The Vapour Pressures of Solutions of Potassium Chloride and Sodium Chloride.

Transactions and Proceedings of the Royal Society of New Zealand, Volume 75, 1945-46, Page 203

The Vapour Pressures of Solutions of Potassium Chloride and Sodium Chloride. By R. A. Robinson. Auckland University College. [Read before the Auckland Institute, April 18, 1945; received by the Editor, April 26, 1945; issued separately, September, 1945.] Summary. Isopiestic measurements have been made between the following pairs of salts: potassium chloride and sodium chloride at 20° and 25°; sodium and barium chloride at 25°; sodium chloride and sulphuric acid at 25°; sodium chloride and lithium chloride at 20°. The vapour pressures of solutions of sodium chloride and potassium chloride at 25° have been calculated using both direct experimental measurements and indirect determinations which can be correlated by means of isopiestic measurements. The calculations are collected as a table of various properties related to the vapour pressure, tabulated at close concentration intervals. Introduction. The isopiestic method of determining the vapour pressure of an aqueous solution was developed by Robinson and Sinclair (1934). The technique involves equilibration of solutions of the salt under investigation and of a reference salt by isothermal distillation of water through the vapour phase from the solution of higher to that of lower vapour pressure until a state of equilibrium is attained, when the concentrations correspond to equal vapour pressures. In practice, successful operation depends on securing adequate thermal conduction between the solutions; otherwise a state of equilibrium is attained, by means of a small temperature gradient between the solutions which creates a condition of equal vapour pressures in the absence of true isothermal equilibrium. The necessary thermal conduction is obtained by the use of silver dishes to contain the solutions and of a thick copper block on which the dishes rest. In the last ten years the method has been applied to about a hundred salts, and the results have been summarized by Robinson and Harned (1941); modifications of the technique have been devised by Janis (1935), Mason (1936), Owen and Cooke (1937), Scatchard, Hamer and Wood (1938), Felsing (1942) and Jones (1943), whilst Gordon (1943) has made a valuable extension of the method to dilute solutions. The efforts of these investigators have resulted in a substantial contribution to the physical chemistry of aqueous solutions. It should not be forgotten, however, that the method is essentially comparative and based on the assumption that a reference electrolyte is available, the vapour pressure of whose solutions is known with sufficient accuracy over a wide range of concentration. The task of evaluating

with some degree of certainty either the vapour pressure or some related property of solutions of a selected salt is therefore one of importance but not, unfortunately, an easy one. Robinson and Sinclair used potassium chloride as a reference salt and, from a survey of the thermodynamic data then available for this salt, made an estimate of the most reliable values of the activity coefficients at concentrations from 0.1M to 4M at 25°. These values were revised by Robinson (1939), the principal change being an increase of all the earlier values by approximately 0.7%. This alteration was occasioned mainly by the demonstration by Harned and Cook (1937) that their e.m.f. measurements on potassium chloride solutions were better fitted to Hückel's equation by using values over the concentration range 0.05 to 1M rather than the range up to 4M previously used by Harned (1929), the activity coefficient at 0.1M being raised thereby from 0.764 to 0.769 and pro rata at other concentrations. By a similar argument Janis and Ferguson (1939) arrived at approximately the same set of reference values for potassium chloride, but Scatchard, Hamer and Wood (1938) were led to values significantly different by allocating different weight to some of the available data. It is evident that the selection of data for the reference salt was largely dependent on the weight attached by different computers to each of the experimental investigations available for calculation. In the last few years there have been published the results of a a number of researches of high accuracy which are relevant to this topic and which can be correlated by isopiestic vapour pressure measurements. It is the object of this paper to present such data and to reconsider the problem of a set of reference values for isopiestic work, using all the data now available. Although the reference salt selected by Robinson and Sinclair was potassium chloride, the recent work which must now be discussed has been concerned more with the properties of sodium chloride solutions, and it will be advisable to consider first the allocation of a set of reference values for this salt; once this problem is solved, the analogous problem with potassium chloride finds a ready solution. For this purpose measurements of any of the following properties must be taken into consideration, provided they are of the requisite degree of accuracy. (a) Direct vapour pressure measurements by either a static or a dynamic method. The results of such determinations may be expressed as p/p°, p being the vapour pressure of the solution and p° that of the pure solvent at the same temperature. Provided that the departure of the vapour from perfect gas behaviour is negligible, we may write p/p° = aw, the solvent activity. Since aw departs but little from unity in dilute solutions, the magnitude of deviations from ideal behaviour in the liquid phase is more clearly emphasized by a derived function, the osmotic coefficient, defined by: φ = — (55.51/v m) In aw, v being the number of ions per molecule of electrolyte and m the molality. The magnitude of the error likely to occur in a vapour pressure determination may be assessed from the work of Shankman and Gordon (1939) on sulphuric acid, which may be taken as repre-

sentative of the best work in this field. For two measurements at 6.671M they give 0 5740 and 0.5744 for the water activity, corresponding to 13.635 and 13.643 mm. of Hg for the vapour pressure, a difference of 0.008 mm. The uncertainty is probably less than this because several measurements are made at each concentration, but even if this can be lowered to 0.002 mm. it corresponds to a difference of 0.0001 in the water activity. The resulting error in the osmotic coefficient is inversely proportional to the molality, being 0.02 at 0.1M, 0.002 at 1M and 0.0004 at 5M. Direct vapour pressure measurements are therefore valuable at high concentrations but with more dilute solutions even the best determinations will suffer by comparison with other methods. (b) Freezing point measurements which yield the activity of the solvent at the freezing point of the solution. Provided that the necessary calorimetric data are available, such solvent activities can be converted to other temperatures for comparison with vapour pressure measurements. These temperature corrections have been described adequately by Lewis and Randall (1923). Freezing point measurements can be made with great accuracy; thus Scatchard and Prentiss (1933) report data which are reliable to 0.0003 in the osmotic coefficient, but this degree of accuracy is often counterbalanced by some uncertainty in the calorimetric data necessary for the temperature correction. (c) E.m.f. measurements on cells without transport of the type: NaxHg | NaCl | AgCl — Ag. Cells of this type measure the activity coefficient, γ, of the salt which is related to the solvent activity by the Gibbs-Duhem equation: — 55.51 dln aw = v m dln(γ m). The solvent activity can therefore be obtained only by integration and the computation is not one which can be made easily with the necessary accuracy. This problem has been discussed recently by Stokes (1945). In contradistinction to the first two methods, the effect of a given error in the e.m.f. on log γ is independent of the molality, 0.01 mv. corresponding to 0.0001 in log γ. The method should, therefore, be applicable at all concentrations but in practice experimental difficulties with alkali metal amalgam electrodes intervene below 0.05M whilst above 2.5M there is some question as to the effect of solubility of the silver chloride electrodes. (d) E.m.f. measurements on cells with transport of the type Ag —AgCl | NaCl (m1) | NaCl (m2) | AgCl — Ag, combined with measurements of the transport number, usually by the moving boundary method. These cells also measure the activity coefficient of the salt, and the water activity and osmotic coefficient are obtained by an integration. The effect of experimental error is again independent of concentration and electrode solubility probably puts an upper limit to the concentration range over which useful measurements can be made. The absence of amalgam electrodes, however, enables measurements to be extended to low concentrations at which other methods are inapplicable with any accuracy. Thus Shedlovsky and MacInnes (1937) have made determinations down to 0.005M.

From what has been said above it is clear that up to a concentration of 0.1M reliance must be placed mainly on the results of measurements on cells with transport, which also involve determinations of transport numbers. Fortunately in the case of sodium chloride both sets of measurements have been duplicated by independent workers with good agreement. Thus Brown and MacInnes (1935) using the transport number data of Longsworth (1932). and their own e.m.f. measurements obtained activity coefficients of sodium chloride up to 0.1M, at which concentration they found — log γ = 0.1088. Later Janz and Gordon (1943) made another set of e.m.f. measurements and, using the transport number data of Allgood and Gordon (1942), were able to duplicate the values of Brown and MacInnes with — log γ = 0.1088 at 0.1M. Furthermore, Harned and Cook (1939), using the cells without transport of Harned and Nims (1932) and the Debye-Hückel equation obtained — log γ = 0 1085. Similar measurements have been made on potassium chloride solutions; thus Shedlovsky and MacInnes (1937) using the transport number data of Longsworth (1932) obtained — log γ = 0.1134. An independent determination by Hornibrook, Janz and Gordon (1942) using the transport number data of Allgood, Le Roy and Gordon (1940) gave — log γ = 0.1137, whilst Harned and Cook (1937) obtained — log γ = 0.1141 from cells without transport. Fortunately these values for potassium chloride can be correlated with those for sodium chloride since the isopiestic ratio between these two salts up to 0.1M is known from the work of Gordon (1943), with more than the accuracy required for this calculation. (By the isopiestic ratio is meant the ratio of the molalities of two salt solutions of equal vapour pressure). This ratio differs only slightly from unity up to 0.1M, and I have least squared the results of Gordon to give a value of R = mkcl/mNacl = 1.0063 at 0.1M NaCl, a value which is fully consistent with new measurements at slightly higher concentrations to be described later in this paper (Appendix I). Up to 0.1M, R is linear in mNaCl. Robinson and Sinclair have demonstrated how the activity coefficient of one salt may be obtained from that of another salt if the isopiestic ratio between the two has been measured. The three determinations of the activity coefficient of potassium chloride may therefore be combined with the isopiestic work of Gordon to give independent determinations of γ for sodium chloride at 0 1M. Calculation shows that this isopiestic work necessitates a value of 0.0048 for log (γNaCl/γkcl) and therefore the above three values of — log γkcl correspond to 0.1086, 0.1089 and 0.1093 for — log γNaCl at 0.1M. Thus six separate determinations have been made with a mean value of — log γNaCl = 0.1088 with a probable error of 0.0002. It follows that — log γkcl = 0.1136. By integration of the activity coefficients up to 0.1M, osmotic coefficients at this concentration are evaluated as φNaCl = 0.9324 and φkcl = 0.9266. Between 0.1 and 1M sodium chloride it is doubtful if direct vapour pressure determinations are sufficiently accurate, but water activities derived from the freezing point measurements of Scatchard and Prentiss (1933) must be considered. These can be corrected to

25° by means of the calorimetric data of Robinson (1932) and Rossini (1931). There are also the e.m.f. measurements of Harned and Nims on cells without transport containing sodium chloride. From these e.m.f.'s water activities or osmotic coefficients may be derived by the method outlined by Stokes. Moreover, there are available similar e.m.f. results on potassium chloride (Harned and Cook, 1937), sodium bromide (Harned and Crawford, 1937), and potassium bromide (Harned, 1929), from which vapour pressures can be calculated. Isopiestic data are also available for these salts, which means that for each concentration at which measurements were made by Harned et al. the concentration of the sodium chloride solution of equal vapour pressure is known. Thus each set of water activities for potassium chloride, etc., can be combined with isopiestic data to give water activities of sodium chloride solutions. The results of these calculations are given in Table I. Table I. Osmotic Coefficients of Sodium Chloride Below 1M. Source NaCl e.m.f.s KCl e.m.f.s NaBr e.m.f.s KBr e.m.f.s F.pt. Mean 0.2M 0.923 0.926 0.924 0.924 0.9255 0.9245 0.3 .021 .022 .919 .923 .9224 .9215 0.5 .919 .923 .917 .923 .9224 .9209 0.7 .925 .928 .923 .920 .9200 .9257 1.0 .936 .937 .935 .933 .9363 .9355 The means of these values will be taken as the best values; the probable error should not be greater than 0.002. At concentrations above 1M sodium chloride there are eight investigations which have either measured the vapour pressure directly or determined some property from which the vapour pressure can be calculated. The results are given in Table II and plotted in Fig. 1, where it has been found convenient to plot (φ — 0.05 mNaCl) rather than the vapour pressures in order to magnify the differences between the various determinations. Two of these involve direct vapour pressure measurements by a static manometric method at 25°; Negus (1922) made measurements at nine concentrations between 1 and 5M, whilst Olynyk and Gordon (1943) made determinations at 15 concentrations between 2.3M and saturation. The two sets are in excellent agreement. Gibson and Adams (1933) made a direct measurement by the static method at 20.28° on a solution saturated at this temperature; this result has been converted to 25° by means of the heat content data of Robinson (1932) and the specific heat values of Rossini (1931) and the value obtained lends good support to the measurement on the saturated solution by Olynyk and Gordon. Lovelace, Frazer and Sease (1921), using an apparatus similar to that of Negus, measured the vapour pressure of nine solutions of potassium chloride at 20° between 1.2 and 3.6M. To utilise these measurements a knowledge of the isopiestic ratio of this salt to sodium chloride at 20° is necessary, and determinations have

been carried out with the results given in Table III. Within the limits of experimental error these isopiestic ratios are found to be linear in mNaCl and have been least-squared to the equation: R = mkci/mNaCl = 1.0111 + 0.0315 mNaCl, valid at 20° between 1 and 4M sodium chloride. There is a mean deviation of 0.0005 and a maximum of 0.0011 between the values of R obtained experimentally and those calculated by the linear equation. Table II. Water Activities of Sodium Chloride Solutions above 1M at 25°. A.—Direct Vapour Pressure Determinations. m aw 1.028, .9661 (1) 2.294, .9210 (2) 3.026, .8923 (1) 3.580, .8695 (1) 4.382, .8346 (1) 4.961, .8087 (1) 6.145, .7532 (2) 1.564, .9475 (1) 2.417, .9163 (1) 3.089, .8896 (2) 3.664, .8660 (2) 4.471, .8305 (2) 5.368, .7901 (2) 2.081, .9287 (1) 2.755, .9027 (2) 3.261, .8827 (2) 3.973, .8530 (2) 4.673, .8217 (2) 5.783, .7704 (2) 2.192, .9246 (1) 2.764, .9023 (2) 3.268, .8815 (2) 4.028, .8506 (2) 4.913, .8110 (2) 6.119, .7542 (3) (1) Negus, (2) Gordon, (3) Gibson and Adams. Their measurements at 20.28° gave aw = .7547, corected to 25° a w = .7542. B.—Vapour Pressure Determinations on other Electrolytes combined with Isopiestic Vapour Pressure Measurements. Potassium Chloride. mkci aw(20°) mNaCl aw(25°) 1.246 .9606 1.188 .9605 2.707 .9459 1.608 .9457 2.245 .9288 2.085 .9284 3.002 .9030 2.736 .9035 4.007 .8903 3.566 .8697 1.510 .9522 1.430 .9520 1.994 .9269 1.864 .9366 2.492 .9208 2.300 .9204 3.578 .8848 3.217 .8843 Barium Chloride. mBaCl2 aw mNaCl 0.8746 .9577 1.269 1.232 .9375 1.845 1.600 .9148 2.458 Sulphuric Acid. mH2SO4 aw mNaCl 1.282, .9498 (1) 1.512 1.918, .9174 (2) 2.386 2.468, .8864 (1) 3.189 3.776, .7964 (2) 5.213 4.339, .7539 (2) 6.118 1.671, .930O (1) 2.038 2.009, .9122 (1) 2.516 2.871, .8595 (1) 3.802 4.218, .7627 (2) 5.923 1.772, .9248 (1) 2.179 2.239, .8995 (2) 2.852 3.659, 8048 (2) 5.027 4.279, .7586 (2) 6.020 (1) Grollman and Frazer. (2) Shankan and Gordon. C.—E.m.f. Measurements on Potassium Chloride combined with Isopiestic Data. mkcl aw mNaCl 1.5 .9524 1.421 3.0 .9038 2.734 2.0 .9363 1.870 3.5 .8870 3.152 2.5 .9201 2.307 4.0 .8701 3.561

Fig. 1.—Deviation Function for Osmotic Coeflicient of Sodium Chloride at 25°. ○Negus—sodium chloride. ▪Olynyk and Gordon—sodium chloride. •Lovelace. Frazen and Sease—potassium chloride. ×Harned and Cook—potassium chloride. ⊕Bechtold and Newton—barium chloride. ▵Gibson and Adams—sodium chloride. ⋆Grollman and Frazen—sulphuric acid. Shankman and Gordon—sulphuric acid. Table III. Isopiestic Ratios of Potassium and Sodium Chloride at 20°. mNaCl R 0.9662 1.0415 1.3014 1.0526 2.4781 1.0887 3.9725 1.1371 1.0186 1.0435 1.3734 1.0541 2.5066 1.0897 3.9963 1.1374 1.0268 1.0426 1.7746 1.0671 2.6108 1.0920 1.2571 1.0517 1.7990 1.0678 3.5145 1.1213 R = mkcl/mNaCl Corresponding to each of the nine concentrations at which measurements were made by Lovelace, Frazer and Sease, there are nine concentrations of sodium chloride of equal vapour pressure; these concentrations are determined by the above equation for the isopiestic ratios at 20°. A small correction has to be made to 25° similar to that employed for the work of Gibson and Adams. Bechtold and Newton (1940) have measured the vapour pressure of barium chloride solutions at 25° by a dynamic method and their measurements at three concentrations are pertinent to this discussion. To utilise them it was necessary to determine the isopiestic ratio between sodium chloride and barium chloride. The requisite measurements were made, and the results are given in Table IV. The barium chloride used was “Baker's Analyzed” material, recrystallised three times from water and used in the form of a stock solution whose strength was determined by the method recommended by Tippetts and Newton (1934), which was found to give very satisfactory results. It was not found possible to represent the isopiestic results by a simple formula, but from a large scale graph of R against mBacl2 it was possible to determine the concentrations of three solutions of sodium chloride of vapour pressures equal to those recorded by Bechtold and Newton for their three barium chloride solutions.

Table IV. Isopiestic Ratios of Sodium and Barium Chloride at 25°. mBaCl2 R 0.8497 1.4466 1.0380 1.4719 1.3472 1.5101 1.5318 1.5308 1.7813 1.5494 0.8862 1.4518 1.2038 1.4937 1.3614 1.5130 1.6147 1.5371 1.7884 1.5476 0.9193 1.4586 1.2133 1.4944 1.3965 1.5171 1.6169 1.5353 0.9726 1.4636 1.2578 1.5003 1.4002 1.5169 1.6400 1.5381 R = mNaCl/mBaCl2 The vapour pressures of sulphuric acid solutions have been measured by Grollman and Frazer (1925) and by Shankman and Gordon (1939), in both cases by the static method. The isopiestic ratio of sulphuric acid and sodium chloride has been measured by Scatchard, Hamer and Wood, but at somewhat widely spaced concentrations. A few more measurements have been made and are recorded in Table V. There is no simple analytical relation between the molality and the isopiestic ratio, but a plot of (mNaCl/mH2SO4) — 0.1 mH2SO4 against mH2SO4 is sufficiently sensitive to enable calculation to be made of the molalities of sodium chloride solutions whose vapour pressures are equal to the sulphuric acid. Table V. Isopiestic Ratios of Sodium Chloride and Sulphuric Acid at 25°. mH2SO4 R 2.0831 1.2585 3.5567 1.3677 4.0465 1.3949 3.0051 1.3331 3.5738 1.3679 4.3242 1.4105 3.1495 1.3429 3.9005 1.3890 4.3481 1.4095 3.4061 1.3586 3.9455 1.3891 4.3537* 1.4118 R = mNaCl/mH2SO4 * In equilibrium with saturated sodium chloride at 6.1467 M. This has been done for each of the concentrations of sulphuric acid at which measurements were made by Grollman and Frazer and by Shankman and Gordon. It is clear that one of the measurements of the former is seriously in error, and this has not been considered further. Finally there are the e.m.f. measurements of Harned and Cook on cells without transport containing potassium chloride, from which water activities in solutions of this salt can be calculated by the method of Stokes. Corresponding to each concentration measured by Harned and Cook there is a solution of sodium chloride of the same vapour pressure, whose concentration is determined by isopiestic work, details of which are given in Appendix I. The results in Table II and Fig. 1 have been derived from eight distinct sources supplemented by four sets of isopiestic ratios and the agreement indicated by Fig. 1 is most encouraging. The selection of the best curve to be drawn through these points is a matter of

personal judgment, but the scatter of the points does not allow much latitude, and it is probable that different weightings would yield substantially the same result. The method employed consisted in plotting each independent set of results separately and drawing a curve through the points from which values were read at round concentrations (each 0.2M). and from this collection of smoothed values a weighted mean was calculated. To each set of determinations a weight was attached proportional to the number of measurements made over each unit of concentration. Thus five measurements between 1 and 3.5 M would be given the same weight in their range of concentration as ten measurements between 1 and 6 M. These weighted means are given in Appendix II, together with the water activities aw or the relative vapour pressure, p/p°, and the activity coefficients evaluated by the method of Randall and White (1926). The agreement between the osmotic coefficients read from Fig. 1 and those observed experimentally is as follows:— Investigators. Number of Measurements. Mean Deviation from Curve. Negus 9 0.002 Olynyk and Gordon 15 0.002 Gibson and Adams 1 < 0.001 Lovelace, Frazer and Sease 9 0.001 Bechtold and Newton 3 0.003 Harned and Cook 6 0.001 Grollman and Frazer 5 0.003 Shankman and Gordon 7 0.003 There are thus eight independent but inter-related results from different laboratories and involving different experimental methods and techniques. As these eight sets lead to osmotic coefficients of sodium chloride in excellent agreement, as witnessed by Fig. 1, the weighted mean should be reliable. It is proper, however, to mention that there are some results which do not support this conclusion. The e.m.f. results of Harned, et al. on sodium chloride, sodium bromide and potassium bromide are in good agreement with the curve of Fig. 1 up to a concentration of 2M, the average deviation being less than 0.002 in φ. At 2.5M and higher concentrations, however, these e.m.f. results correspond to uniformly higher osmotic coefficients, the average discrepancy being 0.006 in φ. It is possible that this can be attributed to solubility of silver halide from the electrodes of their cells, and to test this isopiestic measurements were made on solutions of each of these four alkali halides against the corresponding halide solution saturated with silver chloride or bromide. In the case of sodium chloride no difference could be detected in the concentration of sodium chloride solutions and those of the same vapour pressure saturated with silver chloride. This was also true for potassium chloride. With potassium bromide, however, a solution of 3.8345M KBr without silver bromide was found to have the same vapour pressure as a solution of 3.8657M KBr saturated with silver bromide, a difference of 0.8%. Similarly a solution of 4.4595M NaBr was found to have the same vapour

pressure as 4.4724M NaBr solution saturated with silver bromide, a difference of 0.3%. Thus the presence of silver bromide lowers the isopiestic ratio of sodium chloride to either of these bromides—i.e. the apparent osmotic coefficients of the bromide solutions are raised by the addition of silver bromide, and any deductions that are made about the osmotic coefficient of sodium chloride from experiments on the bromides in contact with silver bromide will result in high osmotic coefficients. This is what is observed when using the e.m.f. data of Harned et al. on sodium and potassium bromide: osmotic coefficients of sodium chloride deduced therefrom are high by about 0.6%. A reasonable explanation is therefore available which gives the direction of the discrepancy to be expected and predicts the order of magnitude of the effect. A precise quantitative calculation of the effect of electrode solubility on the e.m.f. data is not possible because a liquid junction potential of unknown magnitude must have been introduced, but it is satisfactory to have explained the effect semi-quantitatively. Gibson and Adams, in addition to their static vapour pressure determination at 20.28°, made measurements by a dynamic method at 25°. Their osmotic coefficient at 6.004M lies only 0.0013 above the curve in Fig. 1, but at 5.390, 4.794 and 4.274M their osmotic co-efficients are higher by 0.011, 0.010 and 0.007 respectively. Finally, there are the vapour pressure measurements of Pearce and Forden-walt (1932) on sodium chloride by a dynamic method. At 5.5 and 6M their results appear to be high by 0.015 in φ, but at 2.5M the discrepancy is reversed and their results are low by almost the same amount. One further check on these results was possible since Gibson and Adams, in addition to their measurements on sodium chloride, reported that at 20.28° the water activity of 4.116M lithium chloride was 0.8057. In order to incorporate this determination, a few measurements were made of the isopiestic concentrations of lithium and sodium chloride, using lithium chloride prepared by neutralisation of Eimer and Amend's lithium hydrate, the salt being re-crystallised four times from water. The following pairs of solutions were found to have the same vapour pressure: 3.744, 4.571; 3.879, 4.755; 3.940, 4.839; 4.203, 5.194; 4.465, 5.558, the first of each pair of figures being the molality of lithium chloride and the second that of sodium chloride. It follows that at 20° 4.116M lithium chloride has the same vapour pressure as 5.079M sodium chloride, whose water activity should be 0.8057 at 20° and 0 8052 at 25°. That calculated from Fig. 1 is 0.8032, which is in fair agreement with that derived from the data of Gibson and Adams combined with isopiestic measurements. OSMOTIC PROPERTIES OF POTASSIUM CHLORIDE SOLUTIONS AT 25°. From the properties of sodium chloride solutions derived above and the isopiestic ratio of this salt to potassium chloride, given in Appendix I, the water activity, osmotic coefficient, activity coefficient and relative molal vapour pressure lowering of the latter can be calculated. These are given in Appendix II.

Acknowledgments. The author wishes to thank Professor H. S. Harned, of Yale University, and Professor A. R. Gordon, of the University of Toronto, for many interesting discussions of this problem, Mr. R. H. Stokes, for considerable help in the calculations, and Yale University for the grant of a Sterling Fellowship, during the tenure of which part of this work was done. Appendix I. The Isopiestic Ratio of Potassium and sodium chloride at 25°. Considerable research has been carried out on this ratio, partly because it is of importance in setting up a set of standard values for potassium chloride once those for sodium chloride have been decided and also because it enables an estimate to be made of the reliability of the isopiestic method. An extensive series of measurements was made at the Sterling Chemistry Laboratory of Yale University in 1940. Potassium and sodium chloride of “Baker's Analyzed” origin were used, each being recrystallised three times and dried in an electric oven at 300° for 24 hours. Each was of 99.98% purity judged by chloride analysis. Solutions above 1.5M were made by direct weighing of the salts into the dishes; stock solutions were used at lower concentrations, each solution being analysed by chloride determinations. Three different types of dishes were used: (a) round silver dishes of 4 cm. diameter, weighing about 35 grams, referred to subsequently as “light” silver dishes; (b) the set of “heavy” silver dishes, square in shape, weighing 120 grams, previously used by Owen and Cooke (1937); (c) platinum dishes, 2.5 cm. square, weighing 35 grams. Experience showed that the light silver dishes reached equilibrium in 24 hours if the concentrations were above 1M. With diminishing concentrations the time during which the dishes were rocked in the thermostat had to be increased, six days being allowed at 0.1M. In the case of the platinum dishes equilibrium was reached more slowly, as might be expected from the lower thermal conductivity of platinum. Twenty-four hours were sufficient only at concentrations above 2M; between 1M and 2M 48 hours were allowed and up to eight days were required at the lowest concentrations. It was surprising to find that the heavy silver dishes, with thick sides and bases, also required long periods to attain equilibrium, the times allowed being comparable with those for the platinum dishes. Using various combinations of these dishes as indicated in Table VI, Series 1–4, 39 measurements were made at concentrations below 1M. No simple equation relating the isopiestic ratio, R = mkci/mNaCl, to the molality could be found, but interpolation can be made by means of the deviation function (R — 0.05 mNaCl). This is illustrated in Fig. 2, which also includes the data of Gordon on very dilute solutions and those of Janis and Ferguson and of Scatchard, Hamer and Wood above 0.3M. Considering the difficulty of making measurements in dilute solutions, the scatter of these points

Fig. 2.—Deviation Function for Isopiestic Ratio of Potassium and Sodium Chloride below 1M at 25°. ▪ Gordon. ⋆ Janis and Ferguson. ◊ Scatchard, Hamer and Wood. ○ Robinson, using four light silver dishes. • Robinson, using four platinum dishes. □ Robinson, using four heavy silver dishes. X Robinson, using two heavy silver dihses and two platinum dishes. R = mkci/mNaCl is such that considerable confidence can be placed in the curve drawn through them, and it is believed that an isopiestic ratio can be read from this curve with an error of not more than 0.0005. At higher concentrations 23 measurements were made, again using different combinations of dishes. The results are reported as Series 5–8 in Table VI. In the last few months 17 more measurements were made at the University College, Auckland, using only the “light” silver dishes, with B.D.H. “A.R.” salts, each recrystallised twice, dried for a few hours at 300° and then fused in an electric furnace. These measurements are referred to as Series 9 in Table VI. The isopiestic ratio above 1M conforms very closely to a straight line, and in Table VI there are recorded the deviations between the observed isopiestic ratio and that calculated by the equation: R = 1.0104 + 0.03174 mNaCl, the parameters being obtained by the method of least squares. For this the results of Janis and Ferguson and of Scatchard, Hamer and Wood were included. It has been shown that a more complicated equation, such as a quadratic, represents the experimental results no

better.The deviations may be analysed as follows:— Series. No. of Results. Maximum Deviation. Mean Deviation. 5 10 0.0012 0.0004 6 6 0.0011 0.0006 7 4 0.0015 0.0009 8 3 0.0011 0.0007 9 17 0.0013 0.0006 5–9 40 0.0013 0.0006 Scatchard, Hamer and Wood 8 0.0009 0.0004 Janis and Ferguson 7 0.0016 0.0008 It is therefore reasonable to believe that isopiestic values calculated by the above linear equation represent the true values to within 0.05%. Moreover, it is demonstrated that the experimental work is reproducible, closely concordant results having been obtained in four laboratories using different modifications of the technique. Table VI. Isopiestic Ratios of Potassium and Sodium Chloride at 25%°. A. Concentrations below 1M. mNaCl R Series 1. Four Platinum Dishes. 0.15270 1.0113 0.31516 1.0174 0.31968 1.0171 0.75075 1.0333 Series 2. Four Heavy Platinum Dishes. 0.13438 1.0097 0.17889 1.0116 0.68947 1.0313 0.79616 1.0356 0.95396 1.0397 Series 3. Four Light Silver Dishes. 0.10723 1.0067 0.18674 1.0126 0.25018 1.0140 0.36953 1.01197 0.49817 1.0247 0.63956 1.0307 0.89764 1.0386 0.10994 1.0076 0.20896 1.0128 0.19075 1.0168 0.44071 1.0219 0.52433 1.0253 0.72870 1.0327 0.95030 1.0413 0.11050 1.0075 0.23124 1.0146 0.33750 1.0175 0.44204 1.0218 0.60966 1.0286 0.81340 1.0366 0.17140 1.0124 0.24198 1.0138 0.36204 1.0202 0.48525 1.0237 0.62918 1.0287 0.89636 1.0380 Series 4. Two Heavy Silver and Two Platinum Dishes. 0.61794 1.0291 0.92922 1.0396 0.94434 1.0404 0.99505 1.0421 Concentration above 1M. mNaNl R ▵ Series 5. Four Platinum Dishes. 1.0570 1.0439 0 1.6768 1.0632 +4 3.4513 1.1201 -2 4.0120 1.1377 0 1.0919 1.0452 -2 2.5692 1.0916 +3 3.7549 1.1301 -5 1.6355 1.0635 -12 2.6208 1.0931 +5 3.8473 1.1330 -5 Series 6. Four Heavy Silver Dishes. 1.1750 1.0477 0 1.3428 1.0528 +2 1.2276 1.0501 -7 3.7214 1.1276 +9 1.2846 1.0519 -7 4.0858 1.1390 +11 Series 7. Four Light Silver Dishes. 1.0616 1.0445 -4 3.5650 1.1251 -15 1.1314 1.0470 -7 3.0360 1.1078 -10 Series 8. Two Heavy Silver and Twi Platinum Dishes. 1.5406 1.0590 +3 2.1603 1.0784 +6 2.5808 1.0914 +11 Series 9. Four Light Silver Dishes. 1.0055 1.0411 +12 1.0628 1.0445 -4 1.7400 1.0654 +2 2.6616 1.0954 -5 3.3387 1.1162 +2 3.9322 1.1343 +9 1.0439 1.0439 -4 1.3566 1.0539 -5 2.2485 1.0814 +4 2.7996 1.0985 +7 3.3755 1.1179 -4 4.1985* 1.1450 -13 1.0478 1.0435 +2 1.6978 1.0649 -6 2.6062 1.0926 +5 2.9541 1.1050 -8 3.5275 1.1231 -7 * In equiliburin with saturated KCI at 4.8073M. R = mkci/mNaCl ▵ X 10 = R (cale.) —R (obs) where R (cale.) = 1.0104 + 0.03174 mNaCl valid above 1M.

Appendix II. Water Activities, Osmotic Coefficients, Activity Coefficients, and Relative Molal Vapour Pressure Lowerings of Sodium and Potassium Chloride Solutions at 25°. Sodium Chloride Potassium Chloride m aw φ 1+logγ p°-p/M p° aw φ 1+log γ p°-p/M p° 0.1 0.996646 0.9324 0.8912 0.03354 0.996668 0.9266 0.8864 0.03332 0.2 .993360 .9245 .8661 .3320 .993443 .9130 .8562 .03279 0.3 .99009 .9215 .8511 .03303 .99025 .9063 .8573 .03250 0.4 .98682 .9203 .8406 .3295 .98709 .9017 .8233 .03228 0.5 .98355 .9209 .8322 .03290 .98394 .8989 .8124 .03212 0.6 .98025 .9230 .8278 .03292 .98078 .8976 .8038 .03203 0.7 .97692 .9257 .8240 .03296 .97763 .8970 .7967 .03196 0.8 .97359 .9288 .8211 .03301 .97448 .8970 .7907 .03190 0.9 .97023 .9320 .8190 .03308 .97133 .8971 .7854 .03186 1.0 .96686 .9355 .8175 .03314 .96818 .8974 .7809 .03182 1.2 .9601 .9428 .8158 .03325 .9619 .8986 .7733 .03175 1.4 .9532 .9513 .8159 .03343 .9556 .9010 .7676 .03171 1.6 .9461 .96616 .8178 0.3369 .9492 .9042 .7634 .03175 1.8 .9389 .9273 .8208 .03394 .9428 .9081 .7603 03178 2.0 9316 .9833 .8245 .03420 .9364 .9124 .7580 .03180 2.2 .9242 .9948 .8291 .03445 .9299 .9168 .7564 .03186 2.4 .9166 1.0068 .8344 .03475 .9234 .9214 .7554 .03192 2.6 .9089 1.0192 .8402 .03504 .9169 .9264 .7549 .03198 2.8 .9011 1.0321 .8466 .03532 .9103 .9315 .7548 .03204 3.0 .8932 1.0453 .8335 .03560 .9037 .9367 .7550 .03210 3.2 .8851 1.0587 .8608 .03591 .8971 .9421 .7557 0.3216 3.4 .8769 1.0725 .8684 .03621 .8904 .9477 .7567 .03223 3.6 .8686 1.0867 .8766 .03650 .8837 .9531 .7578 .03230 3.8 .8600 1.1013 .8852 .03684 .8770 .9588 .7593 .03237 4.0 .8515 1.1158 .8939 .03713 .8702 .9647 .7610 .03245 4.2 .8428 1.1306 .9029 .03743 .8634 .9707 .7629 .03252 4.4 .8339 1.1456 .9122 .03775 .8566 .9766 .7649 .03259 4.6 .8250 1.1608 .9218 .03804 .8498 .9284 .7670 .03266 4.8 .8160 1.1761 .9315 .03833 .8429 .9883 .7693 .03273 5.0 .8068 1.1916 .9515 .03864 5.2 .7976 1.2072 .9517 .03892 5.4 .7883 1.2229 .9620 .03920 5.6 .7788 1.2389 .9726 .03950 5.8 .7693 1.2548 .9833 .03977 6.0 .7598 1.2706 .9940 .04003 Vapour pressures in columns 2, 5, 6, and 9 are tabulated relative to p° = 23.756 mm. for pure water at 25°. References. Allgood, R. W. and Gordon, A. R., 1942. J. Chem. Physics, 10, 124. —— Le Roy, D. J., and Gordon, A. R., 1940. ibid., 8, 418. Bechtold, M. F. and Newton, R. F., 1940. J. Amer. Chem. Soc., 62, 1390. Brown, A. S. and MacInnes, D. A., 1935. ibid., 57, 1356. Gibson, R. E. and Adams, L. H., 1933. ibid., 55, 2679. Gordon, A. R., 1943. ibid., 65, 221. Grollman, A. and Frazer, J. C. W., 1925. ibid., 47, 712. Harned, H. S., 1929. ibid., 51, 416. —— and Cook, M. A., 1937. ibid., 59, 1290. —— and Cook, M. A., 1930. ibid., 61, 495.

—— and Crawford, C. C., 1937. ibid., 59, 1903. —— and Nims, L. F., 1932. ibid., 54, 423. Hornibrook, W. J., Janz, G. J., and Gordon, A. R., 1942. ibid., 64, 513. Janis, A. A., 1935. Trans. Roy. Soc. Canada, 29. 87. —— and Ferguson, J. B., 1939. Can. J. Research, 17B, 215. See also Janis, A. A., Sheffer. H., and Ferguson, J. B., 1939, ibid., 17B, 336. Janz, G. J. and Gordon, A. R., 1943. J. Amer. Chem. Soc., 65, 218. Jones, J. H., 1943. ibid., 65, 1353. Longsworth, L. G., 1932. ibid., 54, 2741. Lovelace, B. F., Frazer, J. C. W., and Sease, V. B., 1921. ibid., 43, 102. Mason, C. M. and Gardner, H. M., 1936. J. Chem. Education, 13, 188. See also Mason. C. M. and Ernst, G. L., 1936. J. Amer. Chem. Soc., 58, 2032; Mason, C. M., 1938. ibid., 60, 1638. Negus. S. S., Thesis, Johns Hopkins University, 1922. See also Frazer, J. C. W., Direct Measurement of Osmotic Pressure, Columbia University Press, New York, 1927 Olynyk, P. and Gordon, A. R., 1943. J. Amer. Chem. Soc., 65, 204. Owen, B. B. and Cooke, T. F., 1937. ibid., 59, 2273. Pearce, J. N. and Fordenwalt, F. See Pearce, J. N. and Nelson, A. F. 1932. ibid., 54, 3544. Phillips, B. A., Watson, G. M., and Felsing, W. A., 1942. ibid., 64, 244; see also Cudd, H. H., and Felsing, W. A., 1942, ibid., 64, 550. Randall, M. and White, A. M., 1926. ibid., 48, 2514. Robinson, A. L., 1932. ibid., 54, 1311. Robinson, R. A., 1935. Trans. Faraday Soc., 35, 1217. —— and Harned, H. S., 1941. Chem. Rev., 28, 419. —— and Sinclair. D. A., 1934. J. Amer. Chem. Soc., 56, 1830. Rossini, F. D., 1931. Bur. of Standards J. Research, 7, 47. Shankman, G., Hamer, W. J., and Wood, S. E., 1938. J. Amer. Chem. Soc., 60, 3061. —— and Presentiss, S. S., 1933. ibid., 55, 4355. Shankman, S. and Gordon, A. R., 1939. ibid., 61, 2370. Shedlovsky, T. and MacInnes, D. A., 1937. ibid., 59, 503. Stokes, R. H. ibid., in the press. Tippetts, E. A. and Newton, R. F., 1931. J. Amer. Chem. Soc., 56, 1675.