Identify the buffer system

The solution contains a weak base and its salt: $\mathrm{NH_3/NH_4^+}$

Initially in $1\,\text{L}$:

• $\mathrm{NH_3} = 0.1$ mol
• $\mathrm{NH_4Cl} \Rightarrow NH_4^+ = 0.1$ mol

Reaction with added HCl

HCl reacts completely with ammonia: $\mathrm{NH_3 + HCl \to NH_4^+ + Cl^-}$

Added HCl = $0.02$ mol

Therefore, after reaction:

• Moles of $\mathrm{NH_3}$ left: $0.1 - 0.02 = 0.08$
• Moles of $\mathrm{NH_4^+}$ formed: $0.1 + 0.02 = 0.12$

Use Henderson equation for basic buffer

For a basic buffer: $\mathrm{pOH} = \mathrm{p}K_b + \log\frac{[salt]}{[base]}$

So, $\mathrm{pOH} = 4.745 + \log\frac{0.12}{0.08}$

$\frac{0.12}{0.08} = 1.5 = \frac{3}{2}$

Hence, $\log 1.5 = \log 3 - \log 2 = 0.477 - 0.301 = 0.176$

Therefore, $\mathrm{pOH} = 4.745 + 0.176 = 4.921$

Calculate pH

At $298\,\text{K}$: $\mathrm{pH} + \mathrm{pOH} = 14$

Thus, $\mathrm{pH} = 14 - 4.921 = 9.079$

Match the asked form

The question says pH is found to be: $\underline{\hspace{2cm}} \times 10^{-3}$

Since $9.079 = 9079 \times 10^{-3}$

the required nearest integer is: $\boxed{9079}$

Comparison with stored answer

Derived answer = $9079$

Stored correct answer = $9079$

Hence they agree.