20 mL of $0.1 \mathrm{M} \mathrm{NH}_{4} \mathrm{OH}$ is mixed with 40 mL of 0.05 M HCl . The pH of the mixture is nearest to: (Given: $\mathrm{K}_{\mathrm{b}}\left(\mathrm{NH}_{4} \mathrm{OH}\right)=1 \times 10^{-5}, \log 2=0.30$, $\log 3=0.48, \log 5=0.69, \log 7=0.84$, $\log 11=1.04$ )

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Equilibrium

20 mL of

0.1 M NH_{4} OH

is mixed with 40 mL of 0.05 M HCl . The pH of the mixture is nearest to:
(Given:

K_{b} (NH_{4} OH) = 1 \times 1 0^{- 5}, lo g 2 = 0.30

lo g 3 = 0.48, lo g 5 = 0.69, lo g 7 = 0.84

lo g 11 = 1.04

)

Answer: (C)

Millimoles of

NH_{4} OH

20 \times 0.1 = 2

. Millimoles of

HCl

40 \times 0.05 = 2

. They neutralize completely to form

NH_{4} Cl

. Concentration of

NH_{4}^{+}

\frac{2}{60} = \frac{1}{30}

M. For a salt of weak base and strong acid,

pH = \frac{pK _{w} - pK _{b} - l o g C}{2} = \frac{14 - 5 - l o g ( 1/30 )}{2} = \frac{14 - 5 + 1.48}{2} \approx 5.24

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Single correct option