THE DISSOCIATION CONSTANT O F BORIC ACID. 69

IX. -Th,e Dissociation Constmt of Boric Acid. By EDMUND BRYDGES RUDHALL PRIDEAUX and ALFRED

THOMAS WARD.

ON account of their utility as buffer mixtures, various borate solutions have been standardised with the hydrogen electrode, and from these results the apparent dissociation constants of boric acid in these solutions may be calculated. Such constants depend on the agreed status of the hydrogen electrode as repre- senting the best measure yet available of the activity of the hydrogen- ion. If the activities, or effective concentrations, of the ion and the undissociated acid are put equal to the neutralised and the unneutralised part of the acid respectively, complete dissociation of the salts is assumed. The constants are then apparent constants, useful in the calculation of the p H of mixtures not too far removed in concentration from the standards. The apparent constant is calculated by the usual equation, which is conveniently stated in

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70 PRIDEAUX AND WARD :

the form k = Rh/(1 - R), in which R is the ratio of equivalents of alkali to mols. of acid.

It is usually found that E varies with (1) degree of neutralisation, (2) total concentration, and (3) presence of neutral salts.

(1) The following results refer to borax, Na~H,BO,,H,BO,, in which R is 0.5 and h = k , p H = p k .

Schmidt and Finger. Sorensen. Palitzsch. Clark and Lubs. C 0.25 0.10 0.05 0-05 (0.2 KC1) PH 9.3 9-24 9.24 9-14 k x 1O1O 5.0 5.6 5.6 7-2

The authors, at C = 0.02, find p~ = 9-02 and k x 1O1O = 9.55.

A decrease in total concentration thus brings about an increase in E . This change is in the opposite direction to that which has been noted in the case of phosphoric acid (second constant).

The result for boric acid may perhaps be attributed to the break- ing up of the anionic complexes H,BO,',nH,BO,, which are formed in partly neutralised borate solutions, especially a t higher con- centrations (Auerbach, 2. anorg. Chem., 1904, 37, 352 ; Prideaux, Trans. Faraday Xoc., 1915, 15, 76).

In the most dilute solutions the constant is not far from the conductivity constant, 1.7 x

(2) The change in k with degree of neutralisation R may be obtained from the results of Palitzsch and of Clark and Lubs.

We have added some determinations in more dilute solutions. Palitzsch's solutions were made from 0-2M-boric acid mixed with 0-OZM-borax. The total concentrations were therefore not constant. C.C. of b0raxfc.c. of boric acid 0.3/9-7 9.6/9.4 8-0/2.0 9.0/1-0 C 0.196 0.195 0.080 0.065 R 0.00383 0.007 0.25 0.345 k: x 1010 6.5 5.75 3.6 4.1

Clark and Lubs's solutions were made by adding 0-2N-sodium hydroxide to 50 C.C. of O.2M-boric acid and diluting to 200 C.C.

They were therefore 0-05 molar with respect to borate. C.C. of sodium hydroxide/50 C.C. of boric acid 2.61 12-00 21-30 26-70 43.90 PH 7.8 8.6 9.0 9.2 10.0 k x 1010 8.4 7.9 7.4 7.4 7.1

Our solutions were 0.02 molar with respect to borate and 0-06 molar with respect to sodium chloride. The temperature was about 18".

R 0.25 0.50 0-75

Pr 9.02 9.02 9.08 kXl0" 9.6 9.6 8.25

PR 8-54 9.02 9.56

In each series an increase in R is associated with a decrease in k. Also, by comparison (at corresponding concent'rations) of

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THE DISSOCIATION CONSTANT O F BORIC ACID. 71

series 1 with 2 and 3 respectively, it is seen that the addition of neutral salt increases k.

The Constant of Boric Acid Calculated from the Ionic Activities. The activity of the hydrion is taken as that given by the hydrogen

electrode, and the activities of the H,BO,’-ion as that of CIO,’ in solutions of the same ionic strength, as given in the tables of Lewis and Randall’s “ Thermodynamics.” * By means of the activity coefficients, a, we get an expression for the ion activity constant k’ = ha[A]/a[HA].

The activity of the undissociated molecule, in this case H$O,, may perhaps be taken as 1 in dilute solutions by analogy with glycerol and other non-electrolytes. In more concentrated solu- tions it would be greater than unity. The equation given in Lewis and Randall’s book (p. 288), when applied to the freezing- point depression of a 0-066 molar solution of boric acid, 0.129” (Juttner-Arrhenius), gives an activity coefficient of 1.094. On this account, and because the ionic strengths in the buffer solutions quoted above are too high for the application of Lewis and Randall’s tables, the calculations must be restricted to the solutions measured by us.

At R = 0.5, Cborate = 0.02 and CNaCl = 0.06. [H,BO,’] 0.01. The total ionic strength is equal to half the sum of Na’ = 0.07,

The activity of H,BO,’ is taken as that of ClO,’ at this ionic C1‘ = 0-06, H,BO,‘ = 0.01, that is, to 0.07.

strength, that is, 0.65.

The ion activity constant which allows for the effect of all ions present is thus smaller than the apparent constant calculated for the dilute borate. It happens to agree with the constant usually attributed to boric acid. The ion activity constant still shows a fall at higher values of R. We consider that this is to be accounted for in the same manner as the fall in the apparent constant. The correction for ionic strengths does not take account of complex ions.

UNIVERSITY COLLEGE, NOTTINCHAM.

* In these tables the concentrations are expressed in molalities or mols. We have expressed them in mols. per litre, the

[Received, July 25th, 1923.1

in 1,000 grams of water. numerics being almost identical in such dilute solutions.

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