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Q. 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 $x \times 10^{-6} \,M$. The value of $x$ is ________. (Nearest integer)
$\left[\right.$ Given $K _{ w }=1 \times 10^{-14}$ and $\left.K _{ b }=1.8 \times 10^{-5}\right]$

JEE MainJEE Main 2021Equilibrium

Solution:

$\left[ NH _{4}^{+}\right]=0.0504 \,\&\,\left[ NH _{3}\right]=0.0210$
So $K _{ b }=\frac{\left[ NH _{4}^{+}\right]\left[ HO ^{-}\right]}{\left[ NH _{3}\right]}$
$\left[ HO ^{-}\right]=\frac{ K _{ b } \times\left[ NH _{3}\right]}{\left[ NH _{4}^{+}\right]}$
$=1.8 \times 10^{-5} \times \frac{2}{5} \times \frac{210}{504}$
$=3 \times 10^{-6}$