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Volume 76, 1946-47
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The Vapour Pressures of Perchloric Acid Solutions at 25°.

[Read before the Auckland Institute, February 20, 1946; received by the Editor, March 18, 1946.]

Summary.

By means of isopiestic measurements, the aqueous vapour pressures of perchloric acid solutions have been determined at 25° up to a concentration of 16 M. The results have been expressed in terms of water activities (relative humidities), osmotic coefficients and activity coefficients.

Introduction.

Perchloric acid is an electrolyte whose osmotic properties have not been investigated as thoroughly as might be expected for a substance which is easily obtained in a state of purity, has considerable industrial use and bears a structural relation to hydrochloric acid of significance to the theory of ionic solutions. No study using modern technique has been made of the freezing-point depressions or boiling-point elevations of perchloric-acid solutions; the absence of any electrode reversible to the perchlorate ion precludes the use of a concentration cell without transport; two investigations have been made by Schuhmann (1924) and by Popoff, Riddick, Wirth and Ough (1931) of the cell with transport: H2 | HCl | HClO4 | H2, from which it was concluded that up to a concentration of 1M the osmotic properties of hydrochloric and perchloric acid were identical within the limits of experimental error. It is to be noted that this cell contains a liquid junction whose potential has to be calculated by a formula which can only be approximate; any conclusions drawn from potential measurements on this cell must be subject to this approximation. Pearce and Nelson (1933) made vapour-pressure measurements by their dynamic method; the experiments were carried up to a concentration of 12M and the values of the water activity which they observed were converted by calculation to activity coefficients. These, however, were widely different from those calculated from the same experimental results by Redlich and Rosenfeld (1936). We have now made isopiestic vapour-pressure measurements of perchloric acid solutions up to 16M at 25°.

Experimental.

The technique of isopiestic measurements has been described by Robinson and Sinclair (1934). Two sources of perchloric acid were used: Mallinckrodt's 20 per cent. Analytical Reagent and Baker's 60 per cent. “Analyzed” Reagent. As reference electrolytes sodium chloride and sulphuric acid were used; the sodium chloride was a

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sample similar to that used by Robinson (1945) and the sulphuric acid solutions were made up from Baker's “Analyzed” concentrated acid. The stock solutions of perchloric acid and sulphuric acid were analysed by the addition of a slight excess of the stock solution to weighed amounts of sodium carbonate (dried at 265°), the titration being completed, after boiling out carbon dioxide, with dilute sodium hydroxide solution using bromthymol blue as indicator. The accuracy of the method was checked by a parallel analysis of a hydrochloric acid solution whose concentration had been determined by gravimetric silver chloride determinations. In the isopiestic work the acid solutions were contained in platinum dishes and the sodium chloride solutions in silver dishes. All measurements were made at 25°. The experimental results are given in Table I, expressed as molalities of pairs of solutions of equal-vapour pressure, perchloric acid and sodium chloride in the first series, perchloric acid and sulphuric acid in the second. The proper vacuum corrections were applied to all weighings.

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Table I.—Molalities of Isopiestic Solutions at 25°.
mHClO4 mNaCl
0.1161 0.1183
.1178 .1199
.2647 .2743
.3336 .3472
.3815 .3991
.4747 .5011
.5063 .5368
.6685 .7183
.6753 .7255
.9221 1.014
1.106 1.237
mHClO4 mNaCl
1.162 1.308
1.512 1.757
1.707 2.010
2.015 2.425
2.450 3.029
2.560 3.186
2.584 3.223
2.715 3.410
2.930 3.719
3.213 4.132
3.282 4.245
mHClO4 mNaCl
4.001 5.332
4.434 6.023
4.505 6.128
4.525 6.152
mHClO4 mH2SO4
4.399 4.233
5.275 5.129
6.268 6.183
7.011 7.008
8.007 8.278
mHClO4 mH2SO4
8.286 8.555
9.515 10.182
9.978 10.813
10.852 12.058
11.140 12.494
11.468 13.013
12.527 14.677
13.611 16.480
14.583 18.185
15.682 20.213

Calculation of Results.

The data for the first series of measurements, using sodium chloride as reference electrolyte, were plotted as a large scale graph of the isopiestic ratio, R = mNaCl/mHClO4, against mHClO4, from which values of the isopiestic ration were read at every 0.1M perchloric acid from 0.1 to 4.5M. The second series of measurements were treated by plotting the deviation function, R'-0.0289 mHClO4, against mHClO4 where R' = mH2SO4/mHClO4. Values of the isopiestic ratio to sulphuric acid were thus obtained at 0.25M intervals between 4.5 and 16M perchloric acid. Osmotic coefficients of perchloric acid were then calculated from the simple equations:

  • [The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

    ϕHClO4 = RϕNaCl,

  • [The section below cannot be correctly rendered as it contains complex formatting. See the image of the page for a more accurate rendering.]

    HClO4 = 3R'ϕH2SO4

the osmotic coefficients of the reference electrolytes being taken from the data of Robinson (1945) for sodium chloride and of Shankman and Gordon (1939) for sulphuric acid. The water activities (i.e., the relative humidities) of the perchloric acid solutions were calculated from the equation: ϕ HClO4 = (55.51/2mHClO4). In aw. Activity coefficients were calculated by the method of Randall and White (1926). The data are collected in Table II.

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Table II.—Water Activities, Osmotic Coefficients, Activity Coefficients, and Relative Molal Vapour-Pressure Lowerings of Perchloric Acid Solutions at 25°.
m aw ϕ log γ (p°-p)/Mp°
0.1 0.996579 0.9472 1.9049 0.03421
0.2 .993170 .9511 .8908 .03415
0.3 .98970 .9576 .8856 .03432
0.4 .98618 .9656 .8842 .03455
0.5 .98258 .9758 .8861 .03484
0.6 .97888 .9876 .8898 .03520
0.7 .97510 .9998 .8948 .03557
0.8 .97124 1.0125 .9006 .03595
0.9 .96727 1.0263 .9076 .03637
1.0 .96319 1.0409 .9155 .03681
1.2 .9547 1.0719 .9334 .03774
1.4 .9457 1.1064 .9542 .03877
1.6 .9364 1.1407 .9762 .03977
1.8 .9266 1.1748 .9990 .04075
2.0 .9165 1.2102 0.0233 .04175
2.5 .8891 1.3045 .0888 .04434
3.0 .8590 1.4058 .1608 .04700
3.5 .8265 1.511 .2370 .04957
4.0 .7915 1.622 .3181 .05212
4.5 .7548 1.738 .4032 .05449
5.0 .7153 1.860 .4922 .05694
5.5 .6753 1.981 .5832 .05904
6.0 .6343 2.106 .6774 .06095
6.5 .5927 2.234 .7731 .06266
7.0 .5508 2.365 .8718 .06417
7.5 .5097 2.494 .9706 .06537
8.0 .4687 2.629 1.0729 .06641
8.5 .4289 2.764 .1762 .06719
9.0 .3904 2.901 .2811 .06773
10.0 .3195 3.167 .4896 .06805
11.0 .2565 3.433 .7001 .06759
12.0 .2030 3.688 .9075 .06642
13.0 .1583 3.935 2.1124 .06475
14.0 .1223 4.166 .3108 .06269
15.0 .0931 .4.393 .5076 .06046
16.0 .0702 4.608 .6993 .05811

Discussion.

The first point of interest in these results is a comparison of the activity coefficients of perchloric acid and hydrochloric acid, which, as pointed out in the introduction, have been claimed to be almost identical. These activity coefficients are compared in Table III, the data for hydrochloric acid being taken from the paper of Harned and Ehlers (1933).

Table III.—Comparison of the Activity Coefficients of Perchloric Acid and Hydrochloric Acid at 25°.
m 0.1 0.2 0.5 1.0 1.5
γHClO4 0.803 .778 .769 .823 .923
γHCl 0.796 .767 .757 .809 .896

It will be seen that the activity coefficients are only approximately equal, that of perchloric acid being from 0.9 to 1.8 per cent. higher up to 1 M, above which concentration the values for the two acids diverge considerably.

The second point which we wish to emphasise not only demonstrates that this divergence between the activity coefficients becomes very pronounced at high concentrations, but also provides a searching

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test of a relation proposed by Åkerlöf and Thomas (1937), viz., that the logarithm of the ratio of the activity coefficients of two electrolytes is directly proportional to the molality,

  • logγHClO4/γ HCl = Bm,

the proportionality constant being characteristic of the pair of electrolytes. This equation is tested in Table IV, the last column of which gives B = 1/m. logγHClO4/γHCl; if the relation is true, the values of B should be constant. It is evident that it is not true.

Table IV.—Comparison of the Activity Coefficients at high Concentration.
m log γHClO4 log γHCl 1/m log γHClO4/γHCl
4 0.3181 0.2386 0.0199
6 0.6774 0.5057 0.0286
8 1.0729 0.7713 0.0377
10 1.4896 1.0204 0.0469
12 1.9075 1.2451 0.0552
14 2.3108 1.4429 0.0620
16 2.6993 1.6170 0.0673

The values of γHcl were taken from Åkerlof and Teare (1937).

Thirdly, in Table V we compare our results with those obtained by the dynamic vapour-pressure method. We have compared the water activities of Table II with those derived by Pearce and Newton; in making a comparison of the activity coefficients we have not used the values calculated by Pearce and Nelson which are clearly incorrect; in their place we have used the values recalculated by Redlich and Rosenfeld, referred to γ = 0.823 at 1 M.

Table V.—Comparison of Data for Perchloric Acid derived by Different Methods.
m aw (1) aw (2) γ (1) γ (3)
1 0.9632 0.9634 0.823 0.823
2 0.9165 0.9161 1.055 1.054
3 0.8590 0.8597 1.448 1.441
4 0.7915 0.7940 2.080 2.048
6 0.6343 0.6407 4.76 4.48
8 0.4687 0.4722 11.8 11.49
10 0.3195 0.3205 30.9 29.3
12 0.2030 0.2047 80.8 78.1
(1)

From Table II.

(2)

From data of Pearce and Nelson.

(3)

From data of Pearce and Nelson, recalculated by Redlich and Rosenfeld.

Up to 4 M the agreement is good, but at higher concentrations considerable differences are found.

Finally, we have examined the application of the extended Debye-Hückel equation:

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— log γ = 0.5092 √c/ (1+0.3286a√c) — Dc + log (1 + 0.036 m)

where a = mean ionic diameter and D is an empirical constant. Using the density data of Markham (1941) to convert molalities, m, to volume concentrations, c, and a value of a = 4.8 Å and D = 0.131, we obtained the following calculated values:

m 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
γ (calc.) .902 .776 .768 .767 .771 .778 .783 .797 .808 .821
γ (obs.) .803 .778 .768 .766 .769 .776 .785 .798 .808 .823

The mean diameter, 4.8 Å, is considerably greater than that found for hydrochloric acid, 4.3 Å, by Harned and Ehlers.

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Conclusions.
1.

Data for the water activities, osmotic coefficients, activity coefficients and vapour-pressure lowerings of aqueous perchloric acid solutions are available up to a concentration of 16 M at 25°. (See Table II.)

2.

The contention that the activity coefficient agrees with that of hydrochloric acid is true up to 1 M only within 0.9–1.8 per cent. Large differences are found at higher concentrations.

3.

The relation proposed by Åkerlöf and Thomas does not hold if a test is made at high concentrations.

4.

Moderate agreement is obtained with the activity coefficients of Pearce and Nelson as recalculated by Redlich and Rosenfeld.

5.

The Debye-Hückel equation is found to be applicable if the mean ionic diameter is taken to be 4.8 Å.

References.

ÅKerlöf, G., and Thomas, H. C., 1934. J. Amer. Chem. Soc., 56, 593.

—— and Teare, J. W., 1937. Ibid., 59, 1855.

Harned, H. S., and Ehlers, R. W., 1933. Ibid., 55, 2179; see also Robinson, R. A., and Harned, H. S., 1941. Chem. Rev., 28, 426.

Markham, A. E., 1941. J. Amer. Chem. Soc., 63, 874.

Pearce, J. N., and Nelson, A. F., 1933. Ibid., 55, 3075.

Popoff, S., Riddick, J. A., Wirth, V. I., and Ough, L. D., 1931. Ibid., 53, 1195.

Randall, M., and White, A. M., 1926. Ibid., 48, 2514.

Redlich, O., and Rosenfeld, P., 1936. Landolt-Bornstein, “Tabellen,” 3rd Ergänz., p. 2144.

Robinson, R. A., 1945. Trans. Roy. Soc. N.Z., 75, 203.

—— and Sinclair, D. A., 1934. J. Amer. Chem. Soc., 56, 1830.

Schuhmann, R., 1924. Ibid., 46, 58.

Shankman, S., and Gordon, A. R., 1939. Ibid., 61, 2370.