pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :

Ionic Equilibrium PYQ — JEE Main 2017 · Shift 0 · Q16 with Solution

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Correct answer: A

Identify the salt type

The salt $AB$ is formed from:

weak acid: $HA$
weak base: $BOH$

So, $AB$ is a salt of a weak acid and a weak base.

For such a salt, the pH is given by:

\text{pH} = 7 + \frac{1}{2}\log\left(\frac{K_b}{K_a}\right)

Using $pK_a$ and $pK_b$ :

K_a = 10^{-pK_a}, \qquad K_b = 10^{-pK_b}

Hence,

\log\left(\frac{K_b}{K_a}\right) = \log K_b - \log K_a = (-pK_b)-(-pK_a)=pK_a-pK_b

Therefore,

\text{pH} = 7 + \frac{1}{2}(pK_a - pK_b)

Substitute the given values

Given:

pK_a = 3.2, \qquad pK_b = 3.4

So,

\text{pH} = 7 + \frac{1}{2}(3.2 - 3.4)

= 7 + \frac{1}{2}(-0.2)

= 7 - 0.1 = 6.9

Match with the options

\boxed{\text{pH} = 6.9}

So the correct option is A.

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