Chemical and Ionic Equilibrium 2 Question 7

7. 20 mL of $0.1 \mathrm{M} \mathrm{H}{2} \mathrm{SO}{4}solutionisaddedto30 \mathrm{~mL}of0.2 \mathrm{M}\mathrm{NH}{4} \mathrm{OH}solution.The\mathrm{pH}oftheresultantmixtureis\left[\mathrm{p} K{b}\right.of\left.\mathrm{NH}_{4} \mathrm{OH}=4.7\right]$

(2019 Main, 9 Jan I)

(a) 9.3

(b) 5.0

(c) 9.0

(d) 5.2

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Answer:

Correct Answer: 7. (d)

Solution:

  1. The reaction takes place when $\mathrm{H}{2} \mathrm{SO}{4}isaddedto\mathrm{NH}_{4} \mathrm{OH}$ is as follows :

Strong acid Weak base Salt of strong acid

Millimoles at t=020×0.1=230×0.2=6+ weak base

Millimoles at t=t02

So, the resulting solution is a basic buffer $\left[\mathrm{NH}{4} \mathrm{OH}+\left(\mathrm{NH}{4}\right){2} \mathrm{SO}{4}\right]$.

According to the Henderson’s equation,

$$ \begin{aligned} \mathrm{pOH} & =\mathrm{p} K_{b}+\log \frac{\left[\left(\mathrm{NH}{4}\right){2} \mathrm{SO}{4}\right]}{\left[\mathrm{NH}{4} \mathrm{OH}\right]} \ & =4.7+\log \frac{2}{2}=4.7 \ \Rightarrow \quad \mathrm{pH} & =14-\mathrm{pOH}=14-4.7=9.3 \end{aligned} $$