LIBRARY OF THE UNIVERSITY OF CALIFORNIA. RECEIVED BY EXCHANGE Class The Weight of a Falling Drop and the Laws of Tate. The Determination of the Molec- ular Weights and Critical Temper- atures of Liquids by the Aid of Drop Weights. BY RESTON STEVENSON, A.B., A.M. DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PURE SCIENCE IN COLUMBIA UNIVERSITY, IN THE CITY OF NEW YORK. NEW YORK CITY. 1908 EASTON, PA. : ESCHENBACH PRINTING Co. 1908. The Weight of a Falling Drop and the Laws of Tate. The Determination of the Molec- ular Weights and Critical Temper- atures of Liquids by the Aid of Drop Weights. BY RESTON STEVENSON, A.B., A.M. DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY OF PURE SCIENCE IN COLUMBIA UNIVERSITY, IN THE CITY OF NEW YORK. NEW YORK CITY. 1908 E ASTON, PA.: ESCHENBACH PRINTING Co. 1908. at >A -^ / CONTENTS. I. Introduction. Object of investigation 5 II. Apparatus and method 9 III. Results H IV. Discussion of results l8 V. Summary 22 183469. ACKNOWLEDGMENT. This piece of work was suggested by Professor J. L. R. Morgan and was carried out under his direction. Mr. Higgins has helped the author in his preparation of this paper for publication. R. S. OF THE UNIVERSITY OF The Weight of a Falling Drop and the Laws of Tate. The Determination of the Molecular Weights and Critical Temperatures of Liquids by the Aid of Drop Weights* Introduction. Object of the Investigation. In 1864, Thomas Tate, 1 as the result of his experiments with water, announced the following laws: I Other things being the same, the weight of a drop of liquid (falling from a tube) is proportional to the diameter of the tube in which it is formed. II. The weight of the drop is in proportion to the weight which would be raised in that tube by capillary action. III. The weight of a drop of liquid, other things being the same, is diminished by an augmentation of temperature. Tate's experiments were all made with thin- walled glass tubing vary- ing in diameter from o. i to 0.7 of an inch, the orifice in each case being ground to a "sharp edge, so that the tube at the part in contact with the liquid might be regarded as indefinitely thin." His weights were cal- culated from the weight of from five to ten drops of liquid, which formed at intervals of 40 seconds, and were collected in a weighed beaker. Tate's law as we know it to-day, is supposed to be a summation of the first two laws of Tate, but it must be said that it attributes to Tate a meaning that he never indicated and probably never intended. The analytical expression of this faulty law is the familiar W = 2Trry, where Wis the weight of the falling drop, r the radius of the tube on which it forms, and y is the surface tension of the liquid. Of course, 1 Phil. Mag., 4th Ser., 27, 176 (1864). All other references to drop weight will be found in the bibliography of that subject at the end of this paper. Tate's second law shows drop weight to be proportional to surface tension, for the weight of a liquid rising in a tube by capillary action is propor- tional to surface tension; and his first law shows drop weight to be pro- portional to the diameter (or radius) of the tube; but he did not even imply that drop weight is equal to the product of the circumference of contact into the surface tension. The real anyltical expression of Tate's first two laws as he actually announced them, in place of the obove, shold be W=KjD, where K^ is a constant, and D is the diameter of the tube; or, when the drops are all formed on the same tube (z. O^JOiOi^l 10 00 g a-S oooooooooo O O O 4*. 4* 4* 4* K> 00 4 Oi Oi Oi Oi Volumeoffallingdrop.ee. vO ^4 vO 4- Oi Oi M On 4* *jOwtotOf*tovoONOi MOMOOMMOO bbobioOMOooo Specific gravity. 4*vo-4Mtost->O>o^i vO 4* O 00 vO ON vO 4>. O Oi OO 00 00 Cn n Oi 00 Ol Weight of falling drop, tugs. WP.D. ON Oi Surface tension, dynes. % 00 Ol *J If O M 8 S ON IMMMWMMNMM M KJ ON Oi ^4 WF.D. 7. Itl t '-'" H- H- O K) M M M M M .' b b M ^i Oi O jo 23 5 S * ^ II 0? ^ vO ON 1! II rr* n O/*^ k\ 1 ^ \J Is} M -S -b X S Oi * o * M o S ep Oi Oi to *^j O *^ Oi Oi ON -^4 4> a) i6 sion, together with the data necessary for the calculations. The surface tensions given, except those for water, are interpolated from the results determined under the same conditions as our drop weights, i. e., against saturated air of Renard and Guye, 1 those for water being interpolated from the results of Ramsay and Shields, 2 against the vapor pressure of the liquid. K p D , K F D , and K c D , in Table I, and K F D in Tables II and III, are the factors by which the surface tension in dynes must be multiplied to give the drop weight, in milligrams, from these tips. K F D is the con- stant already mentioned in the real analytical expression of Tate's laws,, when the same tip is employed. The tips used in Tables I, II, and III, although made from the same tubing, have slightly different diameters exposed, owing to the bevels being cut at slightly different angles. The diameter of the tubing itself was about 6.5 millimeters. Table I shows the reason for determining the weight of only the falling drop with the more delicate form of apparatus. In order that errors in the interpolations of the values of surface ten- sion, as well as possible errors in the surface tensions themselves, might not influence the conclusions as to the accuracy of Tate's laws, in Table III, where the determinations are the most accurate, a check, has been secured without any direct comparison with surface tension, by substi- tuting the drop weights, of the same liquid at two different temperatures, for the surface tensions in the well-known law of Ramsay and Shields, and then comparing the constancy, for the various liquids, of the constant,, ^temp. w ith that of those of Ramsay and Shields, (& R & s ) and Renard and Guye (k R & G ). In other words, for 7- in dynes, in the relation = = 2.12 ergs,* has been substituted W FT> in milligrams, so that if surface tension (as altered by temperature) and falling drop weight are proportional, for any one liquid from the same tip, one should find the expression ft y &temp. just as constant as the other for all so-called "non-associated" liquids. 1 J. chim. phys., 5, 81 (1907). 2 Z. physik. Chem., 12, 431 (1893). 8 M is here the molecular weight as a liquid, d the density, and t the temperature. All the densities are interpolated from results found in the literature * as were also those of both Ramsay and Shields, and Renard and Guye, so that uniformity in the compared results is thus secured. All chemicals, with the exception of guaiacol (Table I), which was im- pure, were specially purified for the purpose. The drop volumes throughout are each the average of several deter- minations, the extreme variation in tube 3 (Table III) being 0.2-0.4 per cent. TABLE IV. Drop weights for various tip diameters, t = 27. WF.D. WF.D. 6. 190 8.764 D. Substance. DI = 4.68 mm. D 2 = 6.22 D 3 =7.i2. D a . D 2 . Benzene 26.10 34-6o 39. 15 5-577 5-563 Chlorbenzene 29 . 70 40 . 40 45 . 10 6 . 348 6 . 495 Quinoline 41. 15 55.00 62.40 8.792 8.843 In Table IV are given the drop weights issuing from beveled tips of various diameters. These results are not as accurate as some of the others, for tube 2 was used as the burette, and the error in measuring the lower end of the bevel is necessarily large. Under K' are the values of tfre con- stant of Tate's first law, i. e., weight of falling drop divided by the diame- ter of the tip. TABLE V. Substance. Alcohol. . . >-v- 7 Rounded tip. Temp. A in Fig. 3. 58.4 0.907 21.5 0.934 / lor ups 01 various lorms. Approx- Bevel at 30. Sharpened edge, s^face Temp. B i 60. 1 22.5 65.0 22.1 n Fig. 3. .070 .090 .119 .127 Temp. C in Fig. 3. 21. 1 1.123 tensions. 19 22 21 29 Benzene. . . . .... . . Chlorbenzene 64.0 0.932 67-9 .109 27 22.5 0.965 24.0 .129 22.0 I.I45 32 Quinoline. . . 64.0 1.024 72.0 .164 .... ... 38 Water 21.0 23.1 I.04I I.OSO 22.6 25-5 .189 .220 22.6 I.I57 21.0 I.I55 43 72 Average 0.983+0.025 1 Approximately of same diameter. i.i35o.oi7 . I45o.oo8 18 Table V gives the results obtained by use of tips of various forms, but of approximately the same diameter (see Fig. 3). Tip A, here, is rounded at the end, B has a bevel at an angle of about 30, not sufficient to have ABC Fig. 3- the effect of a sharp edge, and C, without bevel, has a very sharp edge. All these were measured in tube 2, and consequently the determinations are not as accurate as those in Table III. TABLE VI. CRITICAL TEMPERATURES. 1 Prom Fr m 7 (^) 2/3 = k(r-d). Substance. M -\d/ R. & G. R. & S. Observed. Benzene 286.6 285.8-289.6 288 280.6-296.4 Chlorbenzene 354-1 357.2-358.4 359-7 360.0-362.2 Pyridine 352.0 344.7-346.9 342 Aniline 439.4 448.1-449.1 404.9 425.7 Quinoline 492 . 3 495 . 6-496 . 9 466 . i <52O And, finally, in Table VI, are the critical temperatures of the liquids in Table III, as calculated by the substitution of the drop weight, W p D , and k icmp for the surface tension 7-, and k in the Ramsay and Shields rela- tion, y(^)" /3 =(r-6), where r is the difference between the critical temperature and that of ob- servation, and M, d and k have the same meaning as before. Discussion of Results. It will be seen, even from Table I, where the experimental error in drop weight is comparatively large, that Contrary to the conclusion of Guye 1 Here, in all cases, the temperature coefficient (k or ktemp.) used is the one found for the specific liquid, and not the average values. 2 Calculated extremes from surface tensions. 8 Given by Ramsay and Shields, Loc. cit. 19 and Perrot, the relationship between drop weight, from a properly con- 1 structed tip, and surface tension in saturated air, 4 is very much more than a first approximation, even when the liquids examined include that giving the highest, and that giving almost the lowest, surface tension known, i. e., water at 70.6 and ether at 16.8 dynes per centimeter. The results in Table II make this conclusion even more striking, for they show that much of the variation in I is due to experimental error. And, finally, Table III, where the accuracy in the determination of drop volume and drop weight was the greatest possible at the time, shows the variation in the constant relationship, for some of the same liquids ex- amined in I and II, to be very small indeed. Here, with five liquids, 5 varying in surface tension from 25.88 to 52.62 dynes, each being studied at two temperatures, the mean value of K F D for all cases, from a certain tip, is 1.226 ;+ 0.0026; the mean error of a single result being +0.0083. Although in these results the error is small, the discrepancy is still too great granting the accuracy of the drop weights and surface tensions to conclude that the proportionality is rigidly exact; even though the agree- ment is about as good as that observed in results for surface tensions by different methods, and little worse than that shown in the results by any one method, by different observers. The error in drop weight cannot in any case exceed 0.4 per cent., taking all things into consideration, and is generally much less, consequently the discrepancy is only to be explained either by errors in the interpolated surface tensions, or by actual failure of the law of proportionality to hold closer than this (due possibly to a very slight and variable, but unnoticeable, rise of the liquids on the walls of the tip). When it is remembered, however, that the interpolations of the values for surface tension were made from smoothed curves, which could not always be made to pass through all the few points available, it becomes very apparent that in some cases errors in the interpolated surface tensions even as high as one per cent., are quite possible. If this be true, the law of the proportionality between falling drop weight (from a proper tip) and surface tension becomes rigid. To prove this directly and conclusively has been impossible, for it could be done only by aid of a more delicate 4 According to Renard and Guye, surface tensions in saturated air and those un- der the vapor pressure of the liquid do not differ by more than 0.5 per cent. 6 Unfortunately, ether could not be used in either tube 2 or tube 3, owing to in- terference of a bulb; and the volume of tube 3 was too small to permit water to be used with the beveled tip. 2O apparatus, with measurements of drop weights at the exact temperatures at which the surface tensions themselves have been determined. 1 Below, however, it is shown that the interpolated values of surface tension for any one liquid are burdened with error, so that analogy would force the conclusion that they, also, are at the root of the error when different liquids are considered. The conclusion follows then, from Tables I, II, and III, and from the be- havior of tip C in Table V, that Tate's second law the weight of a falling drop (from a proper tip) is proportional to the surface tension (against saturated air) of the liquid is true. Because surface tensions calculated from drop weights agree, even with those possibly faultily interpolated from results by capillary rise, as well as those determined by other meth- ods agree with these, when directly determined. Consideration of the columns & temp , R & G ., and k K & s , in Table III, shows that the constants, though calculated from results at only two tempera- tures, are as constant as those of Renard and Guye, which are in each case the mean of determinations made at several pairs of temperatures, and are very much more constant than those of Ramsay and Shields, 2 from results at two temperatures. It will also be observed that the variation of & temp . from its mean value is always (when worth considering) in the same direction as that of Renard and Guye's, for the same liquid. This certainly proves conclusively that, with any one liquid, from any one tip, drop weight is proportional to the surface tension, as it is altered by changes in temperature, for, by substitution of drop weight for surface tension in the Ramsay and Shields expression, leaving out any direct comparison with the interpolated values of surface tensions, a result is obtained which is as constant as that found by the use of directly determined not interpolated surface tensions. And this is true when the interpolated values of surface tension at the two temperatures lead to a discrepancy in the two values of K F D , as calculated for that liquid. Although this proof is not direct, as far as concerns different liquids, it leaves very little possibility of the slight dis- crepancy in K F D being due to anything but the errors in the interpolated sur- face tensions as concluded above. We would conclude from the constancy of & temp ., in Table III, then: 1 This is now being done in this laboratory. 2 Although Ramsay and Shields' s values were calculated from surface tensions ob- served under different conditions, their constants are still to be compared with the others as to constancy. 21 That Tale's third law the weight of a falling drop decreases with in- creased temperature is true. And, further, that the change in drop weight for a change in temperature can be calculated accurately for non- associated liquids, by the substitution of the drop weight at one tempera- ture for the surface tension, and & temp for k in the Ramsay and Shields relation -*, and solving for the other drop weight. Or, knowing the drop weights, & temp ., and the densities, it is possible to find the molecular weight of the liquid, with an accuracy equal to that attained when surface tensions are employed directly in the above rela- tion. Since the molecular temperature coefficient, & temp> , is found to be constant, it is possible, by extrapolation, to find the temperature at which the drop weight would become zero; i. e., the critical temperature of the liquid, for at that point the drop would disappear, there being then no distinction be- tween the gas and the liquid. It is only necessary, for this calcula- tion, to substitute W T D for 7- and & temp . for k, in the other form of the Ram- say and Shields relation, i. e., and solve for the critical temperature (r plus the temperature at which 7- (or W F D ) is determined). (See Table VI.) It must be remembered here, however, that in all cases in which this method has been applied, it has been done so at a disadvantage, for only two points were had through which to draw the curve. Further than that I have worked at low temperatures (never above 80), and consequently must extrapolate from these two points through a much greater distance than either Renard and Guye, or Ramsay and Shields, from their larger number. The first objection holds for all the liquids, though least for benzene, but the second hardly affects benzene, for 73.2 is not far from its boiling-point. With all high-boiling liquids, both objections hold, and both increase with the boiling point (and critical temperature). From the equal constancy of k temp and k, however, it is evident that just as accurate critical temperatures can be calculated from drop weights as from surface tensions, against saturated air, provided in both cases the determinations, 22 from which the molecular temperature coefficients are found, are made at as many temperatures, and carried to as high a temperature. Table IV, it is thought, shows that from such tips, between these diam- eters, there is a direct proportionality between drop weight and diameter of the tip (Tale's first law). At least there is no decided trend in the pro- portional factor, for it varies just as one might expect it to from the known, and fairly large, experimental error. It must be remembered that tips larger than the diameter of the maximum drop would always deliver one constant maximum drop weight; while, when the tip becomes small, there is probably a point beyond which the drop will not decrease appreciably in weight for a considerable change in diameter, for it would then be difficult to prevent in any way the rise of liquid upon walls of the tip. Table V shows that when rounded, a tip behaves differently from the one in Table III ; the liquid rises to various heights on the outer walls, and the diameter of the basis for the drop varies with the nature of the liquid. This is also true, though to a lesser degree, with the tube that is insuffi- ciently beveled. In neither case is K FI) even approximately constant. Tip C, on the other hand, compares very favorably with the other beveled one, used with Tube 2 (Table II). Whatever theory may be advanced, then, as to the tip, it will be seen that the point to be considered is the effect of the tip (Tate's "sharp edge") in delimiting the portion upon which the drop can hang, especially by preventing the rise of liquid upon the walls, for that would be variable with different liquids, and lead to variable weights. Undoubtedly it is only the failure to follow Tate's directions in this respect that has caused the determinations of drop weights, since his time, to negative his conclusions. Summary. The results of this investigation may be summarized as follows: 1. An apparatus is described by which it is possible to make a very accu- rate estimation of the volume of a single drop of liquid falling from a tube, and consequently of its weight. 2. With this apparatus was used a capillary tip, beveled at an angle of 45, which, contrary to those used by other investigators, had the same effect as the one originally used by Tate, i. e., it delimits the area of the tip wetted, by preventing the rise of liquid upon the walls, and thus forces all liquids to drop from one and the same area. 23 3- It is shown that whenever this effect is obtained, either by use of a properly beveled tube, or one ground to a sharp edge, the drop weight has a different meaning than it has when the drop is formed on either a rounded tip, or on one insufficiently beveled. 4. The falling drop from a capillary tip, and not the pendant drop, is proportional in weight to that of the falling drop from a thin-walled tube with a sharp edge. 5. From such tips as were used, it is concluded that Tate's second law the weight of a drop, other things being the same, is proportional to the surface tension (against saturated air) of the liquid is true. 6. It is shown that from such a tip, Tate's third law the weight of a drop is decreased by an increase in temperature is true. 7. Falling drop weights for the same liquid at two temperatures, from such a tip, can be substituted for the surface tensions in the relation of Ramsay and Shields, and molecular weights in the liquid state calculated with an accuracy equal to that possible by aid of surface tensions, under the same, saturated air, conditions. And, by aid of this formula, know- ing the molecular weight of a non-associated liquid, the falling drop weight at one temperature, and the densities, it is possible to calculate the weight of the drop falling from the same tip at another temperature. 8. Critical temperatures can be calculated by aid of Ramsay and Shields' s (M\ 2 f ) 3 = k(r 6), by substituting a drop weight for surface tension, and the molecular temperature coefficient of drop weight for k, with the same accuracy attained by the use of surface tensions (against saturated air), provided the drop weights (from which the coefficient is found) are determined at as many temperatures, and at as high a temperature as the surface tensions. 9. For beveled tips, when the diameters lie between 4.68 and 7.12 mm., Tate's first law the drop weight of any one liquid is proportional, under like conditions, to the diameter of the dropping tube is true. BIBLIOGRAPHY OF DROP WEIGHT ALPHABETICALLY ARRANGED. Autonow, G. N. Bolle, J. Duclaux. Dupre". Eschbaum, F. Guglielmo, G. Guthrie. Guye and Perrot. Hagen. Hannay, J. B. Kohlrausch, F. Lebaigue. Leduc and Larcdote. Lohnstein, F. Mathieu. Ollivier. Rayleigh. Rosset. Tate, T. Traube. Volkmann, P. Worthington. J. chim. phys., 5, 372 (1907). Geneva Dissertation, 1902. Ann. chim. phys., 4th ser., 21, 386 (1870). Ibid., 9, 345 (1866). Ber. pharm. Ges., Heft 4, 1900. Accad. Lincei Atti., 12, 462 (1904); 15, 287 (1906). Proc. Roy. Soc., 13, 444 (1864). Arch, scien. phys. et naturelle, 4th ser., n, 225 (1901); 4t ser., 15, 312 (1903). Berl. Akad., 78, 1845. Proc. Roy. Soc. Edin., 437, 1905. Ann. phys., 20, 798 (1906); 22, 191 (1907). J. pharm. chim., 7, 87 (1868). J. phys., i, 364 and 716 (1902). C. r., 134, 589; 135, 95 and 732 (1902). Ann. phys., 20, 237 and 606; 21, 1030 (1906); 22, 737 (1907). J. phys. [2], 3, 203 (1884). Ann. chim. phys., 8th ser., 10, 229 (1907). Phil.Mag., 5th ser., 20, 321 (1899). Bull. soc. chim., 23, 245 (1900). Phil. Mag., 27, 176 (1864). J. pr. Chem. [2], 34, 292 and 515 (1886). Ber., 19, 874 (1886). Ann. physik. (2), n, 206. Proc. Roy. Soc., 32, 362 (1881). Phil. Mag., 5th ser., 18, 461 (1884); 19, 46 (1885); 20, $ (1885). BIOGRAPHY. Reston Stevenson was born May 5, 1882, in Wilmington, N. C. He received the degree of A.B. at the University of North Carolina, June, 1902 ; A.M. at the same institution, June, 1903. During the years 1 903-^4 and 1 904-' 05 he was assistant instructor in chemistry at The Cornell University where he pursued, simultaneously, graduate work in chemistry and physics. In May, 1905, he accepted a position as research chemist with the Eastern Dynamite Company. He left this company to become chemist at the Hudson River Works of the General Chemical Company. In September, 1906, he left the General Chemical Company to become Tutor in Chemistry at the College of the City of New York, and still occupies this position. He has at the same time completed his graduate work for the degree of Ph.D. at Columbia University. 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