The $\mathrm{OH}^{-}$ concentration in a mixture of 5.0 mL of $0.0504 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}$ and 2 mL of $0.0210 \mathrm{M} \mathrm{NH}_{3}$ solution is $x \times 10^{-6} \mathrm{M}$. The value of $x$ is ______. (Nearest integer) [Given $\mathrm{K}_{\mathrm{w}}=1 \times 10^{-14}$ and $\mathrm{K}_{\mathrm{b}}=1.8 \times 10^{-5}$]

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Equilibrium

The

OH^{-}

concentration in a mixture of 5.0 mL of

0.0504 M NH_{4} Cl

and 2 mL of

0.0210 M NH_{3}

solution is

x \times 1 0^{- 6} M

. The value of

x

is ______. (Nearest integer)
[Given

K_{w} = 1 \times 1 0^{- 14}

and

K_{b} = 1.8 \times 1 0^{- 5}

]

Answer: 3

Mixing the two solutions gives a buffer of ammonia with its conjugate acid, the ammonium ion. The amounts present are

n (N H_{4}^{+}) = 5.0 \times 0.0504 = 0.252 mmol, n (N H_{3}) = 2.0 \times 0.0210 = 0.0420 mmol

Both species occupy the same

7.0

mL, so the ratio of their concentrations equals the ratio of these amounts. For a basic buffer

[O H^{-}] = K_{b} \frac{[ N H _{3} ]}{[ N H _{4}^{+} ]} = 1.8 \times 1 0^{- 5} \times \frac{0.0420}{0.252} = 3.0 \times 1 0^{- 6} M

x = 3

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Integer answer