LIBRARY OF THE UNIVERSITY OF CALIFORNIA. RECEIVED BY EXCHANGE Class 37"? The Temperature Coefficient of the Weight of a Falling Drop as a Means of Estimating the Molecular Weight and the Critical Temperature of a Liquid* DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIRE- MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PURE SCIENCE IN COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK. BY ERIC HIGGINS NEW YORK CITY 1908 EASTON, PA. : ESCHRNBACH PRINTING COMPANY. I90S. The Temperature Coefficient of the Weight of a Falling Drop as a Means of Estimating the Molecular Weight and the Critical Temperature of a Liquid* DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIRE- MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PURE SCIENCE IN COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK. BY ERIC HIGGINS NEW YORK CITY 1908 EASTON, PA. : ESCHBNBACH PRINTING COMPANY. 1908. ^^ OF THE UNIVERSITY OF CONTENTS. Page. Introduction and Object of Investigation 5 Apparatus and Method 6 Results 10 Discussion of Results 16 Summary 18 PART II. On Some New Formulae Relating Various Constants of Non-asso- ciated Liquids 21 183470 ACKNOWLEDGMENT This work was carried out under the direction of Professor J. Livingston Rutgers Morgan at his suggestion. The author begs to tender his sincere thanks for the assistance, advice and encouragement accorded to him during the course of the work by Professor Morgan. E. H. ' r HE UNIVERSITY I The Temperature Coefficient of the Weight of a Falling Drop as a Means of Estimating the Molecular Weight and the Critical Tem- perature of a Liquid. OBJECT OF THE INVESTIGATION. In a recent paper, 1 it was shown that the weight of a drop of liquid falling from a properly constructed tip is proportional for any one diameter of tip, to the surface tension of the liquid; and, further, that when falling drop weights are substituted for surface tensions as measured by capillary rise in the formula of Eotvos, as modified and presented in two forms by Ramsay and Shields, the molecular weights and critical temperatures of liquids can be calculated with an accuracy equal to that attained by the use of the surface tensions found from the capillary rise. The object of the present work was to measure the magni- tude of falling drop weights with the utmost possible accuracy and thus to test the conclusions of Morgan and Stevenson; to determine if irregularities in the constant value (^ temp ) were real or due to experimental error and to conclusively establish the relative value of this method of determination of the molecular weight and critical temperature as compared with other methods for arriving at these values. The results of my work, it may be said here, have not only confirmed the conclusions of Morgan and Stevenson in every respect, as far as concerns any one tip, but in addition have shown 1 Morgan and Stevenson, J. A. C. S., 30* 360-376, 1908. that for the determination of relative surface tensions, the drop method is more accurate than the one in common use, which depends upon capillary rise. Further, they show that the molecular temperature coefficient of drop weight K( tem p) is really a constant, although Ramsay and Shields, for the same liquids, found the corresponding molecular temperature coefficient of surface tension (fe), from capillary rise, to vary so much that for the calculation of critical temperatures it was necessary to first find the exact value of k for the liquid in question. This is not necessary when working with drop weights, the one constant value, holding for all the non-associated liquids studied, and so presumably for all the others. 2 This apparently also makes the drop- weight method at its best, more accurate as a means of determining the molecular weight than any other method, with the exception of that for permanent gases, which is based upon the density. APPARATUS AND METHOD. The apparatus for the measurement of the volume of a single falling drop (Figure i) in construction was essentially the same as that employed by Morgan and Stevenson, differ- ing only in having a more accurate capillary burette (i mm. corresponding to 0.000,046 cc.) and in having the tip joined directly to it, without the interposition of a wider tube. My burette was also of greater length (2.5 meters) thus allowing drops of the liquids having the highest drop volumes to be measured without the use of the bulbs, which were found to be a danger when using the more viscous liquids, owing to drainage difficulties. The smaller diameter of the burette enabled me to obtain more accurate readings, the uniformity of the tube removed difficulties as to drainage, and the absence of a constricted "zero mark" permitted a more deliberate and accurate reading. To obviate the possible loss of a reading due to the meniscus falling in a bend of the burette tube or at the place where the joining 2 See second part. : --_ --, - ... ..._ 1 - - ." ,-."'---'. : ?N ff~ ^ j j 'L || | -. d - _, - ~ i . . ;| - 1- :E FIG. i. THE UNlVPPCf-rx, To HOUM M*IH ilOV FIG. 2. of the two lengths of capillary tubing composing it had distorted the bore, four "zero marks'* at successive dis- tances of one centimeter from one another were scratched upon the burette tubing just above the tip and the exact relative volumes of the intervals between them determined. In all other respects the apparatus was exactly the same as that employed by Morgan and Stevenson and was operated in the same way. The dimensions of the apparatus, 69 X 18 centimeters, introduced difficulties in maintaining a constant and uni- form temperature. The electrically heated thermostat finally adopted for the purpose is shown in Figure 2, and the electrical connections diagrammatically in Figure 3. The heating coil and thermo-regulator placed in the outer vessel (a 60 X 30 centimeter glass anatomical jar) maintained the inner cylinder (another jar, 60 X 20 centimeters) in a bath, the temperature of which varied rapidly within narrow limits. The variation of temperature in the inner vessel was naturally much smaller than this, and it was found easily possible to retain it constant at any temperature, from 24 to 76 within 0.02 for any desired length of time. I be- lieve that this "jacket" system yields the most satisfactory results where the conditions limit the disposition of the heating arrangements, and large instruments are to be dealt with. The vibration of mechanical stirrers being fatal to the accurate determination of drop volumes, the water in both the inner and outer cylinders was thoroughly agitated by a current of air passing through block-tin pipes. The trouble which might be caused by the breaking down of the syphon constant level, owing to the liberation of dissolved air from the cold feed water, was obviated by the air trap shown in the figure. The heating current being heavy (10 to 20 amperes at no volts) was found to be best broken from a surface of mercury beneath water continually supplied from the over- flow of the constant level. The current breaker was operated by twelve "gravity" cells thrown in through a small relay 8 operated through the toluol thermo-regulator by two of the same cells. By thus breaking a very weak current in the regulator no trouble was experienced from the contamina- tion of its mercury surface. The apparatus in this form ran continuously at various temperatures and without attention or cleaning for six months and gave perfectly satisfactory results, the only trouble lying in the impossibility of obtaining glass vessels of this size which were sufficiently well annealed to support the higher temperatures for more than six or eight weeks, as is evidenced by the fact that I was forced to replace these three times during the course of the work. The capillary burette was calibrated with mercury at 20, successive quantities being blown out and weighed, the operation being repeated four times. The summated volumes calculated from these weights differed from that calculated from the weight of the total content (0.1230 cubic centimeter) by only 0.000,003 cubic centimeter. This calibration was further checked by measuring the length of various threads of mercury in all parts of the tube, thus measuring each centimeter of the burette. These results were plotted on a curve from which volumes could be read to 0.000,005 cubic centimeter. In the calibration in air the position of the meniscus was read through an uncorrected lens, taking advantage of its lack of rectilinearity to avoid parallax. In the estimations in the thermostat the same object was attained when taking an observation of the "zero marks" by the use of narrow slits in a mask attached to the outer cylinder centering on similar slits on the opposite side, from which the necessary illumination was obtained from a small electric lamp. The measuring tube itself, when in the thermostat, acted like an uncorrected lens in making read- ings of the values on the graduated scale. This calibration being performed at 20, it was necessary to determine the effect of temperature in dilating the tube and expanding the scale. The volume of a thread of mercury, as given by the curve, was observed at every 10, between DIAGRAM OF ELECTRIC CONNECTIONS FIG. 3. 5 and 85, the mercury being subsequently weighed and its true volume calculated at each of the temperatures. This work showed the effect of dilation to be very small, amounting to but 0.000,000,14 cubic centimeter per centi- meter of length per degree. All volumes read were corrected in accord with this. The possibility of a residual dilation effect on the capillary tube after heating to high tempera- tures was guarded against by working alternately on an ascending and descending thermometer. A series of estima- tions at one temperature occupying at least a day, the passage from low to high, and again to low temperature extended over periods of from six to ten days, thus reducing to a minimum the effect of residual dilation. As a further check on the accuracy of our original calibra- tion and of our assumption of the absence of residual dila- tion, the total content of the burette was measured three times during the course of the work and no appreciable difference observed. As mentioned by Morgan and Stevenson, all difficulties occasioned by condensation on, or evaporation from, the drop when forming is prevented by the production of a "fog" upon the walls of the dropping cup. This condition I find to be most readily induced by dusting fine graphite powder upon the walls of the cup above the liquid. By then heating the liquid to a temperature of 100 (or as near that as possible without causing it to boil) for five minutes and plunging the cup in cold water, vapor is deposited upon the various particles, producing a satisfactory and durable fog. The instrument is then placed in the thermostat and a drop allowed to hang from the tip for an hour. At the end of this time the conditions are such that a drop neither gains nor loses in volume. Before each measurement I assured myself, by drawing the drop back into the burette several times, that such a condition prevailed, and that the drop neither gained nor lost in volume. When passing from one temperature to another the fog can be maintained by allowing a drop to hang from the tip during the change. 10 Since a thermometer could not very well be placed in the dropping cup itself a similar cup containing a fog was placed beside the burette, a certified thermometer taking the place of the tip and no estimation was made until the thermometer within the "blank" had agreed with a similar thermometer within the thermostat for a half hour. Without this some- what elaborate procedure it was impossible to get agreeing results, drop weight being very sensitive to changes in tem- perature. To prove that drainage difficulties were absent, a short thread of liquid was drawn through the tube at various speeds, from one centimeter to one millimeter per second, and the length of the thread measured after each passage, but so long as the walls of the capillary were wetted no alteration in volume could be detected with any of the six liquids used. Morgan and Stevenson measured the volume of a single drop, for it seemed from the work of other investigators that the successive formation of several drops might introduce complications. My work has shown that, in the presence of a perfect fog and constant temperature, a succession of drops (i. e., where the clinging drop remaining after each fall is not drawn back in the burette, but is again increased to the falling point, and simply one final reading made) gives a mean value for one drop that is exactly concordant with that obtained from the measurement of a single drop. Naturally, here, the greatest speed of formation of the drop is somewhat over a minute, owing to the small diameter of the burette. RESUI/TS. My results, in detail, for the same liquids used by Morgan and Stevenson, and also for carbon tetrachloride, are given in Tables I to VI. All my densities were carefully redeter- mined with a 25 cubic centimeters Ostwald pykno meter, and agreed in the main with those collected from various sources by R6nard and Guye. With quinoline, only, was the variation worth considering, and even that did not change II appreciably the values of the surface tension as given by Re*nard and Guye. The chemicals used were the purest obtainable. The aniline, pyridine, benzene and chlor- benzene were Kahlbaum's "Special K," the carbon tetra- chloride, Baker's "Analyzed" and the quinoline Merck's "Pure synthetical;" and all showed the correct and constant boiling-points. In the first column of Tables I-VI is given the temperature ; the second contains the actually determined drop volumes, all from the same beveled tip, approximately 6 millimeters in diameter ; the third the average drop volume and its mean error, assuming no constant error to exist; the fourth the density; the fifth the drop weight, the product of the average drop volume and the density; the sixth the value . (?) -.Gf)', ,;":- /TV AT* 1 2 AI f w l and w 2 being drop weights in milligrams at the tempera- tures ^ and t 2 , and d v and d 2 the densities, while M is the molecular weight. And, finally, the seventh column in three of the tables contains the value /M /My /M \dj -y 2 \d 2 ) as calculated from Re"nard and Guye's surface tensions (fi and 7* 2 ) from capillary rise in saturated air. These are given where four or more temperatures are employed to show the relative variation of the values of K temp and of R&iard and Guye's k, as found for the six liquids, together with the critical temperatures as observed and as calculated from K te mp. an< * k, by aid of the formulas /My w\d) =K, m/ >.(r 6) and /My \d) =kO 6) , 12 where T is the difference between the critical temperature and that of observation. Here I have used for K temp in all cases the actually obtained results most separated as to temperature, and not those from a smoothed curve, as is done for the k values, and has been done by all investigators using the capillary rise method. In Figure 4 the comparative accuracy of drop weights and the surface tensions by capillary rise for the liquids which were studied at three or more temperatures, is also shown graphically, the surface tensions being the very carefully determined ones of Re*nard and Guye against saturated air. It must be noted here that the graphs are only to be com- pared in relative straightness and NOT AS TO SLOPE, for I have as yet made no attempt to express drop weights accu- rately in terms of surface tension. It will be noted that my two intermediate results for pyridine lie somewhat off the curve, one on either side, al- though the low and the high values lead to the satisfactory result for K Ump shown in Table VII. These errors are prob- ably due to slight temperature errors, for pyridine was the first liquid investigated, and our first method for the agita- tion of the water in the inner cylinder was found later to be insufficient. This difficulty was avoided at both the low and the high temperatures, these determinations having been made subsequently. TABLE I. BENZENE. Drop volume, Temp. cc. Mean volume, cc. Density. Drop weight, mmg. II-4 30.2 0.039680 0.039692 0.039674 0.039686 0.037252 0.037285 0.037274 0.037269 0.039683 0.888 35.239 0.000.003 or 0.01% & G. 2.521 1.717 0.03727 0.868 32.350 0.000.007 or 0.02% 2.583 2 230 CO 6 2 .SP 1 .2 I 1 -55 CO ft) Temperatures. FIG. 4. Quinolene Aniline Pyridene Chlorbenzene. Benzene... Drop weight. .. I .. 2 . 3 .. 4 5 Capillary rise. I. Continued. Drop volume, Mean volume, Temp. cc. cc. 68.5 0.034201 O.O342IO 0.034191 0.034202 0.032076 0.032090 00.032081 0.032074 Drop weight, Density. mmg. 0.034201 0.844 26.866 0.000.004 or 0.01% 0.03208 0.827 26.530 o . ooo . 004 or 0.01% . R & G- 2.606 2.380 Drop volume, Temp. cc. (-0.036656 8.2)0.036700 10.036684 39-2 0.033738 0.033729 0-033746 0-033746 50. 8fo. 032647 0.032588 63. 9fo. 031350 0.031300 0.031391 .0.031359 '0.030540 72.2 0.030523 0.030540 0.030529 TABLE II. CHLORBENZENE. Drop Mean volume, weight, cc. Density. mmg. Ktemp. >&R & G- 0.03668 I.I2OO 41.082 0.000.013 or 0.04% 2.568 2.332 0-03374 1.0856 36.628 0.000.007 oro.02% 2.590 2.118 0.03261 1.0730 34-99 0.000.019 or 0.06% 2.545 2.045 0.03135 0.000.018 1.0590 33.200 or 0.06% 2-577 1.938 0.030533 1.0498 32.054 o . ooo . 004 or 0.01% Temp. Drop volume. 24. 2 fO.OI96OO 0.019564 .0.019577 54. oro. 017516 0.017505 JO.OI75IO IO.OI75II III. CARBON TETRACHLORIDE. Drop Mean volume. Density, weight. Kump. 0.01958 1.5823 39.976 0.000.007 or 0.04% 2.567 0.017510 1.5240 26.685 0.000.003 or 0.02% TABLE IV. PYRIDBNE. Dro Drop Temp. Drop volume. Mean volume. Density, weight. Ktemp. /&R&G. 10.5 39-2 58.8 74-2 0.046238 0.046194 0.646228 0.042665 0.042630 0.042585 0.042570 0.042550 0.040312 0.040343 0.040348 0.040238 0.040234 0.038180 0.038153 0.038128 0.038154 0.04622 0.99I 45- 8 4 0.000.014 or 0.036% 2.580 1.57 0.04260 0.962 40.98 0.000.02 or 0.05% 2.440 2.54 Temp. Drop volume. 10.048720 0.048688 0.048662 0.040295 0.943 38.00 0.000.025 or o . 06% 0.038154 0.927 35.37 0.000.01 or 0.025% TABLE V. ANILINE. Drop Mean volume. Density, weight. Ktemp. 0.04869 I.OI38 49.362 2.5685 0.000.017 or 0.03% 2.770 2.31 TABLE V '.Continued. Temp. Drop volume. 0.046154 51-7 0.046159 0.046170 0.046161 67.1 f 0.044436 J0.044432 [0.044428 Mean volume. Density. Drop weight. k R& C. 0.046161 0.9944 45-903 o . ooo . 004 or 0.01% 2.5700 0.044432 0.9810 43.588 0.000.002 or 0.01% VI. Drop weight. Temp. Drop volume. Mean volume Density. 30. M 0.047456 0.047504 55. of 0.045338 { 0.045347 [ 0.045405 65.0 f 0.044474 0.044478 ;o. 044518 0.04748 1.0852 51.525 0.000.024 or 0.05% 0.045363 0.000.021 1.0658 48.344 or 0.05% 2.580 2.570 0.044490 0.000.014 0.03% 1.0576 47.053 Showing K temp k and critical temperatures. Drop-weight results are from the directly observed values at the extreme temperatures, those from capillary rise being from the smoothed curves. TABLE VII. Liquid. Benzene ............. Chlorbenzene ......... Carbon tetrachloride . Pyridine ............. Aniline ............... 2 . 569 Quinoline ............. 2.575 Crit. Crit. Observed kump. temp. k R & G. tcm P* crit. temp. 2.569 288.4 2.12 287.7 ca 288 2-569 359-5 2.10 357.7 ca 360 2.567 285.2 2.19 278.0 ca 284 2-567 347-0 2.07 346-2 ca 344 2.569 425-8 2.01 448.6 ca 426 2.575 520.4 2.21 496.2 <520 2.5694+ 2.n6o.O965 0.013 or 4.6% or 0.05% Mean error of a single result 0.0033 or 0.13% i6 DISCUSSION OF RESUI/TS. A glance at Tables I-VI will show that only in one case is my error in the estimation of the volume of a single falling drop, assuming the existence of no constant error, equal to 0.07 per cent., all others being very much less. Drop weights, calculated from these volumes and the carefully redetermined densities, can then of course, be burdened with no greater error. From the curves in Figure 4, where drop weights in milligrams and surface tensions from capillary rise in dynes are plotted against temperatures, it will be seen that the results of drop-weights are more concordant among them- selves, than are the surface tension values, which allows of but one conclusion the drop-weight method is more accurate than that based on capillary rise, even in the hands of such skilful investigators as R6nard and Guye. If there is then any doubt as to the drop-weight method giving the TRUE relative values of surface tension, rather than the method of capillary rise, one need simply turn to Table VII, in which K Um p for the six non-associated liquids used, is shown to be 2.5694 0-05 per cent., the mean error of a single result being 0.13 per cent., while the variation in the corresponding average k value by capillary rise is 4.6 per cent, from Rnard and Guye's results, and much larger according to those of Ramsay and Shields'. When it is remembered that the Ramsay and Shields formula from which K temp and k are derived, which may be written in the form /M\l /MX* \\dj x 2 \d 2 J = constant 1 2~ A l where x is a term proportional to surface tension, was origi- nally designed for capillary rise results, it is quite evident that drop weight is not only also proportional to TRUE surface tension, but gives better and more consistent values for it than capillary rise. The same reasoning holds also with regard to the critical temperatures, and the Ramsay and Shields formula from which they are calculated except 17 that here the comparison cannot be made quite so satisfac- torily, owing to necessary experimental uncertainty in the determination of critical temperatures. Even here, how- ever, the drop- weight method shows to advantage, for the critical temperatures calculated by it for aniline and quinoline agree well with the experimental values, where those by aid of capillary rise are quite different. Drop weights, then, satisfy the equations that were designed especially for capil- lary rise results better than these themselves do. This form of proof of the advantage in accuracy of the drop method over that depending upon capillary rise is, unfortunately, the only one possible at present, for even a smoothed curve drawn from the capillary rise results is still too much burdened with error to allow any very accurate, direct comparison of the two methods. Owing to the unsatisfactory nature of the curve for the surface tensions from capillary rise, I have omitted any attempt to calculate the single values of the Morgan and Stevenson term & F D , for the different liquids and tempera- tures, but have calculated for the sake of comparison, for I have made no other use of it, one single value of it in the following way : Since K Ump and k are related to each other as the drop weights are to the surface tensions, the ro.tioK fem p k must give the factor by which drop weights in milligrams must be divided to give TRUE surface tensions in dynes per centimeter. This factor is 1.2144 since K temp is equal to 2.5694 and practically invariable, and the mean supposedly correct value of k R &G is 2.116. With the exception of aniline and quinoline drop weights interpokted (or extrapolated) from my curve agree with those found with the same tip by Morgan and Stevenson within a few tenths of one per cent. With aniline and quinoline the difference is slightly larger, but all are well within the limits of error mentioned in their paper. These slight errors, unavoidable at that time with their densities, however, are sufficient to account for the slightly larger value of K Um p and its variation which they observed, i. e., 18 the value 2.598 1.56 per cent, as compared to 2.5694 -- 0.05 per cent., and also for the difference in K FD which in average they found to be 1.226 as against my value of 1.2144. And the same is true for their critical temperatures. Certainly the most striking and important fact brought out by my work is the practically absolute constancy for all the liquids at all the temperatures of the molecular tem- perature coefficient of drop weight, K tfmp for it apparently makes the drop-weight method for large temperature in- tervals, where slight errors in temperatures have little effect, the most accurate known method for the determination of molecular weight, with the exception of that for permanent gases which is based upon the density. The truth of this can be shown by assuming as correct either the maximum, minimum or the average value of K temp in Table VII, and calculating from it by aid of the specific drop weights and densities the molecular weight of any of the liquids given , the maximum error for any of the six liquids being less than 0.05 per cent, when M for the liquid giving the smallest value of K temp is calculated from the largest value found for K Um p and is very much less when the M for any liquid is calculated from the average K,^ for it can be readily shown that the percentage variation in M is equal to 3/2 the per- centage variation in the K temp used for the calculation. Another advantage of the constant value of K Ump is that it is not necessary for the calculation of the critical tem- perature from drop weight, as Ramsay and Shields found it in using the capillary rise values to first find the exact value of the coefficient for the specific liquid in question, for I can simply use the value of K temp as found for any other non- associated liquid. SUMMARY. i. An apparatus is described by which, using the same tip employed by Morgan and Stevenson, the error (assuming the existence of no constant error) in the estimation of the volume (and consequently of the weight) of a single falling 19 drop is reduced to a few hundredths of one per cent. 2. The elimination of their known error and a redeter- mination of the densities confirm all the conclusions of Morgan and Stevenson, as regards any one beveled tip, the more accurate work simply accentuating them and proving the drop-weight method to be even better than they claimed. 3. Drop weights calculated from the experimentally ob- served volumes by the aid of redetermined densities for benzene, chlorbenzene, carbon tetrachloride, pyridene, aniline and quinolene, at the same or nearly the same tem- peratures at which the surface tensions from capillary rise have been measured, show that drop weights are proportional to the temperature, and that the singly determined values lie upon a straight line, whereas the values from capillary rise vary considerably and irregularly, on the one side or the other of such a line. In other words, drop weight leads more accurately to the TRUE surface tensions than does capillary rise. 4. The molecular temperature coefficient of drop weight calculated by aid of the Ramsay and Shields formula /M\l /M\l \dj x 2 \dj 1 -- * = constant, where x is a term proportional to surface tension, which was designed especially for results from capillary rise, is found for the drop weight to be practically invariable for all the six non-associated liquids, while the use of capillary rise leads to a variation of 6.4 per cent, from the average according to the results of R6nard and Guye, and to a still larger one, according to those of Ramsay and Shields. The consequence of this is that the drop-weight method when used for such a temperature interval as I have employed is the most accurate method for the determination of molecular weight known, with the exception of that for permanent gases as based upon the density. And critical temperatures can be more 2O readily and accurately calculated from drop weight than from capillary rise, as is shown for aniline and quinolene by he agreement with experiment when calculated drop weight and the wide divergence when calculated from capillary rise. Second Part. On Some New Formulae Relating the Various Constants for Non- Associated Liquids. It was shown by W. G. Kistiakowsky 1 that the relation holds for a large number of substances where M = molecular weight in liquid state, A = capillary constant (rise in a capillary tube of unit radius), and T = absolute boiling- point, the value of K k varying from 1.04 to 1.17. It has been shown that the drop weight of non-associated bodies is proportional to the surface tension, hence by the equations y = - grhd and w = vd. It is obvious that by substituting b for "A" in the Kistiakowsky rektion I should obtain a constant similar to that obtained from the capillary constant provided the volume be that delivered from unit tip. Since I have insufficient data to enable me to calculate the mag- nitude of v under those conditions, I must employ the drop volume obtained in the preceding work. This will not affect the constancy of the relation but will simply lead to a new empirical constant. *M ~T = Solving for the extrapolated values for drop volume the following results are obtained: . f. Elektrochem. (8) 375, 1902 and (12), 513, 615, 1906. 22 TABLE I. Substance. K. Benzene 67 . 4 Pyridene 67 . 3 Chlorbenzene 68 . 4 Aniline 67 . 6 Quinolene 68.8 Showing the statement to be as generally justifiable for drop volume as for capillary rise despite the extrapolation in the first case since drop volumes have not been estimated up to the boiling-point. In any subsequent use of drop- volume determination as a method for obtaining molecular weights, it would be advantageous if such a formula as the above could be shown to be general at temperatures other than the boiling-point, since the molecular weight of a non- associated body could then be calculated from a single estimation at a temperature which would introduce no extra experimental difficulties. The most probable direction for the formula to take is that of "corresponding states" shown to be at least approximately true by the following results: TABLE II. Mean specific tempera- ture coefficient of Mean molecular Substance. drop volume. co-efficient. Benzene 13315 0.0104 Pyridene 12669 o.oioo Chlorbenzene 09605 0.0108 Quinolene 08717 0.0103 Aniline m75 0.0104 Carbon tetrachloride . . . 06946 o .0107 An agreement closer than that of k (Ramsay and Shields) by the capillary rise method and derived direct from ex- perimental results not from a smoothed curve. It thus seems probable that the formula Mz/__ /p -K-(BT T) 23 will be found to hold at all corresponding temperatures where M = molecular weight, v = drop volume, T = ab- solute temperature of observation. K (BP _ T) = constant for the particular state, i. e., for the difference between the temperature of estimation and the boiling-point. Solving the equation for the formerly obtained experimental values we obtain by extrapolation the numbers shown in Table III. The agreement is very good, considering that the values are nearly all from extrapolated drop volumes, some, as with aniline and quinoline over more than 100 C. The devia- tions from the average are apparently no function of the molecular weight or boiling-point, and are consequently probably due largely to errors of extrapolation. The gen- eralization is, however, likely only to be accurate at tem- peratures not too far removed from the boiling-point as evidenced by the increase of percentage variation in the values for K as we retreat from the boiling-point and by the fact that if it held rigidly very far above the boiling-point it would force the conclusion that the critical temperature of all non-associated bodies lay at the same distance from their boiling-point, a conclusion contrary to fact. Further work may make it possible to correct the formula much as Trouton's law has been modified by Nernst, but for the present approximate accuracy only is attainable. It now remains to show what may be derived from the formula in its present state. i. Use of the formula to derive molecular weight from a single drop-volume determination. The values used for K are those obtained by averaging the numbers shown in Table III, eliminating the values for quinolene and aniline at temperatures less than 80 from the boiling-point so that all experimental values for K are ex- trapolated over the same range. The drop volumes used are those directly obtained, no attempt being made at mutual correction, so that the values are such as would be obtained from isolated determinations. M W w > < S IO .* O M to ON oo M oo co O ON Tj- ON 10 O O ON O O 00 O vS iO (N ON CO ON ON 00 ON ON *O co O o M ON vo O * ON rj- rhoo oo oo oo oo o CO -^- O 00 ON to CO M O ex 10 oo oo oo oo oo co o 00 ON CS - co t^ >O O M (\J M M CO VO l^ O . co cs vo t^ I O vo vo VO VO 00 ON vo ON M ON oo ON VO cs oo ON S OD VO ' N 0> . w a* ; a a S8l.i^-S 25 TABLE IV. Calculated molecular weight Boiling- Molecular from experiments over Substance. point. weight. range of 10 to 60 C. Chlorbenzene 132 112.4 m.8 112.2 Pyridene 114 .5 78.0 79. o 80.0 Aniline 183.5 93.0 100.0 101.0 Benzene . ... 80.4 79.0 79.0 80.0 This gives from estimations burdened with ordinary ex- perimental error as close agreement as necessary for practical work in the laboratory, even assuming the average values of K used to be accurate, which is scarcely probable. The formula has thus sufficient accuracy in its present form for use in the organic laboratory. Mz; T If ~J^T = K(BP T) is generally true in the neighborhood of the boiling-point, it follows that and w = ; hence, if the molecular weight of a body be known the value of the drop volume can be calculated by use of the various values of K and by using the corresponding value for density we can write the formula of Ramsay and Shields: K (B P-T)T M and thus calculate the critical temperature as shown in Table V. TABLE V. /M\* d \d) = g S 3 -1* - E 41 d ^ I " 52A ?S sj 1 j_ a I be :l? &15 c3 1 (3 1 laS ** S *^, S^ri , thus becoming unity and T the boiling-point of the sub 27 stance, T c being the critical temperature, solved by equation 3- if being thus obtained, substitution of any other value for T in Nernst's equation leads to the evaluation of p (the vapor pressure) at any temperature. With TT (critical pressure) and T c thus obtained the values of "a" and "6" in Van der Waals' gas equation are de- ter minable a - 64273 s * ' = -*-- 8 273 7T and still again knowing the value of -* and p we may obtain the latent heat of vaporization from Nernst's 1 , 2 modification of Trouton's law. jt T^ nP j% 7T Summing-up, therefore, I find that for a number of un- associated liquids: (a) From a knowledge of the boiling-point of the liquid and its molecular weight and a density we can by use of drop-volume constants determine with very fair approxima- tion: 1. The surface tension (in terms of drop weight). 2. The critical temperature and pressure, and hence, 3. The vapor pressure at any temperature. 4. The latent heat of evaporation. 1 Nachrichten Kgl. Ges. Wiss. Gottingen, 1906. 3 J. A. C. S., "Bingham," June, 1906. 8 Van der Waals' "Die continuitat des Gasformigen und Flussigen Zustandes," pp. 166-167. "1st der Radius der Attraction bei alien Korperm gleich gross, so muss Capillaritatsconstante fur die verschiedenen Korper dem kritischen Druck proportional sein." 28 5. The value of "a" and "6" in the Van der Waals' equa- tion for the particular body. (6) From a drop-weight determination, by the same con- stants and a knowledge of the boiling-point we can calculate the molecular weight of a body and hence all the values under (a). As to how far the equations in an unmodified form are absolutely general, insufficient data has yet been accumulated to show, nor have the values of K been denned with sufficient accuracy. Further work must be done upon this subject and on formulae and relations derivable from it, the present being more in the nature of a note than any attempt at a full treatment. With approximate accuracy the values for K are : K(B.P.) = 660 K(B.P. 20) = 766 K(B.P. 40) =880 K( B .p._ 10) = 713 K( B .p.- 3 o) = 824 K(Temp.) =2.569 LABORATORY OF PHYSICAL CHEMISTRY, COLUMBIA UNIVERSITY, April, 1908. BIOGRAPHY. Brie Berkeley Higgins was born August 12, 1885, in Sun- derland, Durham, England. He graduated from the Tech- nical Institute, Manchester, in 1903, and Victoria University, Manchester, in 1906. Since that time he has been in the employ of Messrs. Crosfield, Son & Company, of Warrington, England, from whom he has obtained leave of absence to complete his graduate work for the Ph.D. degree at Columbia University. JUH If- 6 Due end of WINlfR Quarter u.p 9 ni 87 subject to reca* after- REC'DLD FEB2371-1PM57 LD21 -100.9,'47(A57028l6)6