1514
B. J. STEEL,JEANM. STOKESAND R. H. STOKES
Vol. 62
INDIVIDUAL ION MOBILITIES IN MIXTURES OF NON-ELECTROLYTES AND WATER BY B. J. STEEL,’JEANM. STOKES AND R. H. STOKES Contribution from the Chemistry Department, University of New England, N.S.W., Australia Received M a y 19, 1968
Individual limiting ion mobilities in aqueous 10% mannitol, 10 and 20% sucrose and 10 and 20% glycerol are evaluated from the limiting conductances and transference numbers. For very large ions the values approach those predicted by Walden’s rule using the values in pure water and the relative viscosities of the mixed solvents, but for small ions and in part,icular for hydrogen ion, the lowering of the mobility is considerably less than is given by Walden’s rule. The applicabilit of an “obstruction” model similar to that suggested by Wang for the self-diffusion of water in protein solutions is discussed:
Introduction In previous papers2 we have presented details of conductance measurements from which the limiting equivalent conductances of a number of electrolytes in sucrose-water and mannitol-water solutions have been evaluated, and have described an improved form of Hittorf apparatus3 by means of which transference numbers in these mixed solvents have been measured. I n this paper we first report some additional conductance and transference number results, then proceed to discuss the influence of the relatively large non-electrolyte molecules on the mobilities of individual ions. Experimental (a) Conductances of Electrolytes in 10% and 20% Aqueous Glycerol Solutions at 25’ .-Glycerol was repeatedly distilled under reduced pressure until the product, after making into a 20% aqueous solution, had a specific conductance of less than 2 X 10-6 ohm-l cm.-l. The density and viscosity of the solution agree with literature value^.^ The electrolytes were purified by methods reported previouslya; conductances were measured in the concentration range 0.001-0.1 N a n d extrapolated as described previouslyab to yield the limiting equivalent conductances reported i; Table I. The oil thermostat was controlled a t 25 f 0.002 and the measurements were made in conventional cells with a Leeds and Northrup Jones bridge.
dium bromide was prepared from analytical reagent hydrobromic acid and sodium hydroxide and several times recrystallized; the dihydrate obtained wasfihydrated in a vacuum The 10% mannitol desiccator and then dried at 400 solution was purified by assage through a column of ionexchange resins supplied &r a commercial water de-ionizing unit; its density and viscosity agreed with those of solutions prepared from several times recrystallized mannitol, and its specific conductance was -10-5 ohm-1 cm.-l. The transference numbers are given in Table 11.
.
TABLE I1 TRANSFERENCE NUMBERS OF CATIONIN 10% AQUEOUS MANNITOLAT 25’, ADJUSTED TO HITTORFFRAMEOF REFERENCE c, mole 1. -1
Potassium bromide 0.01055 0.02176 0.02901 0.04040 0.05138
t+
0.4835
0.4846
c, mole ’
Sodium bromide 0.02060 0.02061 0.03681 0.05395
0.4848
0.4846
0.4853
1. -1 tf
0.3827
0.3836
0.3830
0.3834
Extrapolation of Transference Numbers to Zero Concentration.-T+ measured transference numbers were first converted to the conventional Hittorf frame of reference by the use of data for the solution densities. From each result a transference number t+ ’’ corrected for the electrophoretic effect then was calculated by the equation6 TABLE I &’‘ = + ! f ( ‘ / a - t+)Bzd/C/[(1f Ka)Ao] (1)L LIMITING EQUIVALENT CONDUCTANCES OF ELECTROLYTES IN where Bz is the coefficient of the electrophoretic term in the 10% AND 20% AQUEOUSGLYCEROL SOLUTIONS AT 25OaPb Onsager conductance equation. These values wk;? then Electro10% glycerol 20% glycerol extrapolated to zero concentration on a graph of t+ us. c. AQ R R lyte AQ This is essentially the Longswortha procedure, modified to 96.80 0.6460 0.8151 KC1 122.16 include the effect of ion size in the electrophoretic terms. 97.02 .6397 .8120 KBr 123. l o In the case of potassium bromide the concentration dependence is so slight that the choice of the ion size parameter a .6322 .8073 95.09 KI 121.44 in equational is not a t all critical; for sodium bromide a 93.6s .6461 ,8178 KNOI 118.50 value of 5 A. was assumed. The extrapolated values t+’, 81.57 .6454 ,8140 NaCl 102.93 are given in Table 111. The object of the measurements on 85.14 ,6383 ,8100 AgN03 108.00 a A’ in cm.2 (int. ohm)-’ g. equiv.-’. bR = A’ in mixed TABLE I11 solvent/A’ in water. LIMITINGTRANSFERENCE NUMBERS OF CATION FOR POTASI N AQUEOUS NON-ELECTROLYTE (b) Transference Numbers of Potassium and Sodium SIUM AND SODrUM BROMIDES Bromides in 10% Aqueous Mannitol Solutions.-These SOLUTIONS AT 25” measurements were made with our modified Hittorf apK + ion in KBr paratus3 which employs conductimetric analysis of the Solvent 20% sucrose 0.4876 solution in situ. Potassium bromide was prepared by repeated recrystallization, followed by drying a t 400”. So20% glycerol 0.4910 10% mannitol 0.4846 (1) The conductance measurements in glycerol-water mixtures were water? 0.4847 presented in a thesis by B. J. Steel in partial fulfillment of the requireNa+ in NaBr ments for the degree of Bachelor of Science with Honours in the Solvent 10% mannitol 0.3878 University of Western Australia in 195G. (2) (a) Jean M. Stokes and R. H. Stokes, THISJOURNAL, 60, water7 0.390, 217 (1956);
(1958).
(b) Jean M. Stokes and R. H. Stokes, ibid., 62, 497
(3) B. J. Steel and R. H. Stokes, ibX., 62, 450 (1958). (4) M. Sheely, Ind. Eng. Chem.. 24, 1060 (1932).
(5) R. A. Robinson and R . H. Stokes, “Electrolyte Solutions,” Butterworths, London, 1955, p. 157. (6) L. G . Longsworth, J. Am. Chem. SOC.,64, 274 (1932).
INDIVIDUAL IONMOBILITIEIN NON-ELECTROLYTES AND WATERMIXTURES
JJec., 1958
1515
TABLE IV INDIVIDUAL ION MOBILITIESIN AQUEOUS SUCROSE, GLYCEROL A N D MANNITOL SOLUTIONS AT 25" R = kO(solvent)/k"(water) Glycerol
Sucrose Ion
Rel. fluidity
H+
I< + Na Li + Ag Ca++ Mg++ La+++ N( n-Am)* ClNO,Br c104+
+
+
I-
-+
20% 0.525
20% 0.579
10%
0.756
XQ
R
A0
R
230.2 46.1 31.1 23.6 37.6 34.8 30.9 39.5 9.6 48.2 44.6 48.4 41.2 46.4
0.658 .627 .621 . 610 .607 ,585 ,582 .567 ,550 ,631 . 624 ,619 . 612 . 604
294.3 59.7 40.6 31.0 49.5 46.8 41.8 54.2 13.3 62.2 57.0 63.1 54.1 61.2
0.841 ,812 ,810 .802 ,800 ,787 .788 ,778 ,761 .815 ,810 .807 ,803 ,796
XO
R
10% 0.775 XO
Mannito 10%
R
0.747
A0
R 0.837 ,797 ,790 .778 .780
47.6 32.4
0.648 ,647
60.0 40.8
0.817 ,815
39.1
.632
49..6
.801
292.8 58.6 39.6 30.1 48.3
49.2 46.0 .49.4
,644 .G44 .632
62.1 58.4 63.0
.813 .817 .806
61.1 57.4 62.3
,800 ,803 .797
47.4
.617
61.4
.799
60.9
,792
sodium bromide in 10% mannitol was to provide a check on those using potassium bromide by the Kohlrausch principle of independent ion mobilities, conductance data for both salts being available in this solvent. From the potassium bromide results we obtain for the bromide ion conductance in 10% mannitol X'B~- = (1 - 0.4846) X 120.9 = 62.3 cm.2 ohm-' equiv.-l and from the sodium bromide results 1'~~- = ( 1 0.3878) X 102.06 = 62.5 cm.2 ohm-' equiv.-' This agreement is satisfactory, though not as good as has been obtained in pure water as solvent by the moving boundary method. Individual Ion Mobilities.-In each of the previous investigations the electrolytes were so chosen that the fixing of the limiting transference number for any one of them makes possible the evaluation of the separate mobilities of all the ions by the Kohlrausch principle. Table IV gives the results so obtained. (Though no actual measurements of transference numbers were made in 10% glycerol and 10% sucrose, we have assumed that since in the 20% solutions the transference numbers of potassium bromide differ only slightly from those in pure water, the values for the 10% solutions may be interpolated safely.) Table IV also records the ratio R = Xo(solvent)/ko water for each ion, using accepted values for A' in water.
tween the ions and the added non-electrolyte may occur, the similarity of the results for various added non-electrolytes suggests that such effects are of a minor nature only, and it seems fair to summarize the general position as follows: The addition to water of non-electrolytes which increase the viscosity causes a reduction in the mobility of all ions. This reduction is most marked for large ions, where it approaches the value predicted by Walden's rule, and is least for small ions. Hydrogen ion is the least affected, but even here the mobility lies nearer to the Walden's rule value than t o the unaltered water value. These conclusions are not difficult to account for in a qualitative way: very large ions can be expected to move in accordance with Stokes' law, shouldering aside both water and added non-electrolyte molecules in their progress; small ones, on the other hand, will treat the non-electrolyte molecules as obstacles to be avoided, and will move essentially through a medium of water molecules only, The increased resistance which they experience will be best regarded as due to the increase in the length of their paths in avoiding the obstacles. Discussion The detailed analysis of the actual path of a At the head of the columns in Table IV is the fluidity of each solvent relative to water. If the small ion in a solvent containing water molecules viscous effect on the ionic motion were of the and large non-electrolyte molecules is beyond our simple kind demanded by Walden's rule (or Stokes' powers, but it is worthwhile examining the extreme law),' the relative ion mobility R would be equal to case of such a situation, vix., the case where the the relative fluidity. This behavior is not found sizes of both ion and water molecule are negligible for any of the ions studied. It is most closely ap- compared to the size of the added non-eleotrolyte proached by the very large tetra-n-amylammonium molecules. A further simplification can be made ion, though even here the relative mobility in 20% by treating the latter as spheres. The problem sucrose solution is 5% greater than the relative may now be stated in these terms: what is the gross fluidity. Among the cations the relative mobilities specific conductance of a previously uniform coiiincrease in the order: NAm4+
