrons, produced by the successive additions of a 
 single electron, corresponds to the addition of 8 
 negative charges. The system containing 60 electrons 
 will be the most positive of the series. It can give up 
 1 electron, but only 1, since if it were to give up 2, a 
 system of 58 electrons woulcl result, similar to that 
 
ELECTRONIC THEORY 83 
 
 obtained by the removal of an electron from an atom 
 containing 59 electrons. Such a system would 
 acquire two positive charges of electricity and would 
 possess even greater attraction for external electrons. 
 Therefore, since the atom containing 60 electrons can 
 carry but one positive charge it will resemble in its 
 behavior a univalent positive element. 
 Turning our attention now to the system containing 
 
 67 electrons, we find that the outer ring is very 
 stable, and, as we have seen, the addition of 1 elec- 
 tron would involve a rearrangement resulting in a 
 system having 21 electrons hi the outer ring. Since 
 
 68 is the minimum number of electrons which can 
 exist under these conditions with an outer ring of 21, 
 it follows that an electron may readily be lost. The 
 resulting configuration of 67 electrons, after thus 
 acquiring a negative charge, would immediately lose 
 it again, and the system would thus be incapable of 
 retaining any permanent charge. Its behavior is 
 quite analogous to the rare gases which are known to 
 be inactive chemically. The system containing 66 
 electrons can retain but a single negative charge ; 
 for should 2 electrons be added to it, a configuration 
 involving 68 electrons would result, and that has 
 already been seen to lose electrons easily. This 
 system then resembles in its properties a univalent 
 negative element. 
 
 Proceeding in a similar manner, successively in- 
 creasing the number of electrons, we obtain systems 
 corresponding to univalent, divalent, and trivalent, 
 positive elements at one end of the series, and 
 trivalent, divalent, and univalent, negative elements 
 at the other end of the series. This is analogous to 
 the familiar arrangement of the chemical elements due 
 to Mendeleef , shown hi part in the following table : 
 
84 ELECTROCHEMICAL EQUIVALENTS 
 
 He Li Be B C N O F Ne 
 
 Ne Na Mg Al Si P S Cl A 
 
 When atoms in which the outer rings have a high 
 stability are brought in close proximity to other atoms 
 in which the electrons are less firmly held, an ex- 
 change of electrons may occur. In this interchange 
 the electropositive atoms will acquire a positive 
 charge, and the electronegative atoms a negative 
 charge. The resulting oppositely charged atoms will 
 then unite to form a chemical compound. 
 
 The Electronic Conception of Valence. Sir William 
 Ramsay has put forward the following hypothesis l : 
 "Electrons are atoms of the chemical element, elec- 
 tricity; they possess mass, they form compounds 
 with other elements; they are known in the free 
 state, that is as molecules ; they serve as the bonds 
 of union between atom and atom." According to 
 this hypothesis, when common salt is dissolved in 
 water and undergoes ionization into Na and Cl' ions, 
 the Na ion is to be regarded as an atom of sodium 
 minus an electron, and the Cl' ion as an atom of 
 chlorine plus an electron. That is, the sodium atom 
 may be thought of as a compound of the Na ion with 
 an electron, whereas the Cl' ion may be regarded as a 
 compound of the chlorine atom with an electron. 
 Ramsay represents the union between sodium and 
 chlorine by the equation 
 
 ENa + Cl = NaECl 
 
 where the symbol E denotes the electron. It is the 
 electron, hi other words, that serves as the connecting 
 link between the atoms of sodium and chlorine, - 
 it is another way of representing combining capacity 
 
 1 Ramsay, Jour. Chem. Soc., 93, 778 (1908). 
 
ELECTRONIC THEORY 85 
 
 or valence. We may then define the valence of an 
 element as the number of electrons which the element 
 loses or gains to form chemical bonds. The forma- 
 tion of a chemical bond or linkage between two atoms 
 necessarily involves the transfer of an electron from 
 one atom to another, and this transfer imparts a 
 negative charge to the atom which gains the electron, 
 and a positive charge to the atom which loses the 
 electron. 
 
 The Electronic Conception of Conductance. As has 
 been pointed out, conductors of electricity may be 
 conveniently divided into two classes; the metals 
 and carbon forming the first class, and dissolved or 
 fused electrolytes the second class. The mechanism 
 of electrical conductance, whether metallic or elec- 
 trolytic, may be satisfactorily explained in terms of 
 the electronic hypothesis. Thus, when a difference of 
 potential is established between the ends of a metallic 
 conductor, a stream of electrons immediately begins 
 to flow. This electronic stream constitutes the elec- 
 tric current in the metal and the rise of temperature 
 incident to the passage of the current is to be ascribed 
 to the heat developed by the collision of the electrons 
 with the atoms of metal. Since the electric current 
 is to be regarded as a stream of negatively charged 
 carriers of electricity, we are forced to define the 
 " direction of the current " in a metallic conductor as 
 opposite to that in which the electricity really flows. 
 
 In conductors of the second class the ions of the 
 electrolyte carry the current, each kind of ion par- 
 ticipating in proportion to its current-carrying capacity. 
 Since in the metallic portion of the circuit, including 
 the electrodes, the current consists of a stream of 
 electrons, it follows that at the electrode surfaces 
 there must be an exchange of electrons between the 
 
86 ELECTROCHEMICAL EQUIVALENTS 
 
 electrodes and the ions of the electrolyte. This ex- 
 change of electrons, commonly called an electro- 
 chemical reaction, generally involves only those ions 
 which most readily gain or lose electrons under the 
 conditions. It has been shown hi the preceding 
 section that the liberation or solution of one equiva- 
 lent weight of a substance requires approximately 
 96500 coulombs of electricity. It is evident that if 
 the number of atoms contained in one gram-atom of 
 an element were known, it would be possible to 
 calculate the number of coulombs carried by one 
 electron. It has recently been shown by Perrin that 
 the probable number of atoms in one gram-atom of 
 an element is 68.5 x 10 22 ; assuming this number to 
 be correct, we have 
 
 and multiplying by 3 x 10 9 , in order to convert 
 coulombs into electrostatic units, we have 
 
 96500 x 3 x 10 9 
 e 
 
 68.5 x 10 22 
 or 
 
 e = 4.227 x 10~ 10 electrostatic units 
 
 On comparing this result with Millikan's value for 
 e, viz., 4.4775 x 10~ 10 , it will be observed that the 
 agreement is all that could be desired. The electro- 
 chemical constant or faraday is thus seen to be equal 
 to the product of the charge on the electron and the 
 number of atoms in one atomic weight of an element, 
 
 The following references are given for the benefit 
 of those who may desire to gain more detailed in- 
 formation on various phases of the electronic theory : 
 
ELECTRONIC THEORY 87 
 
 " The Discharge of Electricity through Gases," by 
 
 J. J. Thomson, 
 " Conduction of Electricity through Gases," by J. J. 
 
 Thomson, 
 
 11 Electricity and Matter," by J. J. Thomson, 
 "The Corpuscular Theory of Matter," by J. J. 
 
 Thomson, 
 
 " Beyond the Atom," by J. Cox, 
 "Elements and Electrons," by William Ramsay, 
 11 The Theory of Valency," by J. Newton Friend, 
 "The Nature of Matter and Electricity," by Comstock 
 
 and Troland. 
 
APPENDICES 
 
Appendix 1 
 
 VALENCE 
 
 Textbooks and different authorities use both the 
 terms " valence" and "valency" in different ways 
 and sometimes rather vaguely ; nor is there agree- 
 ment as to the precise physical conceptions repre- 
 sented by them. In electrochemistry that which is 
 represented by them has an important significance 
 and they ought to be clearly understood and used 
 with definite meanings. When the numerical value 
 of a valence is unity, as it is with hydrogen and a few 
 other elements, it naturally falls out of the calcula- 
 tions and is thereby lost sight of, but in all other cases 
 it is a very important factor, for when the valence is 
 twice as great in one case as in another, the amount 
 of electricity required to produce the chemical change 
 will be twice as great. 
 
 When the chemist refers to the " chemical equiva- 
 lents " of two elements, the valence has already been 
 taken into account and therefore is not given as an 
 additional factor and is lost sight of. Thus the 
 chemical equivalents of zinc (valence 2) and hydrogen 
 (valence 1) are 65.37 (the atomic weight of zinc) and 
 2.016 (twice the atomic weight of hydrogen) when they 
 are given with reference to zinc ; or 32.69 (half the 
 atomic weight of zinc) and 1.008 when stated with 
 reference to hydrogen ; the ratios of course are the 
 same in both cases. In these ratios the weights have 
 both been reduced to the same valence, hence the 
 valence need then no longer be stated. The chemist 
 
 91 
 
92 ELECTROCHEMICAL EQUIVALENTS 
 
 therefore often eliminates the valence by referring 
 directly to the " chemical equivalents " ; but in many 
 electrochemical calculations the consideration of the 
 valence as a separate factor so greatly simplifies many 
 of the calculations that it is generally worth while 
 doing so, and it enables a table of equivalents such as 
 the one in this book to be prepared for different 
 valences, thereby often saving the worst parts of the 
 calculations. Those who prefer to use chemical 
 equivalents (in which the valence has already been 
 included) will have to make the electrochemical 
 calculations for hydrogen or some other element, and 
 then by means of the chemical equivalents determine 
 from this the corresponding amount of the element 
 in the problem ; this involves a double calculation. 
 
 Chemists do not seem to be in agreement either as 
 to whether the same physical conception of valence 
 applies equally well to all branches, like organic 
 chemistry and electrolysis. It is believed by the 
 writer however that the following conception of val- 
 ence is in substantial agreement with the generally 
 accepted electronic theory, that it can safely be applied 
 at least to all electrochemical reactions, and that when 
 properly used in calculations it will always give the 
 correct results. This conception will greatly simplify 
 many electrochemical calculations, and it is believed 
 will also give a clearer understanding of the reactions. 
 It serves at least as a useful and reliable working 
 tool in electrochemistry independently of whether or 
 not it applies equally well to non-electrolytes or or- 
 ganic chemistry. 
 
 Bonds. When two different elements are chemi- 
 cally combined to form a compound, it is convenient 
 to consider the force or affinity which holds them 
 together to be represented by chemical bonds. In 
 
VALENCE 93 
 
 electrolytes these bonds, or at least some of them, 
 are of such a nature that they may be broken or 
 created by an electric current. The greater the 
 number of such bonds the greater is the quantity of 
 electricity which is required, hence it is convenient 
 for calculations to specify some unit bond in terms 
 of which their number can be measured and 
 specified. 
 
 Unit bond. The faraday. For convenience this 
 unit bond is conventionally assumed to be the one 
 combining a gram-atom of hydrogen (1.008 grams) 
 with other elements, and by experiment it has been 
 found that it requires a passage of 96,494 coulombs 
 of electricity to break or create this unit bond. This 
 quantity or charge of electricity is now by general 
 consent called a faraday and is usually abbreviated to 
 96,500 coulombs; it may often be more convenient 
 to use its equivalent 26.804 ampere-hours. 
 
 In the generally accepted electronic theory it is 
 supposed that each gram-ion carries a charge l of this 
 amount thru the electrolyte from one electrode to the 
 other, thereby transmitting the current, as explained 
 in Part n. It is where this charge is received or 
 discharged, namely at the electrodes, that the chemi- 
 cal reactions are apparent. From Faraday's law it 
 follows that in electrolysis this bond has the same 
 value when expressed electrically for a gram-ion of 
 any element, hence it serves well as a unit in terms 
 of which the bonds between elements can be ex- 
 pressed or measured. 
 
 Definition of valence. This leads to the definition 
 of valence, which may be said to be the number of 
 
 lU An Enlarged Electron of Practical Size: The Faraday," 
 by Carl Hering, Met. and Chem. Engineering, May 15, 1917, 
 p. 598- 
 
94 ELECTROCHEMICAL EQUIVALENTS 
 
 these unit bonds which each gram-atom has when in 
 combination with other elements. Or expressed elec- 
 trically, valence may be said to be the number of 
 charges, in faradays, which each gram-atom then 
 carries. This definition applies at least to electrolytes 
 and is therefore sufficient for electrochemical calcula- 
 tions ; it is also believed to be the simplest and most 
 useful conception of valence for use in electro- 
 chemistry ; whether it applies also to non-electrolytes 
 and to organic chemistry is perhaps still open to 
 controversy." l 
 
 Thus in one gram-molecule of water, H 2 O, consist- 
 ing of two gram-atoms of hydrogen and one of 
 oxygen, there must be two such unit bonds uniting 
 those elements, as each one of the two gram-atoms of 
 hydrogen has one by definition, that is, hydrogen has 
 a valence of 1 ; therefore the single gram-atom of 
 oxygen must be said to have two such bonds, hence 
 its valence is 2. One gram-molecule of water, 18.016 
 grams, therefore requires two faradays or 53.6 ampere- 
 hours, to break its two bonds. 
 
 A bond always joins two elements, but it may be 
 considered with reference to either of them, as it is 
 in this definition of valence. Thus in the above with 
 reference to the hydrogen there is one bond per atom, 
 hence its valence is 1, but with reference to the 
 
 1 Alexander Smith in his "General Inorganic Chemistry" 
 gives the following definition : " The valence of the atomic weight 
 of an element is the number of atomic weights of hydrogen, or 
 of some other univalent element, which it combines with or 
 displaces." 
 
 J. W. Mellor in his " Modern Inorganic Chemistry " gives the 
 following definition : " The valency of an element is a number 
 which expresses how many atoms of hydrogen, or of other 
 atoms equivalent to hydrogen, can unite with one atom of the 
 element in question." 
 

 VALENCE 95 
 
 single atom of oxygen there are two bonds per atom, 
 hence its valence is 2. 
 
 Ordinarily valences are always whole numbers 
 running from 1 to about 8 ; elements with valences 
 of 1, 2, 3, etc., are called mono-valent, di-valent, tri- 
 valent, etc.; elements like the noble gases which 
 seem never to combine with any other element are 
 best called non-valent, instead of zero-valent, for 
 reasons given below. Much higher valences have 
 been claimed to exist, as also fractional ones, but it is 
 probably safe to say that neither occur in electrolysis, 
 or at least very rarely. 
 
 Non-electrolytic bond. Sometimes a bond joins two 
 atoms of the same element ; a molecule of hydrogen 
 gas for instance is for good reasons considered to be 
 composed of two atoms combined together, that is, it 
 is diatomic. Molecules of some elements have three or 
 four atoms. Such bonds are also assumed to exist in 
 some compounds as expressed hi so-called structural 
 formulas, like the one between the two O's in H-O-O-H 
 for instance. But the writer believes it is safe to 
 say that these bonds have no equivalence in faradays 
 and never seem to enter into any electrochemical 
 calculations ; all such calculations for the usual cases 
 seem to agree reliably with experiment when the 
 making or breaking of this kind of bond is ignored; 
 Faraday's law does not refer to them ; it is believed 
 to be impossible ever to set free the same element at 
 both electrodes, which would mean breaking this 
 kind of a bond electrically. Hence with our present 
 knowledge it seems safe to consider this kind of 
 bond to differ physically from the one combining 
 different elements, at least to the extent that it may 
 be ignored in electrochemical calculations occurring in 
 practice as far as any equivalent in faradays is con- 
 
96 ELECTROCHEMICAL EQUIVALENTS 
 
 cerned. Structural formulas are employed chiefly 
 for compounds which are not electrolytes and there- 
 fore not subject to electrochemical calculations. 
 
 By using the change of valence based on the usual 
 chemical formulas, instead of the valence itself, as 
 described below, it is believed that no errors will 
 arise in neglecting this kind of bond in electro- 
 chemical calculations. In electrolyzing a gram-mole- 
 cule of water, H 2 O, it is well recognized and proved 
 by experiment that it requires two faradays, which 
 means that there were two bonds ; yet in the gaseous 
 hydrogen formed there are two atoms to the molecule, 
 hence there must be a bond connecting them ; this 
 bond was evidently not included in stating that the 
 valence of hydrogen is 1 and that of oxygen 2, nor is 
 it concluded in the chemical formula for water. 
 Whether it originated during electrolysis or existed in 
 the water is perhaps not yet known, but it is known 
 that it does not enter into electrochemical calculations 
 of this kind. 
 
 In a compound consisting of more than two ele- 
 ments, like H 2 SO 4 for instance, the current cannot 
 break it into more than two parts, hence one part 
 (one of the ions) must contain several elements, hi 
 this case it is SO 4 as the current always breaks the 
 bond between the H 2 and the SO 4 instead of the one 
 between the S and the O 4 . It does not necessarily fol- 
 low from this that the bonds between the S and the O 
 are not electrolytic ; they may merely be the stronger 
 of the two ; in fact it is said to be possible to break these 
 bonds electrolytically also, obtaining free sulfur. 
 
 But the kind of bond joining two atoms of the 
 same element seems to be physically different and is 
 not included among those referred to in this book as 
 being represented by a faraday. 
 
VALENCE 97 
 
 Zero valence. If the valence represents the number 
 of bonds in a combination each of which are equiva- 
 lent to a faraday, it follows that the elements can 
 have no valence when they are in their free uncom- 
 bined state as there are then no bonds. That is, the 
 valence of any element in its free state must neces- 
 sarily be considered to be zero. This term is some- 
 times applied to those elements like the inert gases 
 which never enter into any combinations, that is, they 
 never have any valences. It is preferable to distin- 
 guish between these two cases by saying that the 
 latter are non-valent, as hi electrochemistry it is very 
 convenient and sometimes quite necessary to be able 
 to refer to the free or uncombined state of an element 
 as one in which it has a zero valence. 
 
 Valence vs. valency. For this and other reasons it 
 is very desirable to make a distinction between the 
 terms valence and valency, which formerly have been 
 used rather indiscriminately, thereby causing con- 
 fusion. The writer recommends l limiting the term 
 " valence" as above described to represent the number 
 of bonds per atom which the element has in any specific 
 combination, and to limit the term "valency" to 
 express the properly which an element has to combine 
 with others in various proportions. Thus copper for 
 instance is then said to possess the property of having 
 a valency of 1 and 2 ; and when combined in the 
 specific combination of cuprous chloride its valence is 
 1, while hi cupric chloride its valence is 2 ; and in its 
 free state as metal its valence is 0. 
 
 Change of valence. Every electrolytic reaction will 
 be found to be accompanied by some changes in the 
 
 1 " Inadequacy and Inconsistency of Some Common Chemical 
 Terms " Metallurgical & Chemical Engineering, December 1, 
 1916, p. 649. 
 
98 ELECTROCHEMICAL EQUIVALENTS 
 
 valences ; this seems moreover to be a necessary 
 consequence from the above conception that the 
 electric current is always accompanied by the making 
 or breaking of bonds in charging or discharging the 
 ions ; it moreover seems to be in entire agreement 
 with the modern electronic theory, explained in Part 
 II. It is the amount of this change of valence and 
 not the valence itself which in all cases is the basis 
 of the quantitative electro-chemical calculations. The 
 valence factor which enters into these calculations is 
 always the difference between the valence before 
 and after the reaction. Calculations are sometimes 
 simplified and easier to understand by basing them 
 on the changes of valence, as shown elsewhere in 
 the examples where both methods are illustrated. 
 
 As every bond of a gram-atom of any element 
 means that one faraday accompanies the making or 
 breaking of it, one faraday will be required per gram- 
 atom for every unit change of valence. To reduce a 
 valence say from 3 to 2 (as in the reduction of ferric 
 to ferrous sulfate) means going one third toward 
 freeing the element of all of its bonds, that is, toward 
 setting it free. The less the change of valence the 
 less electricity it will require to free a gram of that 
 element or to dissolve it. 
 
 In the cases in which elements in combination are 
 set free, then- valence has been changed from the 
 one they had in combination to zero, hence in such 
 cages and only in such cases is the change of valence 
 numerically equal to the valence which they had in 
 combination. Faraday's law as usually stated in 
 textbooks therefore applies only to this case, which 
 however is the more usual one. But there are cases 
 in which nothing is set free (see Examples 7, 8, 9, and 
 10) tho there is always a change of valence, hence to 
 
VALENCE 99 
 
 become universal this law should refer to the change 
 of valence and not to the valence alone. 
 
 Sign of the valence. To carry out this convenient 
 and useful conception of the change of valence it is 
 sometimes necessary or desirable to designate 
 whether a valence is + or '-, that is, whether the 
 respective ions in electrolysis carry positive or nega- 
 tive charges ; if positive they will travel with the 
 current and tend to go to the cathode ; if negative 
 they will travel against the current and tend to go to 
 the anode. And when set free they give up their 
 charges to the electrode, after which they must 
 necessarily have a valence of zero. 
 
 The conception of negative valences will not 
 generally be found described hi chemical treatises, 
 as chemists do not as a rule take any notice of the 
 sign of the valence, but it is often of advantage 
 to do so in electrochemistry; the conception of 
 negative valences necessarily follows mathematically 
 and physically from the fact that the charges have 
 different signs. The sign is concerned with the 
 direction of the current or with what might be called 
 the direction of the chemical reaction, that is, whether 
 a reduction or an oxidation (adduction) which are 
 chemical opposites. When the signs become reversed 
 in a reaction they are also important factors in 
 determining the electrical quantities hi a reaction, as 
 shown below, but with this exception the signs do not 
 affect the quantities, hence the values given in Table 
 I are applicable as well to + as to valences. 
 
 As every one of these bonds joins two atoms in a 
 combination, it necessarily is positive with reference 
 to one of them and negative with reference to the 
 other. Thus in water, H 2 O, when the two bonds 
 are considered with reference to the hydrogen they are 
 
100 ELECTROCHEMICAL EQUIVALENTS 
 
 positive, but with reference to the oxygen they are 
 negative. 
 
 Most of the elements will in electrolysis always go 
 to one particular electrode and never to the other; 
 that is, they always carry a charge of the same sign ; 
 hydrogen for instance always carries positive charges 
 and therefore goes to the cathode, while oxygen 
 carrying negative charges always goes to the anode. 
 The valence of hydrogen is therefore always + and 
 that of oxygen always -. 
 
 Some of the elements, however, like antimony, 
 carbon, chlorine, nitrogen, etc., sometimes carry 
 positive and sometimes negative charges. Their 
 valences are therefore sometimes + and sometimes - , 
 depending upon the nature of their combination ; it is 
 always the same in the same combination, at least hi 
 all usual cases. These elements must therefore be 
 considered as having both a reducing and an oxidizing 
 or adducing action, depending on the sign of their 
 valence. 
 
 Electrolysis separates a compound or combination 
 of elements into two constituents carrying charges of 
 different signs. The compound in its free state must 
 be considered to have no free charge, that is, a zero 
 valence, it being combined with nothing else. From 
 this it follows that the valences of the constituent 
 elements of a compound multiplied by the number of 
 their atoms, must always add up to zero. Thus in 
 nitric acid, HNO 3 , +1 + 5 6 = 0; or in sulfuric 
 acid, H 2 SO 4 , + 2 + 6-8 = 0. This is often useful in 
 finding the sign of the valence of one of the con- 
 stituents when those of the others are known. 
 
 A radical as a whole may be said to have a valence ; 
 thus SO 4 has a valence of 2, as it must balance 
 with the + 2 in H 2 SO 4 . 
 
VALENCE 101 
 
 As illustrations of changes of signs of the valence, 
 sulfur in H 2 S has a valence of - ? while in the 
 oxide SO 3 it has a valence + 6 to baUne\tbX$( 2V=^ 
 
 - 6 of the 3 . Hence when the -sulfur is adduced 
 or oxidized from the former state, into > 4Jie[ iafte^Jte-. 
 change of valence is from - 2 to +6 which is equal 
 to + 8, the change of valence being the algebraic 
 difference. If this reaction could be carried out 
 electrolytically it would require 8 faradays per gram 
 atom of sulfur, and not 4 as it would be if the 
 signs were neglected. In this change it must pass 
 thru zero valence, which means its free state. 
 
 Another illustration is the adduction or so-called 
 oxidation of methane CH 4 into carbon tetrachloride 
 CC1 4 . In the former it seems that the valence ought 
 to be stated to be -4 and in the latter + 4, hence the 
 change of valence is + 8 and not zero as it would be 
 if the signs were neglected; the + sign before the 
 8 means that it was an adduction or oxidation. Or 
 in reducing nitric acid, HNO 3 , into ammonia, NH 3 , 
 the change of valence of the nitrogen is from + 5 to 
 
 - 3, the difference being - 8, and not 2 as it would 
 be if the signs were neglected ; the sign here 
 means that it was a reduction. 
 
 Chemical reactions. In electrolysis the only purely 
 chemical reactions which accompany the current 
 are reductions and oxidations (adductions) in the 
 sense of these terms given below. They are chemi- 
 cally the same kind of a reaction, differing only 
 in their sign or direction ; each is the direct opposite 
 or reverse of the other ; hence whatever is true of the 
 one, the reverse is true of the other. 
 
 Reduction. Chemical reductions, when interpreted 
 according to modern accepted theories, always mean 
 a reduction or loss of the valence, whether from + to 
 
102 ELECTROCHEMICAL EQUIVALENTS 
 
 or toward 0, or from to -, or from + to -. The 
 reduced products always go to the cathode. Reducing 
 .hydrogen :frdiri water is a reduction of its valence 
 from +1 to 6 for each of the two atoms. When the 
 fo^kis'* af e rediiced'from their combinations to their 
 free state their valences are always reduced from + 
 to 0. When an element has a + valence hi a com- 
 bination it means that it is hi an oxidized state and is 
 capable of being reduced, either toward or to the free state 
 or hi some cases even beyond, to a negative valence. 
 
 Every lowering of the valence should therefore be 
 embraced in the general term chemical reduction, 
 even tho this is not now customary ; it would be more 
 consistent and uniform to do so. When a metal 
 combines with free oxygen, the metal is correctly 
 said to have been oxidized, but the oxygen must be 
 said to have thereby been reduced, as its valence has 
 then been reduced from to -2. This is quite 
 consistent when it is considered that the oxidizing 
 property of the oxygen has thereby been reduced, 
 combined oxygen being a less powerful oxidizing 
 reagent than free oxygen. 
 
 In a general way chemical reduction also means the 
 loss of bonds and the loss of a companion element 
 and is therefore an appropriate term which can con- 
 sistently be extended to include all these features. 
 In the author's opinion it also means a loss of the 
 electric charge, whether positive according to the 
 older conceptions or negative according to the newer 
 ones, provided the conceptions are consistently 
 interpreted, as described below. 1 According to some 
 
 1 For a more detailed discussion, see article on " Oxidation 
 and Reduction in Physical-Chemistry. Consistency of Terms 
 and Conceptions," in the issue of May 1, 1917, Metal. & Chem. 
 Eng., 1917, page 507 by Carl Hering. 
 
VALENCE 103 
 
 writers, however, reduction is claimed to be a gain of 
 negative charges ; at the present writing there seems 
 to be no definite physical proof, it is a deduction 
 involving some disputed definitions. 
 
 It is conventionally assumed all the world over that 
 electricity, water, and gas flow from their positive, 
 high, or compressed state to their negative, low, or 
 rarified state, as is usually indicated by an arrow; 
 conventionally, therefore, it is the positive charge of 
 electricity which flows in the direction of the arrow ; 
 a loss of a charge therefore means that it was a 
 positive charge. According to the older conceptions 
 reduction takes place at the cathode, as it ostensibly 
 does, hence corresponds to a reduction or loss of the 
 positive charge which that ion carried ; after the ion 
 has been set free it has a zero or neutral charge ; 
 its positive charge may be conceived to flow into the 
 cathode and pass off as the current. 
 
 According to the more modern electronic theory, 
 however, it is the negative electricity which is con- 
 ceived to flow in the opposite direction, a positive 
 charge being then the result of a loss of negative 
 electrons ; a loss of a charge therefore means that it 
 was a negative charge. And according to the modern 
 dissociation theory, before any current is applied and 
 before they reach the electrodes the ions have already 
 been dissociated or ionized, whereby they have 
 received their charges ; dissociation means decom- 
 position, hence a reduction of the cation. The true 
 chemical reduction of the cations therefore really 
 took place during this process of dissociation, and as 
 they are then left with a positive charge there has 
 been a reduction or loss of negative electrons during 
 the actual chemical reduction. The final freeing of 
 an element is not an essential part of reduction; 
 
104 ELECTROCHEMICAL EQUIVALENTS 
 
 ferric salts are correctly said to be reduced to ferrous, 
 yet nothing is set free thereby. The final freeing of 
 the dissociated ions is a different and subsequent 
 process, and is not the real reduction. 
 
 Hence, whether based on the conventional or on 
 the more advanced conceptions, a chemical reduction 
 in electrolysis always corresponds to a loss or reduc- 
 tion of electric charges as well as of valence. 
 
 In the author's opinion it should be clearly under- 
 stood that this loss of negative electrons must be 
 regarded as taking place during the process of chemi- 
 cal reduction or dissociation, hence when it is said 
 that H in HC1 for instance has a free positive charge, 
 it refers only to those atoms of the H which have 
 been reduced on being ionized by dissociation ; those 
 which are still combined as HC1 have no free charges, 
 as the HC1 as a combination has no free charges, 
 those of its H and Cl (which are equal) being then 
 combined forming the bond, and their mutual attrac- 
 tion may be said to constitute the force which binds 
 the elements to each other; equal and opposite 
 charges always result in electrical neutrality. 
 
 As neither the free H nor the undissociated com- 
 bination HC1 as such, has any free charge, there can 
 be no loss or gain of free charges during the oxidation 
 of H to HC1; the charges which the H and Cl gain 
 and lose when they combine are equal and opposite, 
 hence neutralize each other. It is therefore wrong, 
 in the author's opinion, to say that because the H in 
 HC1 is usually (and correctly) marked with a + sign 
 above it, indicating that it has a positive charge, it 
 got this charge when it was oxidized by combining 
 with the Cl. It really got this free positive charge 
 when it was thereafter reduced again by dissociation ; 
 the indication of these charges therefore applies 
 
VALENCE 105 
 
 correctly only to the dissociated compounds and not 
 to those elements which are still undissociated. 
 
 Oxidation or adduction. Chemical oxidation, when 
 interpreted according to modern accepted theories, 
 always means an increase or gain of the valence, 
 whether from - to or toward 0, or to +, or - to +. 
 The oxidized products always go to the anode. Oxi- 
 dation of course is independent of whether the 
 element, oxygen itself is involved or not. Altho by 
 general consent the term oxidation has been extended 
 to include combinations with other elements also, 
 Cu + Cl = CuCl being called an oxidation, yet it is 
 thought by some prominent chemists that a less 
 confusing and a more consistent and appropriate 
 term would be desirable ; among all those suggested 
 the best seems to be " adduction," 1 as the prefix 
 "ad-" implies addition to the valence, bonds, ele- 
 ments, and charges, as explained above in the 
 reverse sense for reduction, the prefix " re- " implying 
 a reduction of them; each is then the exact reverse 
 of the other. This term adduction has been adopted 
 in this book as preferable to oxidation. 
 
 What was said above concerning reduction therefore 
 applies hi the reverse sense to adduction or oxidation, 
 hence, in the sense explained above, it is always 
 accompanied by a gain of valence and negative 
 charges, and in a general sense by a gain of bonds 
 and companion elements. 
 
 When an element in combination has a negative 
 valence it means that it is in a reduced state and is 
 
 1 Suggested independently by Dr. Frederick H. Getman, 
 one of the present authors, but was subsequently found to have 
 been proposed, for similar reasons, by Dr. M. L. Hamlin in a 
 paper by Nelson & Falk, Jour. Am. Chem. Soc., 35, December, 
 1913, p. 1812. 
 
106 ELECTROCHEMICAL EQUIVALENTS 
 
 capable of being adduced or oxidized to a positive 
 valence, either to or toward the free state or even 
 beyond. 
 
 To combine a free element with oxygen, fluorine, 
 etc., which is called oxidation or adduction of that 
 element (but not of the oxygen), is to increase its va- 
 lence from to +. But the setting free of sulfur from 
 H 2 S for instance is also an increase of its valence 
 from - 2 to ; it must therefore also be considered 
 broadly as an adduction or oxidation, and in H 2 S the 
 sulfur must be considered to be in even a more 
 highly reduced state than when free ; it can be 
 further oxidized to SO 3 and its valence then becomes 
 + 6. It is also exactly the same process as setting 
 free oxygen from an oxide, as the valence of the 
 oxygen has thereby been increased from 2 to ; 
 it would seem to be preferable to call this ' * adduced 
 oxygen " rather than " oxidized oxygen ; " such free 
 oxygen has a greater oxidizing power than when 
 combined, this power having been added to or in- 
 creased ; the inconsistency lies in the terms and not 
 in the physical facts. 
 
 In the case of cuprous chloride, CuCl, the chlorine 
 has a negative valence and at the anode it tends to 
 be adduced or oxidized to its free state. In that case 
 its adducing or oxidizing power has been increased 
 and therefore it tends to adduce or oxidize some of 
 the remaining CuCl to the cupric salt CuCl 2 (see 
 Example 10). 
 
 Numerical values of the valences. The valences which 
 the elements have in then* different compounds 
 are given above in Table IV revised for this book by 
 the kindness of Dr. Jos. W. Richards. The signs 
 which these valences have are included hi each case. 
 The table gives what he calls the " practical va- 
 
VALENCE 107 
 
 lences," that is, the actual ones irrespective of any 
 interpretation involving what are called structural 
 formulas. 
 
 Some of the elements, like hydrogen, silver, zinc, 
 oxygen, etc., practically have only one valence in all 
 their usual combinations, hence they each have but 
 one electrochemical equivalent; but some other 
 elements, like copper, iron, nitrogen, etc., may some- 
 times have one valence and sometimes another, hence 
 they have several electrochemical equivalents. With 
 some of the latter the electrochemical reaction merely 
 changes the valence from one of its values to another, 
 in which case they may have still another equivalent 
 corresponding to this change ; with iron, for instance, 
 there can be a change of valence of 1, yet it never 
 has this valence. With most of the elements the sign 
 of the valence is either always + or always -, in all 
 their compounds, but with some of them, namely 
 antimony, arsenic, bromine, carbon, chlorine, iodine, 
 nitrogen, phosphorus, selenium, silicon, sulfur, and 
 tellurium, the valences are sometimes + and some- 
 times -, tho always the same in the same combina- 
 tion, at least in all usual cases. 
 
 In the usual electrolytes (tho rare exceptions are 
 claimed to exist) the following general rules may be 
 of service : The valence of hydrogen is always + 1 
 (tho perhaps + 2 in H 2 O 2 ), oxygen always - 2, 
 chlorine in chlorides -1, SO 4 in sulfates 2, NO 3 
 - 1, C1O 3 - 1 ; in metallic solutions in which the 
 metal is the base, the valence of the metals is + and 
 that of the radical . 
 
 As described above, when the valences are given 
 their proper signs and when multiplied by the number 
 of the atoms of an element, they must always add up 
 to zero in any compound. Thus in nitric acid, HNO 3 , 
 
108 ELECTROCHEMICAL EQUIVALENTS 
 
 + 1 + 5-6 = 0, or in ferric sulfate, Fe 2 (SO 4 ) 3 , 
 2(+ 3) + 3(6- 8) = + 6 - 6 = 0. As every one of 
 these bonds has a positive and a negative end, the 
 number of the positive ends must of course equal the 
 number of negative ones. This principle may be 
 used to determine the valence and its sign, for one 
 element of a compound when those for the others are 
 known. 
 
 The valence of an element can also often be de- 
 termined by finding the number of hydrogen atoms 
 which will replace that element in an analogous 
 compound. Thus silver has a valence of 1 because 
 in silver nitrate, AgNO 3 , it replaces one of hydrogen in 
 the analogous compound nitric acid, HNO 3 . Or the 
 valence of silicon is 4 because in its oxide, SiO 2 , it 
 replaces four atoms of hydrogen in the oxide of 
 hydrogen 2(H 2 O), when the amount of oxygen is 
 made the same in both; the valence of oxygen is 
 here considered to be the same in both, it being 
 assumed to have only one valence, an assumption 
 which seems to be generally accepted, tho it is some- 
 times contested. 
 
 The valences of the radical or ion SO 4 must be - 2 
 because hi H 2 SO 4 the hydrogen has a valence of + 1, 
 hence +2-2 = 0. Knowing the valences of SO 4 to 
 be 2, that of iron in the ferric sulfate Fe 2 (SO 4 ) 3 
 must be + 3 because 2(+ 3) + 3(- 2) = 0. 
 
 These simple rules will suffice for most cases 
 occurring in the ordinary and usual electrochemical 
 calculations ; there may be some complicated cases 
 in which there is some doubt ; in such cases one 
 should either consult a chemist or make the electro- 
 chemical calculation by some indirect method by 
 using some other element of which the valence is 
 known, like hydrogen, and then find by purely 
 
VALENCE 109 
 
 chemical calculation what the chemically equivalent 
 amount is of this other element in terms of the one 
 involved in the problem. Examples illustrating this 
 method are given in Section IV, altho there is 
 probably no doubt in any of these as to what the 
 valences are. 
 
 Strength or intensity of bonds. Each of these chemical 
 bonds in electrolytes represents the same quantity 
 of electricity, namely one faraday, which is the 
 charge carried by a univalent or monovalent gram- 
 ion, and is therefore the same for all the elements, 
 yet what might be called the strengths or intensities 
 of the bonds, measured in terms of the energy which 
 they represent when made or broken, is quite different 
 in different combinations of elements. 
 
 As all these bonds are alike in the quantity of 
 electricity which they represent, it follows that the 
 greater the number of these bonds in any combina- 
 tion, that is, the greater the valence, the greater will 
 be the quantity of electricity involved. In this sense 
 the greater the valence the greater the strength or 
 intensity of the total combining power. But quantity 
 of electricity by itself is not energy, hence it does not 
 represent the strength or intensity in the sense of 
 energy ; it is only one factor of energy in the same 
 sense that either feet or pounds are only one of the 
 factors of foot-pounds of energy. Coulombs or 
 ampere-hours must be multiplied by volts hi order 
 to express the energy. The so-called heat of com- 
 bination of a chemical reaction (more correctly 
 the energy of combination, as in electrolysis this 
 energy does not appear as heat) truly expresses the 
 energy. 
 
 While these unit bonds represented by a faraday 
 are alike for all elements, yet the energy represented 
 
110 ELECTROCHEMICAL EQUIVALENTS 
 
 by a unit bond may be and generally is quite different 
 for the different elements and even for the same 
 element in different combinations. The true strength 
 or intensity or degree of chemical affinity is better 
 expressed in terms of energy. The energy in joules 
 (the product of the volts and the coulombs) repre- 
 sented by one of these bonds is equal to the faraday 
 expressed in coulombs, namely 96,500, multiplied by 
 the volts required for producing the chemical separa- 
 tion (an endothermic reaction), or by the volts 
 generated by their formation in the case of a battery 
 (an exothermic reaction). For instance, in the 
 decomposition of a gram-molecule of water, H 2 O, 
 there are two bonds each representing 96,500 cou- 
 lombs ; if the decomposition voltage is 1.5 the 
 strength of each bond measured in terms of energy 
 is 96,500 x 1.5 = 144,750 joules ; and as one joule 
 = 0.000,2778 watt-hours, this is equal to 40.2 watt- 
 hours. As there are two bonds^the total strength is 
 80.4 watt-hours; this means that it will take 80.4 
 watt-hours of energy to decompose a gram molecule 
 of water equal to about 2 + 16 = 18 grams. If the 
 value of the faraday is taken in ampere-hours, namely 
 26.80, and is then multiplied by the volts (1.5), giving 
 40.20 watt-hours per bond, the calculation becomes 
 simpler. But great care must be taken hi using the 
 correct voltage of decomposition, as other factors 
 enter when it is measured ; the voltage here referred 
 to is that determined from the so-called heat of 
 chemical combination usually stated in calories. 
 For monovalent ions the number of volts is equal to 
 this energy of combination expressed in kilogram 
 calories per gram-molecule, divided by 23.061 ; for 
 multivalent ions this constant must be multiplied by 
 the valence. 
 
VALENCE 111 
 
 For calculations of the energies involved in electro- 
 chemical reactions other than those stated in the 
 headings of the columns of Table I, appropriate 
 treatises should be consulted, as this is beyond the 
 intention of the present descriptive remarks on 
 valence. 
 
 C. H. 
 
Appendix II 
 
 ELEMENTARY PRINCIPLES OF CHEMICAL 
 REACTIONS AND CALCULATIONS 
 
 The following brief statements of a few of the 
 elementary principles of chemistry are given here tc 
 enable one who is not a chemist to follow more 
 intelligently the chemistry necessarily involved hi the 
 electrochemical calculations described in this book, 
 For the less usual kinds of calculations some further 
 knowledge of chemistry may be necessary, while for 
 the more involved problems treatises on chemistry 
 must be consulted. For some of the more complex 
 cases the necessary facts are not yet known, and 
 then- explanations are still controversial. 
 
 Elements; atoms; molecules; radicals; combinations; sub- 
 scripts. There are known at present 83 elementary 
 substances, called the chemical elements, which alone 
 or hi various combinations with each other constitute 
 all matter; they are all given in Table I, and are 
 generally represented by the symbols given in the 
 second column. For convenience hi describing the 
 reactions between these elements and for making 
 calculations, it is assumed that certain extremely 
 small unit particles of them exist, called atoms. 
 Chemical compounds are made up of various com- 
 binations of these atoms, and are represented by 
 formulas in terms of then* symbols ; in a compound 
 the numbers of these atoms in the smallest possible 
 particle of the compound, which is called a molecule, 
 
 112 
 
CHEMICAL REACTIONS AND CALCULATIONS 113 
 
 are indicated by subscripts. Thus H 2 O means that in 
 this compound two atoms of hydrogen (H) and one of 
 oxygen (O) are combined to form one molecule of 
 this chemical compound, which is water. CuSO 4 
 means that one atom of copper (Cu), one of sulfur (S), 
 and four of oxygen (O) are combined to form one 
 molecule of what is called copper sulfate. Subscripts 
 therefore denote the number of the atoms of any 
 particular element in a molecule. These compounds 
 are formed by the union of these atoms in those 
 proportions, and they may be decomposed again into 
 then* elements by breaking this union. Sometimes a 
 fractional part of a molecule is for convenience called 
 a radical, but it does not exist by itself; thus SO 4 
 is a radical in CuSO 4 , ZnSO 4 , Fe 2 (SO 4 ) 3 . In elec- 
 trolysis a radical may sometimes be considered to act 
 like an element; thus in the electrolysis of CuSO 4 
 the Cu goes to the cathode and the SO 4 to the anode. 
 
 Electrolytes; electrodes. If hi their liquid states, 
 either molten or dissolved, these compounds conduct 
 an electric current and are decomposed by it, they are 
 called electrolytes. The passage of a current thru 
 them always changes them chemically in some way 
 (reduction, adduction, or oxidation) at the two places 
 where the current enters and leaves the liquid ; 
 these places are at what are called the electrodes; 
 the one thru which the current enters the liquid is 
 called the anode, and the one thru which it leaves, 
 the cathode ; this is true whether the current enters 
 from an outside source, as hi the case of an elec- 
 trolytic bath, or whether it is generated internally as 
 in a battery. 
 
 Reactions; equations; coefficients. When brought into 
 contact with each other, many of these chemical 
 compounds act in various ways on each other, pro- 
 
114 ELECTROCHEMICAL EQUIVALENTS 
 
 ducing chemical changes ; these actions are called 
 chemical reactions ; they are generally expressed in 
 the form of an equation showing the constitution 
 of the mixture before and after the reaction. The 
 number of atoms has, of course, not been changed, 
 hence must always be the same on both sides of 
 these equations. The number of molecules of these 
 substances required to produce these reactions is 
 indicated by numbers preceding them called coeffi- 
 cients. Thus 
 
 3 Pb + 8 (HNO 3 ) = 3 Pb(NO 3 ) 2 + 2 NO + 4 H 2 O 
 means that three atoms of lead, Pb, and eight mole- 
 cules of nitric acid, HNO 3 , will react on each other to 
 produce three molecules of nitrate of lead, Pb(NO 3 ) 2 , 
 and in doing so will set free two molecules of nitric 
 oxide gas, NO, and four molecules of water, H 2 O ; the 
 number of atoms of each kind before and after the 
 reaction will be found to be the same, and, of course, 
 must always be made to be the same in writing out 
 the equation to make it balance. The coefficients 2, 
 3, 4, and 8 in the above equations indicate the number 
 of molecules involved. 
 
 When with the aid of platinum electrodes an elec- 
 tric current is then passed thru a solution of this 
 nitrate of lead, which is an electrolyte, it decomposes 
 this salt into one atom of free lead, Pb, one of 
 oxidized lead, PbO 2 , and one of nitric acid, HNO 3 . 
 The reactions before and after are then shown by the 
 following equation, which in order that it shall balance 
 must include two molecules of water, H 2 O, which 
 also enters into the reaction. 
 
 2 Pb(NO 3 ) 2 + 2 H 2 O = Pb + 4 HNO 3 + PbO 2 
 
 Relative weights; atomic, molecular, and formula weights. 
 The relative weights of the atoms of the elements, 
 
CHEMICAL REACTIONS AND CALCULATIONS 115 
 
 that of oxygen being by convention assumed to 
 be 16, are called the " atomic weights " and are 
 given in column 3 of Table I. Adding together the 
 atomic weights of all the atoms forming a molecule, 
 being careful to note the subscripts (the coefficients 
 are not concerned), gives the so-called molecular 
 weight, or preferably the formula weight, of the whole 
 molecule, and the proportional part of this total 
 weight which is due to any one of the elements, or 
 group of elements, is then easily determined by 
 simple proportion. Thus for nitrate of lead, Pb(NO 3 ) 2 , 
 taking the respective atomic weights from the table 
 gives the molecular or formula weight : 207.20 + 
 2 (14.01 + 16 x 3) = 331.22. The lead forms 207.20 
 ~ 331.22 = .626 of it (62.6%) or nearly 2/3 ; the two 
 parts of the radical NO 3 form the other third ; and the 
 six oxygen atoms (6 x 16 = 96) form 96 + 331.22 = 
 .29 or nearly 30 % of it. 
 
 Actual weights; gram-atoms; gram-molecules; gram-ions. 
 Such atomic weight calculations however give merely 
 relative weights or proportions, but not absolute 
 weights in grams or pounds. In order to get the 
 latter all these ideal diminutive atoms are for con- 
 venience supposed to be enlarged the same number 
 of millions of times until the enlarged oxygen atom 
 weighs 16 grams, then all the actual weights of the 
 correspondingly enlarged atoms of all the other 
 elements will be as many grams as is expressed 
 numerically by their atomic weights. These are 
 called gram-atoms or sometimes " one atomic 
 weight ; " or when added together for a molecule 
 they are called gram-molecules. They then become 
 tangible quantities which are easily weighed, a gram- 
 molecule of water for instance being about 18 grams, 
 or 18 cubic centimeters ; a gram-atom of copper being 
 
116 ELECTROCHEMICAL EQUIVALENTS 
 
 63.57 grams or about a seventh of a pound. Simi- 
 larly in electrochemistry a gram-ion means an ion or 
 electrochemical unit which weighs as many grams as 
 is expressed by the sum of the weights of its con- 
 stituent parts. 
 
 Valence. When an atom combines with or can 
 replace only one atom of hydrogen, it is said to have 
 a valence of 1 ; when it combines with or replaces 
 2, 3, 4, etc., atoms of hydrogen, its valence is 2, 3, 4, 
 etc., respectively. Some elements have several va- 
 lences. The subject of valence hi electrochemistry is 
 treated more fully hi Appendix I. 
 
 Chemical equivalents. By a chemical equivalent or 
 equivalent weight or combining proportion, is meant 
 that chemical quantity or amount of a substance which 
 can chemically replace or be substituted for or com- 
 bine with another, or which in a chemical equation 
 corresponds to another. Thus hi sulfuric acid, H 2 SO 4 , 
 two hydrogen atoms are the chemical equivalent of 
 one of copper in CuSO 4 , as each could quanti- 
 tatively replace the other; a given electric current 
 will electrolyze chemically equivalent amounts of 
 different substances, hence a current which will set 
 free 2 gram atoms of H (2.016 grams), will set free 
 one gram atom (63.57 grams) of Cu from CuSO 4 . 
 Furthermore H 2 and SO 4 may be said to be chemically 
 equivalent amounts as they combine in those 
 amounts ; so are Cu and SO 4 . Or in the equation 
 
 Al + 3 HC1 = AlCls + 3 H 
 
 one of aluminum, Al, and three of hydrochloric acid, 
 HC1, may be said to be chemically equivalent, or 
 chemically combining quantities, for in any other 
 proportions they would not form this product. Hence 
 for every pound of aluminum to be dissolved the 
 
CHEMICAL REACTIONS AND CALCULATIONS 117 
 
 chemically equivalent amount of hydrochloric acid 
 required (not including the water in which the acid is 
 dissolved) is easily calculated, it being in the propor- 
 tion of the atomic weights or formula weights in the 
 equation, namely as 3 (1.008 + 35.46) = 109.4 is to 
 27.1 ; that is, 1 pound of aluminum will require 
 109.4/27.1 = 4.04 pounds of acid. 
 
 Reduction and adduction or oxidation. As far as the 
 chemical changes produced by electrolysis are con- 
 cerned there are in general two classes of chemical 
 reactions called reduction and adduction or oxidation ; 
 they are the direct opposites of each other, each being 
 the reversal of the other ; they are the same in kind 
 but opposite in direction or sign. When, for instance, 
 a metal has been obtained in its free state from a 
 solution of it, say in an acid, the metal is said to have 
 been reduced; while when a free metal has been 
 dissolved say by an acid and brought into a state of 
 solution, the metal is said to have been oxidized, but 
 as this term is confusing and misleading when this 
 combining element is some other one than oxygen 
 the new term adduction (the antithesis of reduction) 
 is here recommended. (See further reference to it 
 under Valence, Appendix I.) For instance, metallic 
 copper obtained from the solution CuCl 2 is said to 
 have been reduced; while when metallic copper is 
 dissolved by hydrochloric acid to form CuCl 2 it is 
 said to have been adduced or oxidized. Electro- 
 chemically there is always apparently a chemical 
 reduction of some kind at the cathode (like the 
 deposition of a metal), and a chemical adduction or 
 oxidation at the anode (like the dissolving of a metal). 
 
 Chemical affinity. Some elements or groups of 
 elements have a very strong tendency to combine 
 while with others it is weak, and with still others 
 
118 ELECTROCHEMICAL EQUIVALENTS 
 
 there is none at all ; the stronger affinity will in 
 general overpower the weaker. In electrochemical 
 calculations involving merely the quantities of sub- 
 stances set free or dissolved or changed by a given 
 current, that is, in such as are calculated with the 
 aid of the present tables, this factor of affinity does 
 not enter, as a given current will set free or dissolve 
 the same amount of any one element whether that 
 element is tightly or loosely combined with other 
 elements, provided that the valence is the same. 
 The intensity of this chemical affinity will have an 
 effect on the voltage that is required to bring about 
 the reactions or is produced by it, but it has no effect 
 on the number of coulombs or ampere-hours that are 
 required for electrolyzing a given quantity of the 
 material. 
 
 Primary and secondary reactions. In electrolysis the 
 current will produce certain chemical reactions, after 
 which the products produced may react chemically on 
 each other or on some other substance present ; the 
 former is called a primary reaction and the latter a 
 secondary one, as it is not produced directly by the 
 current. In the electrolysis of sulfuric acid, H 2 SO 4 , 
 for instance, the hydrogen is set free at the cathode 
 which is a true primary reaction ; but the SO 4 which 
 goes to the anode, cannot exist as such and therefore 
 combines with the hydrogen of the water always 
 present, setting free oxygen at the anode. This latter 
 is sometimes called a secondary reaction, tho on the 
 other hand it may be claimed that the electrolytic 
 process has not been completed until definite com- 
 pounds have been produced, and not merely radicals. 
 It may also be said that as the amount of sulfuric 
 acid is the same after the reaction as before, while 
 the water diminishes, it was the water and not the 
 
CHEMICAL REACTIONS AND CALCULATIONS 119 
 
 acid which was electrolyzed. If the anode is of 
 copper it will be dissolved by the SO 4 ions forming 
 CuSO 4 , which would seem to be a true primary 
 reaction. 
 
 It is sometimes difficult to discriminate between the 
 two reactions ; in some cases authorities differ and no 
 generally accepted definitions to distinguish clearly 
 between them seem to exist ; but when reactions do 
 not take place exactly simultaneously with the passage 
 of the current and in exact proportion to it, or when 
 they continue after the current ceases, they are 
 unquestionably secondary. The author suggests that 
 in view of the fact that some energy changes are 
 generally involved in all chemical and electrochemical 
 reactions, a primary reaction may be said to be the 
 one whose energy (endothermic or exothermic) 
 appears in the electric circuit, while a secondary 
 reaction is one whose energy does not appear in the 
 electric circuit. 
 
 C. H. 
 
Appendix III 
 
 CONVERSION FACTORS USED IN ELECTRO- 
 CHEMICAL CALCULATIONS 
 
 Taken from Bering's " Conversion Tables." 
 Length. 
 
 1 centimeter = 0.3937 inch 
 
 1 inch = 2.540 centimeters 
 
 Surface. 
 1 sq. inch 
 1 sq. decimeter 
 1 sq. decimeter 
 1 sq. foot 
 
 Volumes. 
 1 cb. centimeter 
 1 cb. centimeter 
 1 cb. inch 
 1 quart 
 1 liter 
 1 liter 
 1 gallon 
 1 gallon 
 1 cb. foot 
 1 cb. foot 
 
 Weights or Masses. 
 1 gram 
 
 1 pennyweight (troy) 
 1 ounce (advp.) 
 1 ounce (troy) 
 1 pound (advp.) 
 1 kilogram 
 
 Weights and Volumes. 
 1 pound per gallon 
 1 kilogram per liter 
 
 6.452 sq. centimeters 
 15.50 sq. inches 
 0.1076 sq. foot 
 9.290 sq. decimeters 
 
 1 milliliter 
 
 0.06102 cb. inch 
 16.39 cb. centimeters 
 
 1.101 liters 
 
 1.057 quarts (U. S. ; liquid) 
 
 0.2642 gallon (U. S. ; liquid) 
 
 3.785 liters 
 
 0.1337 cb. foot 
 28.32 liters 
 
 7.481 gallons (U.S.; liquid) 
 
 15.432 grains 
 1.555 grams 
 
 28.35 grams 
 
 31.10 grams 
 0.4536 kilogram 
 2.205 pounds (avdp.) 
 
 0.1198 kilogram per liter 
 8.345 pounds per gallon 
 120 
 
CONVERSION FACTORS 
 
 121 
 
 Waler. 
 
 1 liter 
 1 gallon 
 1 cubic foot 
 1 pound 
 1 pound 
 1 pound 
 1 kilogram 
 
 Energy (heat). 
 
 2.205 pounds 
 8.345 pounds 
 62.43 pounds 
 0.4536 liter 
 0.1198 gallon 
 0.01602 cb. foot 
 0.2642 gallon 
 
 1 joule = 0.2389 gram calorie 
 
 1 thermal unit (BTU) = 252.0 gram calories 
 1 watt-hour = 0.8600 kg. calorie 
 
 1 kg. calorie = 3.968 thermal units 
 
 1 kg. calorie = 1.163 watt-hours. 
 
 Power. 
 
 Iwatt 
 
 1 gram calorie per 
 
 second 
 
 1 horse-power 
 1 kilowatt 
 
 0.2389 gram calorie per second 
 
 4.186 watts 
 0.7457 kilowatt 
 1.341 horse-powers 
 
 Electrochemical Equivalents 
 given in Table I). 
 
 Grams per watt-hour 
 
 Kilograms per horse- 
 power-hour 
 
 Pounds per kilowatt- 
 hour 
 
 Pounds per horse- 
 power-hour 
 
 in Energy (other than those 
 
 0.0373 x 
 0.0278 x 
 0.0822 x 
 
 0.0613 x 
 
 atomic weight 
 
 change of valence x volts 
 
 Watt-hours per gram = 26.8 x 
 Kilowatt-hours per 
 
 pound = 12.2 x 
 
 Horse-power-hours = 
 
 per kilogram = 36.0 x 
 Horse-power-hours 
 
 per pound = 16.3 x 
 
 change of valence x volts 
 atomic weight 
 
122 
 
 ELECTROCHEMICAL EQUIVALENTS 
 
 Electrochemical energy. 
 For monovalent ions : 
 
 Volts = kilogram calories per gram molecule x 0.0434 
 For multivalent ions divide the volts thus obtained by the 
 
 valence 
 
 Electrolytic deposits. 
 1 gram per sq. deci- 
 meter 
 
 1 pound per sq. foot = 
 1 pound per year 
 
 1 pound per year 
 
 1 pound per day (of 24 
 
 hours) 
 
 1 gram per minute 
 1 short ton per year 
 1 pound per hour 
 
 0.02048 pound per sq. foot 
 48.82 grams per sq. decimeter 
 
 0.002738 pound per day (of 24 
 
 hours) 
 0.0008624 gram per minute 
 
 0.1826 short ton per year 
 1160. pounds per year 
 
 5.476 pounds per day 
 
 4.383 short tons per year (day 
 
 of 24 hours) 
 
 (The year is considered to be 365 4 days.) 
 
 C. H. 
 
Appendk IV 
 
 GLOSSARY 
 
 The numbers refer to the pages on which the definitions or explanations 
 will be found. 
 
 Adduction 105, 117 
 
 " at anode. 5, 57, 117 
 
 Affinity, chemical 117 
 
 Anions 55 
 
 Anode 54,113 
 
 Atom 112 
 
 " vs. ion. . 58 
 
 Atomic weight 114 
 
 Atomicity 29 
 
 Avogadro's law 2 
 
 Binary electrolytes 69 
 
 Bivalent 2 
 
 Bond 9*2 
 
 positive and negative 99 
 
 " unit 93 
 
 Cathode 64,113 
 
 " particle 74 
 
 " rays 73 
 
 Cations 65 
 
 Change of valence 97 
 
 Charge, unit 64, 93 
 
 Chemical affinity 117 
 
 Chemical equivalents . . 63, 116 
 
 Coefficient 113 
 
 Combinations, chemical . . 112 
 Conductance, electronic . . 85 
 
 Copper coulometer 68 
 
 Corpuscle 78 
 
 Coulomb 31, 65 
 
 Coulometer. . 66 
 
 Diatomic 2 
 
 Direction of current 86 
 
 Di-valent , 2,95 
 
 Electrochemical constant 64, 65 
 " equivalent 65 
 
 Electrodes 54, 113 
 
 Electrolysis 54, 113 
 
 Electrolyte 53,64,55 
 
 Electron 78 
 
 Electrons, valence 79 
 
 Element 112 
 
 Endothermic 110 
 
 Equations, chemical 113 
 
 Equivalent, chemical 116 
 
 Exothermic 110 
 
 Faraday, the 3, 29, 93 
 
 Faraday's law 3, 5, 62, 64 
 
 Formula weight 114 
 
 Fourth state of matter 74 
 
 Fundamental law for gases 
 
 1, 9, 23, 29 
 
 Gram-atom 115 
 
 Gram-ion 31, 115 
 
 Gram-molecule 115 
 
 Ion 55 
 
 " vs. atom.. 58 
 
 Joule, 
 
 110 
 
 123 
 
124 
 
 GLOSSARY 
 
 Migrations of ions 55, 60 
 
 Molecular weight 114 
 
 Molecule 112 
 
 Mon-atomic 2 
 
 Mono-valent 95 
 
 Negative valence 99 
 
 Non-electrolytes 64 
 
 Non-valent 95, 97 
 
 Oxidation 105, 117 
 
 " at anode .. 6, 57, 117 
 
 Poles , 54 
 
 Primary reactions 118 
 
 Quaternary electrolyte ... 69 
 
 Radiant state of matter ... 74 
 
 Radical 112 
 
 Reactions 113 
 
 " primary 118 
 
 " secondary. ..56, 118 
 
 Reduction 101, 117 
 
 " at cathode 5, 57, 117 
 Relative weights 114 
 
 Salts 24 
 
 Secondary reactions ... 56, 118 
 
 Sign of valence 99 
 
 Silver coulometer 66 
 
 Subscripts 112 
 
 Ternary electrolyte 59 
 
 Titration coulometer 71 
 
 Tri-valent 95 
 
 Unit bond 93 
 
 " charge 64 
 
 Valence 5, 85,93,94, 116 
 
 " change of 4,97 
 
 " electrons 79 
 
 " negative 99 
 
 " number of electrons 85 
 
 " sign of 99 
 
 " unit charges 64 
 
 " vs. valency. ..... 97 
 
 " zero 5,96,97 
 
 Valency 97 
 
 Valent, non- 95, 97 
 
 Voltameter 66 
 
 Volume coulometer 69 
 
 Water coulometer 69 
 
 Zero-valence 6, 95, 97 
 
INDEX 
 
 Adduction, defined. . . 106, 117 
 
 " again 105 
 
 " at anode. 5, 67, 117 
 " examples.... 42, 46 
 " sign of valence 99 
 
 Affinity, defined 117 
 
 " 110 
 
 Ampere-hours per cubic foot 23 
 " " per gram.. 12 
 " " per liter... 23 
 " " per pound. 12 
 
 Anions, defined 65 
 
 Anode, defined 64, 113 
 
 " consumption of . . . 33 
 
 " reaction 57 
 
 Atom, defined 112 
 
 " of electricity.... 84, 79 
 
 " stability of 82 
 
 " structure of 79 
 
 " vs. ion 68 
 
 Atomic weight, defined. . . 114 
 
 " table 12 
 
 Atomicity 29 
 
 Atoms, number of 86 
 
 " constitution of 80 
 
 Avogadro's constant 9 
 
 " law, defined. . 2 
 
 B 
 
 Battery, depolarizer .... 36, 37 
 
 " poles of 66 
 
 " storage 45 
 
 Binary electrolyte 59 
 
 Bivalent 2 
 
 Bond, defined 92 
 
 Bond 86 
 
 " non-electrolytic 95 
 
 " positive and negative 99 
 
 " strength of 109 
 
 " unit 93 
 
 Bunsen cell 39 
 
 Bureau of Standards cou- 
 
 lometer . . 67 
 
 Calculations, method of . . 28 
 
 Calories 110,121 
 
 Cathode, defined 54, 113 
 
 " particle 74 
 
 " rays, defined ... 73 
 " " deflection. 76 
 
 " reaction 57 
 
 Cations, defined 55 
 
 Change of sign of valence 
 
 48, 50, 101 
 Change of valence, defined 
 
 4,97 
 examples 
 36, 37, 43, 48 
 " Table I 8 
 
 Charge, free 104 
 
 " magnitude 77 
 
 " on electron 86 
 
 " ratio to mass. ... 75 
 
 " value of 78,79 
 
 " unit 64,93 
 
 Charged ions 58 
 
 Chemical affinity, defined 117 
 
 " " 110 
 
 " calculations. ... 112 
 " compounds 24 
 
 125 
 
126 
 
 INDEX 
 
 Chemical equivalents, defined 
 63, 116 
 
 " " 32,91 
 
 " reactions, defined 101 
 
 " " 112 
 
 Chemistry, elementary prin- 
 ciples 112 
 
 Coefficients, defined 113 
 
 " ignored 39 
 
 Combination heat 109 
 
 Combinations, defined . . . 112 
 " of elements, 
 
 table IV 24 
 
 Combining capacity 84 
 
 Compounds, chemical .... 24 
 Conductance, electronic . . 86 
 Conduction, electrolytic. . 93 
 
 Conductors, class of 63 
 
 " second class . 85 
 
 Conversion factors 120 
 
 Copper anode 33 
 
 " chloride 38 
 
 " coulometer 68 
 
 Corpuscles 78 
 
 Coulomb, defined 31, 65 
 
 Coulombmeter, see coulome- 
 ter 66 
 
 Coulombs per cubic c.m. 23 
 " per milligram .. 12 
 
 Coulometer, defined 66 
 
 " Bureau of Stand- 
 ards 67 
 
 copper 68 
 
 " silver 66 
 
 " titration 71 
 
 " volume 69 
 
 " water 69 
 
 " weight 66 
 
 Cubic c.m. per coulomb . . 23 
 " feet per 1000 amp. hrs.23 
 
 Current, direction of 85 
 
 " electronic stream 85 
 
 Decomposition voltage ... 110 
 
 Depolarizers 33, 36, 37 
 
 Description of tables 7 
 
 Diaphragm 66 
 
 Diatomic 2 
 
 Direction of current 85 
 
 Discharge in vacuum 73 
 
 Dissociation theory 57 
 
 " " applied 103 
 
 Di-valent 2, 95 
 
 " element 83 
 
 Double duty, of acid 51 
 
 " " of current. . . 46 
 Drop, volume of a 78 
 
 Electricity is not energy . . 109 
 
 " atom of 79,84 
 
 Electrochemical constant, 
 
 defined 64, 65 
 
 Electrochemical equivalent, 
 
 calculations 28 
 
 Electrochemical equivalent, 
 
 defined 65 
 
 Electrochemical equivalent 
 
 by weight 12 
 
 Electrochemical equivalent 
 
 of gases 23 
 
 Electrochemical reaction . 86 
 
 Electrodes, defined. . . .54, 113 
 
 " no deposits on 42 
 
 Electrolysis, defined ... 54, 113 
 
 " section V 53 
 
 Electrolyte 63,54, 65 
 
 Electrolytic conduction . . 93 
 
 Electron, defined 78 
 
 " enlarged 93 
 
 Electrons connect atoms . 84 
 " distribution of . . 80 
 " gain and loss of 
 
 85, 103, 105 
 
INDEX 
 
 127 
 
 Electrons, mass of 79 
 
 source of 79 
 
 valence 79 
 
 Electronic conception of 
 
 conductance . 86 
 conception of 
 
 valence 84 
 
 current stream 85 
 
 " theory 73 
 
 theory, deduc- 
 tions 103 
 
 Electrophysical law 9, 23 
 
 Elements, defined 112 
 
 " combinations of.. 24 
 
 " list of the 12 
 
 " with + and - 
 
 valences 107 
 
 " relation to elec- 
 trons 80 
 
 " symbols of 12 
 
 " valences of 12,24 
 
 Endothermic 110 
 
 Energy constant 110 
 
 " coulombs x volts.. 109 
 " electrochemical . . 122 
 " of combination ... 109 
 
 " of reactions 109 
 
 Equations, chemical, defined 
 
 113 
 
 Equivalent, chemical, de- 
 fined. . 63, 116 
 chemical, 32, 91 
 
 Examples 28 
 
 Exothermic . . .110 
 
 Faraday, the, defined. 3, 29, 93 
 
 " 3,7,29,98 
 
 " applied to calcu- 
 lations 29, 31 
 
 Faraday's law, defined 
 
 3, 5, 62, 64 
 
 Faraday's law 93 
 
 " " constants of 4 
 " " correction of 
 
 4,5 
 limitations 
 
 of 4,43,98 
 " " universal 4, 99 
 
 Force of migration 62 
 
 Formula weights, defined . 114 
 Fourth state of matter. ... 74 
 
 Free charges 104 
 
 Fundamental constants, by 
 
 weight. . . 7 
 constants, gases 
 1, 9, 23, 29 
 
 data 7 
 
 " law, by weight 3 
 
 " " gases 
 
 1, 9, 23, 29 
 laws.. 1 
 
 Gases, equivalents of .... 23 
 
 Glossary of terms 123 
 
 Gram-atom, defined 115 
 
 Gram-ion, defined 31, 115 
 
 Gram-molecule, defined . . 115 
 
 Grams per ampere-hour 12, 21 
 
 " per watt-hour 12 
 
 Heat of combination 109 
 
 Horse-power 121 
 
 Hydrogen, example 33 
 
 intermediate 
 
 element .... 32 
 
 " weight of 33 
 
 Intensity of bonds 109 
 
 Intermediate reactions .... 40 
 Involved reactions . . 41 
 
128 
 
 INDEX 
 
 Ion, defined 65 
 
 " vs. atom 58 
 
 Ions, activity of 59 
 
 Joules 
 
 110 
 
 Kilograms per 1000 amp. hrs. 
 
 12,21 
 per kilowatt-hour 12 
 
 Kilowatt 121 
 
 Kilowatt-hours per kilogram 12 
 
 Liter of hydrogen, weight. 33 
 Liter of oxygen, weight ... 9 
 Liters per ampere-hour ... 23 
 
 M 
 
 Manganese peroxide 
 Mass, ratio to charge 
 Matter, fourth state of . . 
 Metallic conductance . . . 
 
 Methane, oxidized 
 
 Migration 
 
 " speeds of . . . . 
 Milligrams per coulomb . 
 
 Molecular layer 
 
 " weight, defined . 
 
 Molecules, defined 
 
 Mon-atomic 
 
 Mono-valent. . 
 
 . 37 
 
 . 75 
 
 .. 74 
 
 . 85 
 
 . 101 
 55, 60 
 
 . 61 
 
 . 12 
 
 . 55 
 
 . 114 
 
 . 112 
 
 . 2 
 
 . 95 
 
 . 122 
 
 ions 
 
 N 
 
 Negative charge flows 103 
 
 " " sign 58 
 
 . " valence 37, 99 
 
 " " example 
 
 48,50 
 Nitric acid reduced . . . 101 
 
 Non-conductor 63 
 
 Non-electrolytes 54 
 
 Non-valent 95, 97 
 
 Nucleus, positive 79 
 
 Organic compounds non- 
 conductors 54 
 
 Oxidation, defined 105, 117 
 
 " a gain 105 
 
 " at anode 5, 57, 117 
 " examples.. ..42, 46 
 " sign of valence. 99 
 
 Oxygen, weight of liter .... 9 
 
 Poles, defined 54 
 
 Positive charge flows .... 103 
 " " mass of.. 80 
 
 " " sign of... 58 
 
 " " size of... 80 
 
 " nucleus 79 
 
 Pounds per 1000 amp. hrs. 12 
 " per kilo watt-hour. 12 
 
 Practical valences 106 
 
 Primary battery 34 
 
 " reactions, defined 118 
 
 Quaternary electrolytes. . 59 
 
 Radiant state of matter. . . 74 
 
 Radical, defined 112 
 
 electrochemical 
 constant of ... 43 
 
 Reactions, defined 113 
 
 " chemical 101 
 
 " intermediate . . 40 
 
 " involved 41 
 
 " primary and sec- 
 ondary, def'd 118 
 
INDEX 
 
 129 
 
 Reactions, secondary, de- 
 fined 56 
 
 secondary example 41 
 Reduction, defined. . . 101, 117 
 
 99 
 
 " again 103 
 
 " a loss... 101,104 
 " at cathode 
 
 5, 57, 102, 117 
 Reduction, conception of . 103 
 
 " example 42 
 
 Relative weights, denned . 114 
 
 S 
 
 Salts 24 
 
 Second class conductors . . 85 
 Secondary reactions, defined 
 
 56, 118 
 
 " " example 41 
 
 Sign of valence 6, 99 
 
 " " " example. 48, 50 
 
 Silver coulometer 66 
 
 " standard equivalent 7 
 
 Speeds of ions 61 
 
 Stability of atoms 82 
 
 Storage battery 45 
 
 Strength of bonds 109 
 
 Structural formulas 24, 96 
 
 Structure of atom 79 
 
 Subscripts, defined 112 
 
 " ignored 38 
 
 Supersaturation 77 
 
 Symbols of elements 12 
 
 Ternary electrolytes 59 
 
 Thermal unit 121 
 
 Thermo-chemical, equivalents 
 109 
 
 Titration coulometer 71 
 
 Tri-valent 95 
 
 " element . 83 
 
 Unit bond 93 
 
 " charge 64 
 
 Univalent element. . 83 
 
 Vacuum discharge 73 
 
 Valence, defined 
 
 5, 85, 93, 94, 116 
 
 " , 91 
 
 " a number 97 
 
 " change of, defined 
 
 4,97 
 
 it ft - 
 
 examples 
 36, 37, 43, 48 
 " Table I 8 
 change of sign 
 
 48, 50, 101 
 
 " electronic 84 
 
 " electrons 79 
 
 " fractional 95 
 
 " negative 37, 99 
 
 " " example 
 
 48,50 
 number of electrons 
 
 85 
 of compound =O 
 
 50, 100, 107 
 " of radical. . . .43, 108 
 
 " rules 107 
 
 " sign of 6, 99 
 
 " unit charges. ... 64 
 
 " vs. valency 97 
 
 " zero 5,95,97,98 
 
 " " example. 49, 98 
 Valences add up to zero 
 
 50, 100, 107 
 numerical values of 
 24,106 
 
 practical 24,106 
 
 of the elements, 
 Table IV.. 24 
 
130 
 
 INDEX OF AUTHORS 
 
 Valency, defined 97 
 
 " 91 
 
 " a property 97 
 
 " vs. valence. .... 97 
 
 Valent, non- 95, 97 
 
 Velocity of cathode particles 74 
 Voltage of decomposition . 110 
 
 Voltameter, defined 66 
 
 Volume coulometer. . 69 
 
 W 
 
 Water coulometer 69 
 
 Watt-hours 110 
 
 " per gram 12 
 
 " per pound 12 
 
 Zero valence 5, 95, 97, 98 
 
 " " example. . .49, 98 
 Zinc in battery 34 
 
 INDEX OF AUTHORS 
 
 Arrhenius 58 
 
 Bates 71 
 
 Blanchard 59 
 
 Boernstein 9 
 
 Bureau of Standards VI, 7, 67 
 
 Clarke 7 
 
 Comstock 87 
 
 Cox 87 
 
 Crookes 73 
 
 Daneel 71 
 
 Falk 105 
 
 Faraday 64, 62 
 
 Friend 87 
 
 Getman 105 
 
 Hamlin 105 
 
 Heimrod 66 
 
 Hering ... .V, 93, 97, 102, 120 
 
 Jones 59 
 
 Kohlrausch . . . . * 70 
 
 Landolt 9 
 
 Le Blanc 66 
 
 Mellor 94 
 
 Mendeleef 83 
 
 Millikan 78 
 
 Nelson 105 
 
 Nicholson 80 
 
 Oettel 68 
 
 Perrin 74, 86 
 
 Ramsay 84, 87 
 
 Richards, J. W... VI, 24, 106 
 Richards, T.W 66 
 
 Smith 94 
 
 Stokes 78 
 
 Talbot 59 
 
 Thomson, J. J 74, 79, 87 
 
 Troland 87 
 
 Washburn 71 
 
 Wilson. . 77 
 
YA 
 
 995706 
 
 Engineering 
 Ltbnry 
 
 THE UNIVERSITY OF CALIFORNIA UBRARY