ON THE VISCOSITY OF CERTAIN SALT SOLUTIONS. By B. E. Moore. HE subject of 'Viscosity was first taken up by Poiseuille , 1 -L who used a method depending upon the transpiration of the liquid through capillary tubes. Coulomb,* in studying the same subject, observed the damping of a magnetic needle or bar when vibrating in the liquid investigated. - This method was also exten- sively used by O. E. Meyer , 2 Grotian , 3 and others. Still a third method has been developed by Helmholtz, who placed the solution to be studied in a hollow sphere, and observed the behavior of the sphere when oscillated. These methods have led to very different results. Konig 4 modified the method of Coulomb and used in the place of the swinging rod, a sphere, the equation of motion of which Kirchhoff had solved, and for which the theory can be completely developed. For calculation Konig made use of the expression by Kirchhoff as extended and completed by Boltzman, and reached the conclusion that the values obtained for viscosity by Coulomb’s method were in complete agreement with the results obtained by allowing the liquid to flow through a capillary tube. Though the agreement 1 Memoirs des Savants Etrangers, T. IX. Pogg. Ann., Vol. LVIII., p. 434. 2 Pogg. Ann., Vol. CXIII., pp. 55, 193, 383. 3 Pogg. Ann., Vol. CLVII., p. 130. 4 Wied. Ann., Vol. XXXII., p. 193. 321 3 22 B. E. MOORE. [Vol. III. of results by the different methods is of great interest and importance, yet observers have generally preferred the original method due to Poiseuille, and that because of its simplicity. The method requires also a considerably smaller amount of the solution, and admits of a much easier and more accurate tempera- ture regulation. Among the earlier investigations on the subject of viscosity may be mentioned those of Graham, 1 whose results suggest the presence of hydrates in solution. He states further that “slow transpiration and low volatility go together.” Later investi- gations by Rellstab 2 dealt with several organic liquids, while numerous experiments were made by Hiibner 3 on the salts of the chloride family. Sprung 4 investigated a great many cases of varying concentration and temperature, the latter ranging from o° to 6o° C. Hagenbach 5 developed the mathematical formula for transpira- tion. His expression for viscosity (rj) reduces, when correction for the velocity of flow is omitted, to the form known as Poi- seuille’s formula: v = — 1 ^ lst ■ Herein r denotes the radius of the 8 Iv capillary ; h , the height of pressure column ; j, specific gravity, and therefore the product of h and ^ the pressure ; v represents the volume that transpires in time, t\ and l is used to designate the length of the capillary tube. Pribam and Handl 6 have made extensive observations on the viscosity of organic solution and stochiometrical relations of the same. The careful work of Gartenmeister 7 in this field should not be omitted. Grotian 8 was the first to make extended com- parisons of viscosity and conductivity of salt solutions. Slotte’s 9 investigations cover a number of chromates and he shows that the temperature variation in viscosity, 77, can be expressed by a for- mula, 7} = c( 1 + bt) n , where c, b , and n are constants of the liquid. 1 Royal Society Proceedings, XI., p. 381. i860. 2 Inaugural Dissertation, Bonn, 1868. 5 Pogg. Ann., Vol. CIX., p. 385. 3 Pogg. Ann. Vol. CL., p. 248. 6 Wien Ber., Vols. 78, 80. 4 Pogg. Ann., Vol. CLIX., p. 1. 7 Zeitschrift die Ph. Chem., Vol. VI., p. 524. 8 Pogg. Ann., Vol. CLVII, p. 130; Vol. CLX. , p. 238. Wied. Ann., Vol. VIII., p. 530. 9 Wied. Ann., Vol. XIV., p. 13. No. 5.] VISCOSITY OF SALT SOLUTIONS. 323 Since the announcement of the dissociation theory by Arrhenius, the subject of viscosity of solutions has had a much deeper interest, and experiments have been carried on, both trying to establish some stochiometrical relation, and to establish a relation between viscosity and conductivity. With this idea in view, Arrhenius has made many investigations. In his first experiments 1 he shows that the viscosity is a function of x and y } or H (x, y), where x and y express either percentage of substance in solution, or gram- equivalent per liter. We may say rj = H(x, y)=A x B y , where A and B are constants of the solution. For a single salt in solution this reduces to rj = A x . Wagner 2 and Reyher 3 validified this law for a great many solutions. In Gartenmeister’s 4 experiments the Arrhe- nius exponential formula is not so well satisfied. Reyher found a characteristic relation between the friction or viscosity of free acids and those of the sodium salts, according as a strong or weak acid was present. This variation he made to depend upon the unequal dissociation of the strong and weak acids. The dissociation theory has given great confidence to the belief in a relation of viscosity to conductivity. However, G. Wiedemann , 5 previous to this theory, noticed that the friction which the ions undergo varies in the same way as inner friction ; i.e. viscosity. The mobility of the ions must then be a function of their fluidity. Arrhenius showed that conductivity did not depend upon fluidity alone. This investigator made a strong point when he showed that the introduction of a non-conducting substance into an elec- trolyte affected both its conductivity and its viscosity in the same way . 6 Other experimenters, by a direct comparison of conductiv- ities and viscosities, have come to the conclusion that while the conductivities of a series of salts increased, the viscosities in gen- eral decreased. However, the increasing and decreasing series stand in no definite ratio to each other. The following experiments have followed much in the same line. 1 Zeitschrift die Ph. Chem., Vol. I., p. 285. 2 Zeitschrift die Ph. Chem., Vol. V., p. 31. 3 Zeitschrift die Ph. Chem., Vol. II., p. 744. % 4 Zeitschrift die Ph. Chem., Vol. VI., p. 524. 5 Pogg. Ann., Vol. XCIX., p. 177. 6 Zeitschrift die Ph. Chem., Vol. IX., p. 487. 3H • # B. E. MOORE. [Vol. III. The viscosities of a series of salts have been determined, and, in so far as was possible, the conductivities of the same compared with their viscosities. The method employed was the one due to Poiseuille, the apparatus being similar to that used by Arrhenius. A glass vessel A (Fig. i), of about 24 c.cm. capacity, is connected with two tubes, a and b, above and below respectively. Each tube has a diameter of about 4 mm. A stopcock closes a about 4 cm. from A. b was joined to a capillary tube d , some 40 cm. long. The lower end of the capillary dips into the solution to be studied, contained in a glass vessel, B, of about 200 c.cm. capacity. B is kept water- tight by means of a rubber cork e> and is encased in a brass support h. Exactly 50 c.cm. of the solu- tion was always brought into the vessel B, and the extremity c of the capillary brought into the plane of the upper edge of the brass casing h. This was done to secure a constant average height of pressure in all cases. But this was later proven to be an unneces- sary precaution, as a change in the length of the capil- lary, amounting to 18 cm., only made a difference of 2.5 seconds in the transpiration of water at i8°C. The liquid is brought into the vessel A to some point a ' by exhausting the air through a rubber tube Lg — qJ ' v f. The time of flow was taken between two marks Fig j on tubes a and b. As the mean height of the pressure column is constant, it is evident that the pressure of the different liquids subjected to transpiration varies directly as their specific gravities. So that to obtain the transpiration at constant pressure, it was only necessary to multiply the observed time of flow by the specific gravity of the solution. The time of flow of water at i8°C. was taken as standard. The ratio of the •corrected time of flow of a solution to that of water gives the relative viscosity in terms of water as unity. Should the absolute viscosity be desired, it is only necessary to multiply this result by the absolute value of water. Relative values only have been calculated, as the object was to make a comparison of solutions. The temperature was regulated by a water-bath, and two ther- No, 5.] VISCOSITY OF SALT SOLUTIONS. 325 mometers enabled one to note the temperature to tenths of a degree. Hagenbach’s correction for velocity of transpiration was sufficiently small to neglect in all cases. The specific gravities of the solutions were determined by means of a calibrated Mohr’s balance, which enabled one to take readings to the fourth decimal place. It was part of the original intention to make the solutions from -Weighed portions of the salts and of fixed molecular (eg. double normal, normal, half normal, etc.) contents, but the discovery of a mistake in the weight of a crucible made it necessary to interpret in many cases the per cent of salt in solution from tables of percentages and specific gravities. Solutions of K 2 C0 3 , KOH, NaOH, and K 2 S0 4 were made from Kohlrausch’s tables . 1 Solutions of Na 2 C0 3 , KHC0 3 , NaHC0 3 , KHS0 4 Na 2 HP0 4 , NaH 2 P0 4 , K 2 C 2 0 4 and NaHC 4 H 4 O e were made fr.om carefully weighed quantities of the silts. Solutions of K 3 P0 4 , K 2 HP0 4 , KH 2 P0 4 were kindly loaned by Herr Forch. All other solutions were made from Landolt and Bernstein’s Tabellen ( 2 te Atiflage). The specific gravities of solu- tions of Na 2 C0 3 check well with Kohlrausch’s tables, but not so well with those of Landolt and Bernstein. The specific gravities of Na 2 HP0 4 differ also slightly from the latter tables and in solu- tions of K 2 C 2 0 4 the difference is quite large. However, specific gravities of K 2 C 2 0 4 interpolated from Landolt and Bernstein’s Tabellen give a viscosity curve of doubtful character. The time of flow was noted over considerable range of tempera- ture from which the time transpiration at 18 0 was graphically inter- polated. By repeated observation the error in time is reduced to about 0.3 seconds. In the following table of observations and results, m denotes the gram-molecular contents ; j, the specific gravity ; T, the time ; and 77, the calculated viscosities. In the rows containing neither T nor j , the values of m and 77 have been graphically interpolated. 1 Kohlrausch : Leitfaden der practical Physik, 7 te Auflage. 3 26 B. E. MOORE. [VOL. III. Table I. Na 2 C 0 3 NaHCOg m T V m T •>7 0 00 0.9987 197.0 1.000 0.00 0.9987 194.5 1.000 0.25 1.0250 220.6 1.120 0.25 1.0139 205.5 1.057 0.5 1.0517 251.0 1.274 0.5 1.0286 218.0 1.121 1.0 1.0980 328.5 1.667 1.0 1.0575 245.0 1.260 2.0 1.1880 616.2 3.128 k 2 co 3 KHCO s 0.00 0.9987 197.0 1.000 0.00 0.9987 194.5 1.000 0.25 — — 1.059 0.25 1.0146 200.5 1.031 0.273 1.0340 210.0 1.066 0.495 1.0298 206.5 1.062 0.4788 1.0577 223.0 1.132 0.5 — — 1.065 0.5 — — 1.138 1.0 1.0581 218.0 1.121 0.9456 1.1100 258.0 1.310 1.98 1.1149 250.0 1.285 1.0 — — 1.341 2.0 — — 1.290 1.974 1.2183 381.0 1.934 2.0 — — 1.950 Table II. NaHS 0 4 NaOH m T V m 1 T V 0.00 0.9987 194.5 1.0000 0.00 0.9987 194.5 1.0000 0.25 1.0186 206.0 1.059 0.25 1.0099 206.0 1.059 0.5 1.0386 214.0 1.100 0.5 1.0212 215.5 1.108 1.0 1.0753 245.0 1.260 1.0 1.0425 240.0 1.234 2.0 1.1475 315.5 1.622 2.0 1.0843 299.0 1.537 4.0 1.2810 559 0 2.874 4.0 1.1551 552.0 2.837 k , so 4 8.0 1.2786 1470.0 7.557 0.00 0.9987 194.5 1.000 KOH 0.1195 1.0165 198.1 1.019 0.00 0.9987 194.5 1.0000 0.125 — — — 0.25 — — 1.025 0.243 1.0328 204.5 1.051 0 456 1.0212 203.0 1.044 0.25 — — 1.052 0.5 — — ■ 1.051 0.49 1 .0650 214.0 1.100 0.92 1.0433 213.5 1.098 0.50 — — 1.106 1.00 — — 1.110 KHSO d 1.82 1.0864 235.5 1.211 2.0 1.237 0.00 0.9987 194.5 1.0000 4.0 1.1793 307.0 1.578 0.5 1.0439 209.5 1.075 6.8 1.2900 452.0 2.324 1.0 1.0866 223.5 1.149 2.0 1.1712 263.0 1.352 No. 5.] VISCOSITY OF SALT SOLUTIONS. 3 2 7 Table III. NaoHPOj m $ T V m T V 0.00 0.9987 194.5 1.000 0.00 0.9987 194.5 1.000 0.125 1.0190 211.3 1.086 0.125 — — 1.098 0.25 1.0366 231.4 1.189 0.14 1.0222 214.9 1.105 0.5 1.0741 277.5 1.427 0.25 — — 1.220 0.276 1.0440 242.3 1.246 0.50 1.504 NaH 2 P0 4 0.54 1.0860 367.2 1.579 0.00 0.9987 194.5 1.000 0.25 1.0184 209.3 1.076 ^3 ru 4 0.5005 1.0391 230.0 1.182 1.001 1.0776 274.0 1.409 0.00 0.9987 194.5 1.000 2.002 1.1677 450.0 2.313 0.125 1.0227 208.5 1.070 0.25 1.0471 219.0 1.126 KH,PO, 0.5 1.0933 252.5 1.298 1.0 1.1805 342.2 1.759 0.00 0.9987 194.5 1.000 0.25 1.0220 205.5 1.057 rw 2 nru 4 0.5 1.0442 223.0 1.146 1.0 1.0885 254.0 1.306 0.00 0.9987 194.5 1.000 0.125 1.0167 202.0 1.039 T t nn 0.25 1.0343 213.0 1.095 0.5 1.0700 234.0 1.206 1.0 1 ; 1383 300.0 1.542 0.00 0.9987 194.5 1.000 2.0 1.2633 449.0 2.309 0.25 1.0120 207.0 1.064 0.5 1.0251 222.3 1.143 1.0 1.0508 255.0 1.311 2.0 1.1022 338.3 1.739 Na 3 P0 4 328 B. E. MOORE . [VOL. III. Table IV. N & 2C4H4O6 NaKC 4 H 4 O e m $ T V m T V 0.00 0.9987 194.5 1.000 0.00 0.9987 194.5 1.000 0.141 1.0185 209.0 1.075 0.20 1.0273 212.5 1.092 0.25 f — 1.148 0.25 — — 1.112 0.281 1.0368 226.0 1.162 0.40 1 . 05(7 231.0 1.188 0.5 — — 1.335 0.50 — — 1.252 0.562 1.0730 269.0 1.383 0.789 1.1087 287.0 1.476 1.0 — — 1.823 1.0 — — 1.679 1.121 1.1427 395.0 2.031 1.656 1.2112 484.0 2.488 H 2 C 4 H 4 O e k 2 c 4 h 4 o 6 0.00 0.9987 194.5 1.000 0.00 0.9987 194.5 1.000 0.233 1.013 207.5 1.067 0.1815 1.0267 205.5 1.057 0.25 — — — 0.25 — — 1.080 0.467 1 .0269 221.5 1.139 0.363 1 . 0525 . 220.0 1.131 0.5 — — 1.160 0.5 — — 1.195 0.833 1.0542 256.0 1.316 0.7345 1.1036 255.0 1.342 1.0 — — 1.412 1.0 — — 1.489 1.478 — 330.0 1.696 1.48 1.2072 363.0 1.866 1.666 1.1092 365.0 1.853 1.5 — — ( 1 . 883 ) c 4 h g o 4 k 2 c 2 o 4 0.00 0.9987 194.5 1.000 0.00 0.9987 194.5 1.000 0.242 1.0076 204.2 1.050 0.25 1.0283 204.0 1.049 0.25 — — 1.052 0.5 1.0571 214.5 1.103 0.483 1.0166 215.0 1.105 1.0 1.1121 239.5 1.232 0.5 — — ( 1 . 110 ) 1.5 1.1663 270.2 1.389 H 2 C 2 0 4 NaHC 4 H 4 0 6 0.00 0.9987 194.5 1.000 0.00 0.9987 194.5 1.000 0.25 — — 1.045 0.147 1.0121 205.5 1.056 0.326 1.0116 206.0 1.059 0.25 — — 1.094 0.5 — — 1.072 0.294 1.0256 217.0 1.116 0.665 1.0300 217.5 1.118 0.441 1.0386 228.5 1.175 0.848 1.0370 224.5 1.154 0.5 — — ( 1 . 198 ) 1.0 — — ( 1 . 199 ) No. 5 .] VISCOSITY OF SALT SOLUTIONS. 329 Curves. The curves (Figs. 2 , 3 , 4 , and 5 ) correspond to Tables I., II., III., and IV. of data respectively. The curve for H 2 S0 4 (Fig. 3 ) is drawn from data by Grotian and is given in order to show 0.25 0.50 0.75 1. m. 1.25 1.50 1.75 2.m. Fig. 2. the effect of displacing an atom of hydrogen in sulphuric acid. Curves for K 2 S0 4 and KH 2 P0 4 are not shown, as they nearly coincide with 2 KOH and H 3 P0 4 respectively. Discussion of Results. The viscosity of sodium salts is invariably greater than that of the potassium salts, and both are greater than that of the corre- sponding acids. The effect of the hypothetical displacement of the first atom of hydrogen by a given base is generally not so marked as the second displacement by the same base. NaHC 4 H 4 0 6 is an exception. The effect of the second atom of Na and K in the phosphoric acid group (see Fig. 4 ) is very marked. Whether 330 B. E. MOORE. [VOL. III. the difference is due to the position of the hydrogen atom in the molecule is a question, perhaps, easier to raise than to answer 1.6 1.5 1.4 1.3 1.2 1.1 V satisfactorily. Coincident with the entrance of the second atom of Na or K is the change from marked acid to basic character, which also suggests that the first change in H 3 P0 4 (= H — P0 2 — OH — OH) took place in the hydroxide radical, the second in the acid radical, and the third again in the hydroxide radical. The curve for KH 2 P0 4 lies too near H 3 P0 4 to be credited exten- sively. More confidence is to be placed in the results for H 3 P0 4 than KH 2 P0 4 , as Slotte’s observa- tions for H 3 P0 4 fall practically upon the curve here given for that acid. Again the neutral phos- phate Na 3 P0 4 breaks up very easily in the presence of H 2 0 into the ordinary phosphate Na 2 HP0 4 and NaOH, which would make one accept the viscosity curve Na 3 P0 4 with some hesitation. So that on the whole it would be rather difficult to draw conclusions 0.25 0.50 0.75 .1. m. Fig. 4. 0.25 0.50 0.75 1. m. 1.25 1.50 1.75 2.;m. Fig. 3. I No. 5.] VISCOSITY OF SALT SOLUTIONS. 33* concerning changes in the radicals from the viscosities. So much difficulty does not present itself with the organic compounds. The addition of (CH 2 ) 2 to C 2 H 2 0 4 (=COOH — COOH) (see Fig. 5 , curves), giving COOH -CH 2 — CH 2 - COOH, increases the vis- Fig. 5. cosity over three times as much as the substitution of potassium for hydrogen in (COOH) 2 . The farther substitution of two hydroxyl radicals for two atoms of H in (CH 2 ) 2 gives also a marked increase, and also greater than % the effect of potassium substi- 332 B. E. MOORE. [Vol. III. tuted in H 2 C 2 0 4 . Again, a comparison of curves for H 2 C 2 0 4 and K 2 C 2 0 4 with the curves for C 4 H 6 0 4 and K 2 C 4 H 4 O e shows a marked difference in the effects of potassium on the two salts. In the first pair of solutions potassium entered the carboxyl,, giving COOK — COOK, while in the second group the element potassium has worked upon the hydroxide, yielding COOH — CHOK-CHOK-COOH. A rrhenins Exponential Formula. When Arrhenius announced the exponential formula, r\ — A x r he only tested it to 1.5 gram-molecule solutions. Wagner, who- validified the law for so many solutions, did not go above the normal solution. So that it was thought well to see if such a formula would hold for more concentrated solutions. To test the validity of the law for very dilute solutions, where the law is most serviceable, it would be necessary to limit oneself to very narrow range of and small changes in temperature. It would be imperative to use a bulb A (Fig. 1) of smaller volume and a capillary d (Fig. 1) of very small bore. The latter invariably clogs and prevents accurate results. Even such precautions would, at the best, only give very small differences, and failure to observe these precautions could not account for the variations from the logarithmic law observed in these experiments. The logarithmic curve, which would represent the viscosities of the more dilute solutions of NaOH, e.g. would, if extended to 4 and 8 molecule solutions, give values 36 per cent and 75 per cent too small respectively. No other solutions show so great a divergence. Yet in the double normal solutions the agreement is rarely better than 3 per cent to 5 per cent. Conductivities and Viscosities. The values for A in the following table have been taken direct from the tables of observations on y, except in the phosphoric acid group, where A is reckoned from the equation y = A x and x — m = J. The conductivities K are those of the normal solu- tions except when otherwise noted. Only those salts are given No. 5.] VISCOSITY OF SALT SOLUTIONS . 333 for which the conductivities could be learned. They are divided in four groups corresponding to Tables I., II., III., and IV. of Viscosities respectively. Table V. Substances. - A 10 9 • K iNa 2 C0 3 1.274 42.7 |NaHC0 3 1.121 37.9 |K 2 C0 3 ...... 1.138 66.2 1KHC0 3 ...... 1.065 61.3 NaOH 1.234 149.0 KOH 1.11 171.8 fNa 2 S0 4 — 47.5 2 NaHS0 4 1.10 — f K 2 S0 4 1.106 67.2 \ khso 4 1.075 173.6 iNa 3 P0 4 1.305 97. 5 1 iNa 2 HP0 4 1.260 79.6 j- 3 X 2 normal solution. \ NaH 2 P0 4 1.105 69.8) |H 3 P0 4 1.08 20.0 |C 4 H 6 0 6 1.160 46.04 1 \ c 4 h 6 o 4 1.110 16.03 V Yg normal. fC 2 H 2 0 4 1.070 26.7 J |K 2 C 2 0 4 1.100 68.8 That, while the viscosities in general decrease, the conductivities of a series of salts increase, as noted in the early part of this article, cannot be concluded at all from these salts. This action is notice- able, however, in passing from the sodium salt to the potassium in the first and second group, but when one passes either from sodium carbonate or from potassium carbonate to the acid salts, viscosities and conductivities increase and decrease together. The sulphates behave in the same manner. In the third or phosphate group, in passing from Na 3 P0 4 to H 3 P0 4 , both viscosities and conductivities decrease. In the fourth or organic group, there is an irregularity in the conductivity column. This list, though small, is enough to show that there is little hope for a successful comparison of vis- cosity and conductivity, without an extended series of observations, 334 B. E. MOORE. [Vol. III. and that, too, with dilute solutions in which the increase in the viscosity of the solvent will be largely due to the ions, as it is the viscosity of the latter alone with which we have to deal in conductivity. Conclusions. 1. The viscosity of solutions decreases quite rapidly with rise in temperature, but the character of this decrease is very different for different concentrations and for different salt solutions. 1 2. Stochiometrical relations, though doubtless existing, are neither very definite nor convincing. 3. The Arrhenius exponential formula or law, though affording an excellent method for comparison of viscosities of dilute, even normal, solutions, does not hold good for the more concentrated solutions. 4. More extended observations must be made upon the relation of viscosity to conductivity, perhaps even some new method of comparison arrived at, before the two subjects are placed in their right relation. 1 Thorpe and Rodgers, Proc. Royal Soc., 55, p. 148, have pointed out that tempera- tures of equal slopes is an excellent method for comparison of viscosity. These experi- ments were in a measure completed when the article by Thorpe and Rodgers appeared, and the range of temperature not wide enough to make such a comparison.