A certain buffer solution contains equal concentration of 3.9 10^… - Vidyadip

MCQ

A certain buffer solution contains equal concentration of $3.9 \times {10^{ - 5}}$ and $HX.$ The ${K_b}$ for ${H^ - }$ is ${10^{ - 10}}.$ The $pH$ of the buffer is

✓
$4$
B
$7$
C
$10$
D
$14$

✓

Answer

Correct option: A.

$4$

(a) ${X^ - } + {H_2}O$ $ \rightleftharpoons $ $O{H^ - } + HX$

${K_b} = \frac{{[O{H^ - }]\,\,[HX]}}{{[{X^ - }]}}$

$HX ⇌ {H^ + } + {X^ - }$

${K_a} = \frac{{[{H^ + }]\,\,[{X^ - }]}}{{[HX]}}$

$\therefore \,{K_a} \times {K_b} = [{H^ + }]\,\,[O{H^ - }] = {K_w} = {10^{ - 14}}$

Hence ${K_a} = {10^{ - 4}}$

Now as $[{X^ - }] = [HX],\,\,pH = p{K_a} = 4$.

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