prove that pH=1/2[pKw+pKa+log C] for weak acid strong base salt solution

U.Divyatejasree Grade: 12

        prove that pH=1/2[pKw+pKa+log C] for weak acid strong base salt solution

3 years ago

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Vikas TU

9510 Points

							 Derivation for Strong base and Weak acid reaction.
A- + H2O;      HA + OH-
     Here HA is weak acid considered.
As 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.
From 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=1/2[pKw+pKa+log C].
Proved.