THE DISSOCIATION CONSTANTS OF PHOSPHORIC ACID. 423

L.-The Dissociation Constants of Phosphoric Acid. By EDMUND BRYDGES RUDHALL PRIDEAUX and ALFRED THOMAS

WARD. THE '' apparent " constants of a dibasic acid may in part be calculated from the simplified equations

E l = hRjl - R . * (la) k2 = h(R - 1),'2 - R . (1b)

R is the ratio of equivalents of alkali to mols. of acid. ( la) is used when h is large relatively to k, ; (lb) when h2 is small relatively to k,. k,,k, are replaced by k& of phosphoric acid.

The Xecond Constant.-The usually accepted value, 1.95 x 10-7 (Abbott and Bray), reproduces fairly well the neutralisation curve of 0-1 molar acid. But for exact work the variations with concen- tration and with R must be taken into account.

Variation with R.-At the point NaH2P0,, R = 0, E, = h2/C, Different experimenters give discordant values of k, ; for example, 8-6 x 10-8 (Salm), 1.47 x (Sorensen), 1.2 to 4.8 x 10-7 (Prideaux), 8 x 10-7 (Blanc, J . Chim. Phys., 1920, 18, 34). At higher degrees of neutralisation, k, is accurately determined by equation (1 a).

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424 PFtIDEAUX AXD WARD :

Sorensen’s values (C = 0.0667) :

R ......... 0.01 0.05 0.20 0.5 0.8 0.95 lo7 x k ... 1-16 1.35 1.44 1-54 1.67 1.74

Clark and Lubs’s values (C = 0.05) : R ......... 0.17 0.25 0.4 7 0.59 0.70 0.90 107 x E . . . 1.3 1.3 1.425 1.46 1.48 1.49

Thus the apparent constants and R increase together ; this effect is more marked at higher concentrations.

Variation with C.-The results used are those already quoted , together with those of Michaelis and Kruger (Biochem. Z., 1921, 119, 307) and one of ours; all at a constant R = 0.5.

C ......... 0-10 0.0667 0-05 0.0335 0.02 0.0133 0.0033 0.0013 lo’ x E . . . 2.0 1.54 1-43 1.25 1.15 1-02 0.853 0.817

Value of k, at very Low Concentrations.-In the mixture a t R = 0.5 the buffer pa is very close to neutrality and therefore the buffer effect will persist down to low concentrations. Advantage was taken of this fact by Michaclis t o obtain a limiting value of k, = 0.80 x lo-’.

But such an extrapolation should, if correctly carried out, always lead .to pk = pE of pure water. A solution of which the regulated pH is far from 7 will begin to lose its regulating power a t higher concentrations; the actual constant of the acid becomes less important in determining p,, whilst the term containing E, and C becomes more important. The p-C curves will alter their direction and, so far as they allow a good extrapolation, will also lead to pk = 7, in this casc far from the true constant. By the determination of p H in presence of neutral salts and extrapolation of the graph so obtained to zero salt concentration, Afichaelis and Garmendia (Biochem. Z., 1914, 67, 431) found that the limiting k2 is 0.58 x 10-7. This would appear to be a sounder method than the above.

The Second Constant deduced from Activity Coe,cients.-We make use of the definitions, etc., given in Lewis and Randall’s “ Thermo- dynamics.” The ionic strength is equal to the stoicheiometrical molality of the ion multiplied by the square of its valency, and the total ionic strehgth is equal to the sum of the strengths of kations and anions divided by 2. In dilute solutions, the activity coefficients of a given strong electrolyte are the same in all solutions of the same ionic strength.

The activity coefficients of uni-, bi-, and ter-valent anions at the calculated ionic strengths are taken to be those of ClO,’, SO4”, and Fe(CN)G”’, respectively. Since the ionic strengths of even the most

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THE DISSOCL4TION CONSTANTS OF PHOSPHORIC ACID. 425

dilute solutions are in some cases beyond the highest value (0.1) given in the table, i t has been necessary to extrapolate slightly. The concentrations being far too high in the case of most of the results quoted above, we have determined the following in 0.02 molar solutions.

n ......... 0.6 0.75 1.00 1.50 2.00 p ~ r ......... (3.94 7.41 8.70 11.57 11-98

The “ activity ” second constants are caIculat,ed from the first two, together with those of iV1ichaelis.

G ......... 0.00335 0.020 0.0134 0.00335 10’ x kis 5.72 6.05 5.82 5-85

The closer approach to constancy of k, lends support to the view that this is the true constant.

The Third Constant.-The value k3 = 3.6 x 10-13 obtained by means of the conductivities and distribution ratios of ammonium phosphate solutions is quite incompatible with the values of h occurring during the neutralisation of phosphoric acid by strong alkali (T., 1911, 99, 1224). Since the former value is still given in text-books, i t seems desirable to confbm this conclusion from a wider selection of material.

The point Na,HPO, is difficult to define experimentally, but gives k3 approximately. From Sorensen’s h at R = 1.0 and the equation h, = k2k3, using k2 = 1.74 x (at R = 0.95), we have Jc3 = 2-6 x 10-l2.

The mean value calculated from the results of Ringer, Salm, and Prideaux at C = 0.1 (ca.) and R = 1.03 to 1-33 is k3 = 2.8 x 10-12 (equation 1 b) .

In dealing with dilute solutions which approach N%PO, in composition, a correction is introduced in the form k3 = h(x - [OH])/ (x $- [OH]), in which x = R - 1.

Authors. Ringer. Blanc. Authors. Ringer. c‘ ......... 0.02 0.075 0.012 0.02 0.06 R ......... 1-5 1.67 2.0 2.0 2.0 10l2 x h 2.7 1.7 I 1.05 0.87 1W2 x k 1.54 2.45 2-3 2.0 5.3

Note.-Thc alkalinity of the solution of trisodium phosphate was determined by Blanc with the aid of indicators and k was calculated by the ordinary equation of hydrolysis.

The Third Constant deduced from Activity Coeficients.-The last two results in our table are available. A second approximation is required in order to obtain the amount of sodium hydroxide corresponding to [OH]. At C = 0.02, R = 1-5, h = 2.7 x 10-12,

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426 PRIDEAUX AND WARD : CALCULATIONS ON THE

[OH] = 2.75 x 10-3; the total ionic strength is 0-084 and the activity coefficients are : [OH] = 0.85, [HPO,"] = 0.28, and [PO4"'] = 0.22. The activities of [HPO,"] and [PO4"'] are 0.0138 and 0.00672, respectively, whence k is 1.3 x 10-l2. From the last result k is 1.0 x 10-l2. This is the limiting constant.

UNIVERSITY COLLEGE, NOTTINGITAM. [Beceived, July 30th, 1923.1

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