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Volume 76, 1946-47
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The Vapour Pressures of Potassium Ferricyanide and Thorium Nitrate Solutions at 25°.

[Read before the Auckland Branch, 1946; received by the Editor, June 23, 1946.]


The vapour pressures of solutions of potassium ferricyanide up to 1.4M and of thorium nitrate up to 5.2M have been determined at 25°. The results have been used in support of a generalisation that ions of high negative charge are more effective in causing departure from ideal behaviour than are ions of opposite charge. It is shown that this is consistent with extensive hydration of positive ions in contrast to negative ions which should not be hydrated to any marked extent.


The vapour pressure lowering of an ideal solution is given by:

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where Δp is the difference between p°, the vapour pressure of the pure solvent, and p, the vapour pressure of a solution, the mol fraction of the solute being N2. For dilute aqueous solutions this approximates to:

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m being the molality expressed as mols per 1,000 g. of water. If the solute is an electrolyte, allowance must be made for the dissociation into ν ions, giving the expression:

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It is known that electrolytic solutions exhibit marked deviations from the ideal behaviour and the Debye-Huckel theory accounts successfully for these deviations in the case of dilute solutions by taking into account the effect of electrostatic attraction between the ions. This effect diminishes the vapour-pressure lowering, and in the simplest case, where the ions are assumed to act as point charges, the vapour lowering of an aqueous solution at 25° is calculated to be:

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where μ is the total ionic strength of the solution. This is more usually expressed in terms of the osmotic coefficient ϕ = -55 51/m.ln p/p°,

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ϕ = 1-0.3909√μ

or the activity coefficient:

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-log f = 0.5092z1z2√μ,

z1 and z2 being the valencies of the ions.

A closer concordance with experimental results is obtained if the Debye-Hückel equation is evaluated for the case of ions of finite diameter, by introducing a parameter, a, “the distance of closest approach of two ions.” The expression for the activity coefficient becomes:

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-log f = 0.5092 z1z2√μ/1+0.3286a√μ).

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Although this correction extends the concentration range over which the equation is valid, it predicts an activity coefficient decreasing continuously with increasing concentration. Experimentally it is found that the activity coefficient does not decrease as rapidly as theory predicts and in many cases passes through a minimum and then increases to high values at high concentrations. Hückel has examined the problem further and has proposed the extended equation:

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-log f = 0.5092 z1z2√μ/(1+0.3286a√μ)—Bμ

where B is a parameter characteristic of the electrolyte. The last term is supposed to allow for the changing dielectric constant of the solution, but, although the equation predicts the activity coefficient up to about μ = 1, the equation does not rest on a very sound foundation and fails to account for the experimental results at high concentrations. Further theoretical advances seem to be very difficult, and therefore it would appear profitable to pursue the experimental side.

It will be noted that, although the valencies of the ions enter into the above equations, no distinction is made between positive and negative charges on the ions. Thus theory predicts the same activity coefficient for a 2 : 1 valent salt such as calcium chloride and for a 1 : 2 valent salt such as sodium sulphate. This is undoubtedly true in the limiting case of very dilute solutions, but in recent years sufficient data have been accumulated to show that it does not hold for concentrated solutions. Data are available for twenty-seven salts of the 2 : 1 valency type, including the nitrates, chlorides, bromides and iodides of magnesium, calcium, strontium and barium, the chlorides of manganese, copper, iron, cobalt and nickel, together with zinc, cobalt, copper, and uranyl nitrate and magnesium and zinc per-chlorate. The number of salts of the 1 : 2 valency type is smaller; they include five alkali metal sulphates, sodium thiosulphate, fumarate and maleate and sodium and potassium chromate. At a concentration of 1M the activity coefficients of twenty-five of the 2 : 1 salts range from 0.929 for magnesium iodide to 0.334 for calcium nitrate, whilst those of the 1 : 2 salts range from 0.322 for sodium fumarate to 0.202 for sodium sulphate. Thus the 2 : 1 salts tend towards perfect behaviour more than 1 : 2 salts, although there is one exception to this rule, namely, strontium nitrate, which has an activity cofficient of 0.271 at 1M, slightly less than that of lithium sulphate at the same concentration. Moreover, it is probable that barium nitrate would also be an exception if solubility limitations did not preclude measurements up to this concentration. Nevertheless, although there is some overlapping, the tendency towards high activity coefficients for 2 : 1 salts and low activity coefficients for 1 : 2 salts is sufficiently marked to possess significance. It is therefore logical to enquire if the same distinction is to be found in salts of higher valency type. Among 3 : 1 salts lanthanum chloride has been measured by Mason (1938) and Robinson (1939) and eight other trivalent metal chlorides by Mason (1941). All nine have activity coefficient of the same order. The only measurements on 1 : 4 salts were those of Robinson (1937) on potassium ferrocyanide. Salts of the 1 : 3 and 4 : 1 valency type were therefore required and, unfortunately,

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the choice proved to be very limited; only potassium ferricyanide and thorium nitrate proved suitable among the available materials and vapour pressure measurements were therefore made on these salts (Tables I and II) and the osmotic and activity coefficients calculated (Table III).

The activity coefficient results are plotted in Fig. I. As representative of uni-bivalent salts calcium chloride, as 2 : 1 salt, and sodium sulphate, a 1 : 2 salt, have been selected. In the second panel of Fig. I the data for potassium ferricyanide, a 1 : 3 salt, are compared with those of lanthanum chloride, a 3 : 1 salt, and the comparison is completed with thorium nitrate, a 4 : 1 salt, and potassium ferrocyanide, a 1 : 4 salt.

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Fig. I.—Activity Coefficients of Salts of Different Valency Type.

Although the number of salts available for study is limited, Fig. I does suggest that the generalisation described above can be extended to salts of higher valency type. The rule may now be stated in this form: the vapour-pressure lowering, the osmotic coefficient and the activity coefficient are reduced more by an ion of negative charge than by an ion whose charge is the same in magnitude but negative in sign, i.e., negative charges are more effective than positive charges in causing deviations from ideal behaviour.

It is not the object of this paper to enter into the difficult mathematical theory of concentrated solutions. Qualitatively, however, our results suggest that only positively charged ions undergo

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extensive hydration, probably increasing in extent with the magnitude of the charge. Hydration, by removing “free” solvent, increases the effective concentration of the solution and also the activity coefficient. Indeed, hydration would seem to be the only mechanism whereby we can explain the very high values of the activity coefficients of salts like calcium chloride in concentrated solution. The values for lanthanum chloride and thorium nitrate are not so high, but when we remember the very high charges on these cations which should result in considerable ion-pair formation and therefore in very low activity coefficients, like those observed for potassium ferricyanide and ferrocyanide, we can only conclude that some compensating mechanism must intervene to raise the activity coefficients to the observed values. Again hydration would appear to be the only force of sufficient magnitude. On the contrary, the very low activity coefficients observed when the high-valency ion has a negative charge, consistent with ion-pair formation between ions such as potassium and ferrocyanide, indicates that hydration of negative ions must be small in extent. For these reasons we put forward the view that ionic hydration is a phenomenon associated with positive rather than negative ions.


Potassium ferricyanide was crystallised from A.R. material. Thorium nitrate was prepared from commercial thoria and recrystallised three times from slightly acid solution. Isopiestic vapour pressure measurements were made by the method of Robinson and Sinclair (1934), using platinum dishes for both salts. Sodium chloride and sulphuric acid were used as reference electrolytes. Potassium ferricyanide proved to be a difficult salt to work with and, although we are convinced that the accuracy of the results is more than sufficient for our present purpose, high accuracy is not attributed to the data. It is possible that the measurements on thorium nitrate are in some error from hydrolysis; but we found no difficulty in obtaining reproducible and consistent results. The experimental results are given in Tables I and II and the osmotic and activity

Table I.—Isopiestic Solutions of Potassium Ferricyanide and Sodium Chloride at 25°.
K3Fe(CN)6 NaCl K3Fe(CN)6 NaCl K3Fe(CN)6 NaCl K3Fe(CN)6 NaCl
0.1357 0.2083 0.1976 0.2954 0.3864 0.5691 0.4813 0.7058
.6544 .9478 .7225 1.049 .8316 1.212 .9716 1.432
1.102 1.638 1.209 1.812 1.431 2.170
Table II.—Isopiestic Solutions of Thorium Nitrate and Sodium Chloride or Sulphuric Acid.
Th(NO3)4 NaCl Th(NO3)4 NaCl Th(NO3)4 NaCl Th(NO3)4 NaCl
0.0502 0.0916 0.0820 0.1489 0.1958 0.3633 0.3630 0.7090
4625 .9348 .6054 1.294 .8332 1.897 1.068 2.583
1.147 2.849 1.332 3.422 1.477 3.840 1.635 4.306
1.700 1.926 1.926 5.175 2.038 5.534 2.244 6.148
Th(NO3)4 H2SO4 Th(NO3)4 H2SO4 Th(NO3)4 H2SO4 Th(NO3)4 H2SO4
2.564 4.880 2.634 4.992 3.095 5.730 3.151 5.820
3.674 6.576 4.247 7.328 5.151 8.447 5.201 8.498

The above tables express the experimental results as molalities of solutions of equal vapour pressure.

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coefficients calculated therefrom are given in Table III, which also contains similar data for lanthanum chloride, recalculated from the experimental work of Mason (1938) and Robinson (1939). In making these calculations we have used the data for sodium chloride given by Robinson (1945) and for sulphuric acid by Shankman and Gordon (1938).

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Table III.—Osmotic' and Activity Coefficients of Potassium Ferricyanide, Lanthanum Chloride and Thorium Nitrate at 25°.
K3FeCy6 LaCl3 Th(NO3)4
m ϕ γ ϕ γ ϕ γ
0.05 .793 .447 0.676 0.350
0.1 0.727 0.336 .786 .384 .675 .279
.2 .695 .266 .802 .337 .685 .225
.3 .682 .231 .836 .323 .705 .203
.4 .678 .210 .875 .323 .734 .192
.5 .676 .195 .915 .328 .770 .189
.6 .676 .183 .957 .338 .807 .188
.7 .679 .175 1.004 .353 .846 .191
.8 .685 .169 1.052 .371 .885 .195
.9 .694 .164 1.102 .394 .925 .201
1.0 .705 .161 1.154 .421 .965 .207
1.1 .715 .158 1.208 .451 1.004 .215
1.2 .727 .156 1.266 .488 1.044 .224
1.3 .738 .154 1.325 .530 1.084 .235
1.4 .750 .153 1.384 .577 1.120 .246
1.5 .764 .153 1.442 .630 1.155 .256
1.6 1.502 .689 1.192 .269
1.8 1.623 .830 1.259 .296
2.0 1.748 1.012 1.325 .326
m ϕ γ
2.5 1.455 0.405
3.0 1.546 .486
3.5 1.616 .568
4.0 1.659 .647
4.5 1.688 .722
5.0 1.706 .791

We thank the Chemical Society for a grant from their Research Fund which has assisted this work.


Mason, C. M., 1938, J. Amer. Chem. Soc., 60, 1638.

—— 1941, Ibid., 63, 220.

Robinson, R. A. and Sinclair, D. A., 1934, Ibid., 56, 1830.

Robinson, R. A., 1937, Ibid., 59, 84.

—— 1939, Trans. Faraday Soc., 35, 1229.

—— 1945, Trans. Roy. Soc. N.Z., 75, 203.

Shankman, S., and Gordon, A. R., 1939, J. Amer. Chem. Soc., 61, 2370.