Salt of a Weak Acid and a Strong Base:

The solution of such a salt is basic in nature. The anion of the salt is reactive. It reacts with water to form a weak acid and OH- ions.

A- + H2O;   ↔   HA + OH-

                        Weak acid

Consider, for example, the salt CH3COONa. It ionises in water completely to give CH3COO- and Na+ ions. CH3COO- ions react with water to form a weak acid, CH3COOH and OH- ions.

CH3COO- + H2O  ↔   CH3COOH + OH-

C(1-x)                         Cx           Cx

Thus, OH- ion concentration increases, the solution be­comes alkaline.

Applying law of mass action,

Kh = [CH3COOH][OH-]/[CH3CO-] = (Cx×Cx)/C(1-x) = (Cx2)/(1-x) )  ...... (i)

Other equations present in the solution are:

CH3COOH ↔ CH3COO- + H+,       Ka = [CH3COO-][H+]/[CH3COOH]      ...... (ii)

H2O ↔  H+ + OH-,                 Kw = [H+][OH-]    ....... (iii)

 

From eqs. (ii) and (iii),

log [OH-] = log Kw - log Ka + log[salt]/[acid]

-pOH = -pKw + pKa + log[salt]/[acid]

pKw - pOH = pKa + log[salt]/[acid]

pH = pKa + log[salt]/[acid]

Considering eq. (i) again,

       Kh = cx2/(1-x)      or    Kh = Ch2/(1-h)

When h is very small, (1-h) → 1

or     h2 = Kh/C

or     h =  √Kh/C

[OH-] = h × C = √(CKh) = √(C*Kw/Ka)

[H+] = Kw/[OH-]

= Kw/√(C*Kw/Ka) = √(Ka*Kw)/Kc

-log [H+] = -1/2log Kw - 1/2log Ka + 1/2log C

pH =  1/2pKw +  1/2pKa +  1/2log C

= 7 + 1/2pKa +  1/2log C.

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