CONDUCTANCE and VISCOSITY of CONCENTRATED AQUEOUS SALT SOLUTIONS a T 50.50 by M

802 CHEMISTRY: RICE AND KRA US PROC. N. A. S.

CONDUCTANCE AND VISCOSITY OF CONCENTRATED AQUEOUS SALT SOLUTIONS A T 50.50 By M. JOHN RICE, JR.,* t AND CHARLES A. KRAus METCALF RESEARCH LABORATORY, BROWN UNIVERSITY Communicated June 12, 1953. Our knowledge of the electrical conductance and the viscosity of concentrated salt solutions is very limited. Campbell and Kartzmark1 have measured the conductance and the viscosity of solutions of silver nitrate and ammonium nitrate in water at 950 up to saturation. Seward2 has measured the conductance and viscosity of solutions of tetrabutylammonium picrate in butanol at 93° over the complete range from pure solvent to pure fused salt; Strong' has measured the conductance of some quaternary ammonium salts in benzene at 250 up to fairly high concentration but viscosity data are for the most part lacking. Moessen and Kraus4 have measured the conductance of solutions of tetrabutylammonium bromide and tri- methylammonium chloride in bromine at 250 to fairly high concentrations but there are no viscosity data for these solutions. The same is true of potassium iodide in iodine at 140°C. which was measured by Lewis and Wheeler.5 Cesium formate has been reported to be soluble to the extent of one mole of salt to one-half mole of water at 5'.6 However, this datum is in error; the limit of solubility is one mole of salt to approximately two moles of water. However, potassium formate is soluble to the extent of approximately one mole of salt to 1.1 mole of water at 500. The conductance and viscosity of solutions of these two salts have been measured at 50.50 to near saturation. Solutions of the potassium salt were measured to lower concentration in order to approximate the value of A0. In the preparation of cesium formate, cesium chloride was converted to cesium nitrate by repeated treatment with nitric acid. After repeated recrystallizations, the nitrate was converted to carbonate by treatment with oxalic acid in the presence of a small amount of water and subsequent calcination. The carbonate was converted to fonnate by neutralization with formic acid and evaporating to dryness. The salt was recrystallized by dissolving it in 96%0 alcohol and adding ether to precipitate the desired proportion of salt. The final product was dried in vacuo at 1500 for 4-5 hours, m.p. 264°C. (corr.). The nitrate, when tested spectroscopically, showed no traces of metallic elements other than cesium. Potassium formate was prepared by neutralizing potassium carbonate with formic acid and evaporating to dryness. The salt was recrystallized from 96%o alcohol on addition of ether. The product was dried in vacuo at 1500 for 8 to 10 hours. This material was found to contain 1.5% water. Downloaded by guest on September 30, 2021 VOL. 39, 1953 CHEMISTRY: RICE A ND KRA US 803

The water could be completely removed by regrinding the salt and heating in vacuo at 1500 for 10 hours. When necessary, operations were carried out in a dry-box. The solutions were made up in the cells in which their conductance was measured. ThrIee cells of different constants were employed. Two of these were of the Erlenmeyer type with the electrode chamber attached to the outside of the flask. These cells were similar to those described by Daggett, Bair, and Kraus,7 although much smaller. The third cell con- sisted of two cylindrical tubes which were joined at the bottom by a 55-mm. length of smaller tubing of approximately 5 mm. diameter. The cylindrical cells were closed by ground glass caps which carried tubes at the ends of which were sealed platinum electrodes that normally projected into the solution. The cell constant of this cell was 38.430 and was independent of the precise setting of the caps or the volume of solution in the cell. This cell was provided with stopcocks so that the solution could be forced from one arm to the other by air pressure for the purpose of mixing. The other two cells had constants of 0.3081 and 10.669. Cell No. 1 was of approximately 300 cc. capacity and was used for meas- uring the most dilute solutions. A known weight of salt was introduced and weighed quantities of water were added successively. When the cell was full, the greater portion of the solution was withdrawn into a weight pipette and a new series of additions of water was begun. Cell No. 2 had a capacity of approximately 800 cc. and was used for intermediate concentrations. Measurements could be made with a minimum volume of 50 cc. of solution. The desired concentration range could be covered by merely adding known weights of water to a known weight of salt. Cell No. 3 had a capacity of approximately 100 cc. and measurements could be made with a very small volume of solution. The desired concentration range could be covered by merely adding successive weights of water. To determine the densities, known solutions were made up by adding known weights of water to known weights of salt in a large weighing bottle. Samples of these solutions were transferred to a pycnometer which had been calibrated at 50.50. Since the density of the solutions varies slightly from linearity, data are given for densities at a series of concentrations. The density of dry cesium formate was determined by weighing the de- hydrated salt in a pycnometer under hexane. From the weight of hexane and its density and the weight of salt, the density of the salt is readily computed. Assuming the density of hexane to be 0.6550, the density of the salt was found to be 2.99. The density of potassium formate was taken to be 1.91.8 Viscosities were measured with a modified Ostwald viscometer. The viscometer was provided with a ground glass cap and solutions were made up in the viscometer. The instrument was calibrated with water and the Downloaded by guest on September 30, 2021 804 CHEMISTRY: RICE AND KRA US PROC. N. A. S.

time of efflux was determined as a function of volume of water. The viscometer with its contents was weighed on a sensitive balance. Concen- tration could be changed by addition of water and further dilution could be made by withdrawing a known weight of solution and then making further addition of water. Densities of solutions in water at 50.50 are given for cesium formate and potassium formate in tables 1A and 1B, respectively. Molal concentrations appear in column 1, molar concentrations in column 2, and densities in column 3.

TABLE 1 DENSITY OF FORMATE SOLUTIONS AT 50.50C. (A) CESIUM FORMATE - .- (B) POTASSIUM FORMATE MOLAR MOLAR CONCENTRATION, C DENSITY CONCENTRATION, C DENSITY 0.00 0.9878 0.00 0.9878 1.193 1.142 3.967 1.160 2.414 1.303 5.643 1.232 4.892 1.613 9.452 1.392 9.068 2.147

TABLE 2 CONDUCTANCE OF FORMATE SOLUTIONS AT 50.50C. (A) CESIUM FORMATB - (B) POTAS$IUM FORMATE EQUIVALENT EQUIVALBNT MOLAR CONC. COND. MOLAR CONC. COND. 10.13 24.80 6.503 63.03 10.06 24.84 3.492 96.17 9.034 33.18 10.45 30.82 6.913 54.33 8.602 44.24 4.629 81.78 15.52 9.780 0.8104 138.1 13.66 14.65 0.5430 145.8 0.5999 142.2 0.3055 153.5 0.2722 154.2 3.231 98.84 0.1543 161.6 2.437 109.5 2.404 110.4 1.785 118.9 1.325 126.4 1.400 125.6 0.07471 168.7 0.01973 176.6- 0.01038 179.8

Conductance data for the cesium and potassium salts are presented in tables 2A and 2B, respectively. Molar concentrations are given in column 1 and equivalent conductances in column 2. Viscosities for solutions of cesium formate and potassium formate are given in tables 3A and 3B, respectively. Molar concentrations are given in column 1, relative viscosities in column 2, and absolute viscosities in centipoises in column 3. Downloaded by guest on September 30, 2021 VOL. 39, 1953 VCHEMISTR Y: RICE AND KRA US 805

In tables 4A and 4B are presented values of the conductance-viscosity product for the cesium and potassium salts, respectively, at rounded molar concentrations. In column 2 are given values of the ratios of moles of salt per mole of water. Values of equivalent conductance and of viscosity TABLE 3 ViscosITY OF FORMATE SOLUTIONS AT 50.50C. (A) CESIUM FORMATE- -(B) POTASSIUM FORMATS-. MOLAR CONC. *7 X 102 POISES MOLAR CONC. X X 102 POISES 9.605 2.612 13.95 5.173 8.203 1.809 8.224 1.463 6.834 1.338 6.090 1.028 3.989 0.8500 4.199 0.8277 2.808 0.7313 3.125 0.7296 5.819 1.117 15.64 8.223 1.784 0.6533 12.26 , 3.403 0.7496 0.5847 10.38 2.216 1.516 0.6245

TABLE 4 CONDUCTANCE-VISCOSITY PRODUCT OF FORMATES AT 50.5°C. MOLBS H20 PBR II X 102 MOLAR CONC. MOLE SALT CONDUCTANCE POISES A-7-PRODUCT (A) Cesium Formate 0.00 ... 192.9 0.5449 1.051 0.25 ... 157.2 0.560 0.879 1.00 0.01893 134.0 0.610 0.817 2.00 0.04080 115.5 0.670 0.774 4.00 0.09141 88.8 0.840 0.746 7.00 0.1981 52.8 1.37 0.723 9.00 0.3018 32.7 2.22 0.726 10.00 0.3704 25.0 2.95 0.738 (B) Potassium Formate 0.00 ... 187.9 0.5449 1.024 0.50 ... 145.4 0.565 0.822 1.00 0.01889 132.8 0.593 0.788 3.00 0.06223 102.3 0.725 0.742 5.00 0.1150 78.8 0.905 0.713 7.00 0.1802 58.3 1.165 0.683 9.00 0.2634 41.0 1.680 0.689 13.00 0.5176 16.8 4.09 0.687 14.00 0.6146 13.6 5.19 0.706 15.50 ... 9.9 7.89 0.781 appear in columns 3 and 4, respectively, and values of the conductance- viscosity product in column 5. In figure 1 are shown plots of the equivalent conductance of cesium and potassium formates as a function of the square root of molar concentration. At low concentrations (not shown on figure), the conductance of the ce- Downloaded by guest on September 30, 2021 806 CHEMISTRY: RICE AND KRAUS PROC. N. A. S.

sium salt parallels and lies several A-units above that of the potassium salt. This is due to the fact that the conductance of the cesium ion is several A-units higher than that of the potassium ion. According to Noyes and Falk,9 the conductance of the cesium ion at 18°C. is 3.5 A-units greater than that of the potassium ion. These early measurements are not of high pre-

MOLAR CONCENTRATION FIGURE 1

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0 5 10 MOLAR CONCENTRATION FIGURE 2

cision and the precise difference in the conductance of the cesium and potassium ions at 50.50 remains uncertain. However, it is safe to assume that the conductance of the cesium ion is the greater. We have extrapolated the conductance of potassium formate to zero concentration, using the A - %/C plot. We obtained the value 187.9 at 50.50. Downloaded by guest on September 30, 2021 VOL. 39, 1953 CHEMISTRY: RICE AND KRA US 807

Using the data of Harned and Owen,10 for the conductance of the formate ion at 250 and those of Auerbach and Zeglin11 for the conductance of sodium formate at 180, we obtain a value of 76 for the conductance of the formate ion on extrapolating linearly to 50.50. From the equations of Har- ned and Owen we obtain a value of 112.1 for the conductance of the potassium ion at 50.50. Thus, we have the value of 188.1 for the limiting con-

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0 wI ~~~~~Cs02CH z 07 z cl ~~~~~~~K02CH 0 00.6 ' ' ' ' I I O 5 10 15 MOLAR CONCENtRATION FIGURE 3

* e Data of Campbell a Kortzmork 0O.8

07 > < Cs02~~C90CH 50 5- 50.5*~~~~~95CH 5; eAqNO395 0.6

0 za 0 0.5 NH4NO 95°

0 0.1 02 0.3 Q4 05 0.6 0.7 0.8 MOLES SALT PER MOLE WATER FIGURE 4 ductance of potassium formate at 50.50 in good agreement with our extrapolated value. At higher concentrations, the conductance curves of the two salts inter- sect at a concentration of approximately 2.5 molar. At still higher concentrations the curves diverge increasingly. At the highest concentrations measured, the conductance of cesium and Downloaded by guest on September 30, 2021 808 CHEMISTRY: RICE AND KRAUS PROC. N. A. S.

potassium formates are 24.80 and 9.38, respectively. At a concentration of 10 molar, the conductances are 25.0 and 33.7, respectively. While the conductance of electrolytes at low concentrations is governed by the interaction between their ions, in concentrated solutions conductance is mainly dependent on the viscosity of their solutions. In figure 2 are shown values of the absolute viscosity of solutions of the two formates as a function of molar concentration. As may be seen from the figure, viscosity increases markedly with concentration in the case of both salts, being somewhat greater for the cesium salt. For a 10-M solution, the viscosity of the cesium salt is 5.4 times that of the pure solvent. For the potassium salt it is 3.9 times that of the solvent at 10 molar and 14.8 times that of the solvent at 15.5 molar concentration. Up to a concentration of C = 12, the measured viscosities in centipoises may be reproduced reasonably well by the equation: v = 0.545 + 0.0755C - 0.0135C2 + 0.003C3 for cesium formate, and by v = 0.545 + 0.0473C - 0.004C2 + 0.00107C3 for potassium formate. To a first order of approximation, the conductance of a completely dissociated electrolyte at different concentrations is proportional to the re- ciprocal of the viscosity of the solutions. Accordingly, we may compen- sate for the viscosity effect by multiplying the conductance by the viscosity. If the electrolyte is completely dissociated into its ions and the nature of the ions undergoes no change, the product should remain constant. In figure 3 are shown values of the conductance-viscosity product for the two formates as a function of concentration to near saturation. The product for the cesium salt is greater than that of the potassium salt over the entire concentration range. At low concentrations, the product for the cesium salt is greater than that of the potassium salt by an amount that corresponds to the greater conductance of the cesium ion. At lower concentrations, when the viscosity effect is small, the conductance falls off sharply with increasing concentration in accordance with theory. As concentration increases, the two curves diverge as a result of the greater viscosity of the solutions of the cesium salt. At a concentration of 5 molar, the curves flatten out over a considerable concentration range. The product for cesium formate appears constant between 6 and 9 molar; for potassium formate it is constant between 7 and 13 molar. Over these ranges of concentration the number of moles of water per mole of salt decreases from 6 to 3 for the cesium salt and from 5 to 2 for the potassium salt. It is apparent that at a concentration in the neighborhood of 4 to 5 molar, where the solutions contain approximately 10 moles of water per Downloaded by guest on September 30, 2021 VOL. 39, 1953 CHEMISTRY: RICE AND KRA US 809

mole of salt, the character of the conductance process undergoes marked change. At these higher concentrations, the conductance-viscosity product changes but little while the number of water molecules becomes com- parable with the number of ions in solution. The hydration of the ions must be changing in this region. Apparently, the increase in mobility due to decreasing hydration just compensates for the increase in viscosity and the conductance-viscosity product remains constant. It will be noted that at the highest concentrations the curves for both salts have a marked upward trend. Campbell and Kartzmark have measured the conductance and viscosity of concentrated solutions of silver nitrate and ammonium nitrate in water at 95°. Values of the conductance-viscosity product for these salts along with our own for the formates are shown in figure 4, moles of salt per mole of water being plotted as abscissae. At lower concentrations, the product for the two nitrates falls off more sharply than it does for the formates. This is due to the lower values of dielectric constant and viscosity of water at the higher temperature, which results in larger values of the constants a and ft of the Onsager equation. At higher concentrations the curves for the two nitrates differ from each other as they do also from those of the formates. For ammonium nitrate the product decreases continuously up to the highest concentration measured, two moles of water per mole of salt. The product for silver nitrate passes through a pronounced minimum at a concentration which corresponds approximately to 12 moles of water per mole of salt. At concentrations above the minimum, the curve rises and appears to flatten out but its precise form at the higher concentrations cannot be determined because of the scattering of the experimental values. In going from 22 to 9 moles of water per mole of salt, the conductance- viscosity product for silver nitrate decreases 0.8%; in going from 9 to 6 moles of water per mole of salt the viscosity increases 27% while the conductance-viscosity product increases 9%. To the best of our knowledge, silver nitrate is completely dissociated into its ions. As the number of water molecules per mole of salt decreases, the hydration of the ions must decrease. However, over the concentration range from 22 to 9 moles of water per mole of salt, it is difficult to account for the larger effects that are observed on the basis of hydration alone. One cannot but wonder whether the postulates that underlie the theory of dilute electrolyte solutions remain applicable at high concentrations. The product for ammonium nitrate at higher concentrations is much lower than that of the other salts. One is led to suspect that ammonium nitrate is not completely dissociated into its ions at high concentrations. There is a possibility of hydrogen bonding between the ammonium and the nitrate ions. From the density data, the volume change accompanying the process of Downloaded by guest on September 30, 2021 810 CHEMISTRY: RICE AND KRA US PROC. N. A. S.

solution of the two formates at different concentrations has been computed. Values are shown graphically in figure 5. For cesium formate there is a volume contraction of 11.6 cc. at a concentration of 1 molar; it decreases gradually to a value of about 8.5 cc. at 5 molar and remains sensibly constant at higher concentrations. The volume contraction for potassium formate at 1 molar is 8.7 cc.; with increasing concentration the contraction

-4 -

0 z a-0 w80

w -2

0 5 10 15 MOLAR CONCENTRATION, C FIGURE 5 decreases sharply and levels off at a value of approximately 2.3 cc. at a concentration of 5 molar. A 5 molar solution contains approximately 8 moles of water per mole of salt. All properties of these solutions indicate a change in the nature of these solutions in the neighborhood of 10 or 8 moles of water per mole of salt. It is difficult to escape the conclusion that the laws governing concentrated salt solutions differ fundamentally from those of dilute solutions. It is not to be expected that the properties of concentrated solutions may be accounted for by merely modifying somewhat the laws that apply at low concentrations. * The investigation here reported was supported by ONR under Contract N7onr 35809. t This paper is based on a portion of a thesis presented by M. John Rice, Jr., in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Brown University, June, 1953. 1 Campbell, A. N., and Kartzmark, E. M., Can. J. Chem., 30, 128 (1952). 2 Seward, R. P., J. Am. Chem. Soc., 73, 515 (1951). 3 Strong, L. E., Ibid., 72, 186 (1950). 4 Moessen, G. W., and Kraus, C. A., these PROCEEDINGS, 38, 1023 (1952). Downloaded by guest on September 30, 2021 VOL. 39, 1953 GENETICS: DANFORTH AND CENTER 811

6 Lewis, G. N., and Wheeler, P., Proc. Am. Acad., 41, 419 (1906). 8Sidgwick, N. V., and Gentle, J. A. H. R., J. Chem. Soc., 121, 1837 (1922). Daggett, H. M., Jr., Bair, E. J., and Kraus, C. A., J. Am. Chem. Soc., 73, 1709 (1951). 8 Schr6der, H., Ber., 14, 21 (1881). 9 Noyes, A. A., and Falk, K. G., J. Am. Chem. Soc., 34, 455 (1912). 10 Harned, H. S., and Owen, B. B., The Physical Chemistry of Electrolytic Solutions, 2nd ed., The Reinhold Publishing Corp., New York, 1950, p. 172. Auerbach, F., and Zeglin, H., Z. phys. Chem., 103, 178 (1922).

DEVELOPMENT AND GENETICS OF A SEX-INFL UENCED TRAIT IN THE LIVERS OF MICE* BY C. H. DANFORTH AND ELIZABETH CENTER DEPARTMENT OF ANATOMY, STANFORD UNIVERSITY SCHOOL OF MEDICINE Communicated June 8, 1953 It is generally recognized that there are many traits which may be influenced by the sex of the individual in which they occur. If one of the principal genes necessary for its appearance is located in the Y-chromosome a trait is designated as sex-limited, if in the X-chromosome as sex-linked, and if in addition a major autosomal gene is also necessary the trait is commonly referred to as sex-influenced. However clear-cut these categories may appear in their verbal formulation, it is probably true that one could arrange a finely graded series from traits that are sex-limited in the strictest sense to those whose expression has little or no relation to sex. We wish at this time to report a condition in the mouse liver which might serve as one member of such a series, and to call attention to features in its development which explain why, on genetic grounds alone, this particular trait might sometimes appear to be almost completely sex-limited, and at other times not. Morphology of the Trait.-The liver of the mouse, like that of many re- lated rodents, is commonly described' as consisting of four primary divi- sions, a right lateral, a medial, a left lateral and a posterior, each of which, except for the left lateral, is in turn subdivided into two major lobes. In the present connection we are concerned with the right lateral division, whose smaller posterio-lateral, and larger anterio-medial components may conveniently be designated as lobes 1 and 2, respectively. The manifesta- tions in which we are especially interested involve only lobe 1, the dis- tinctive features of which may be mentioned briefly. In the females this lobe has the appearance of a somewhat distorted tri- angular pyramid whose base is penetrated by the inferior vena cava and whose apex is bent backward over the ventro-medial aspect of the right Downloaded by guest on September 30, 2021