Related Formula
pOH = pKb + [Salt][Base]$$\text{pOH} = \text{p}K_{\text{b}} + \log \frac{[\text{Salt}]}{[\text{Base}]} $$
pH = 14 - pOH$$\text{pH} = 14 - \text{pOH} $$
Core Logic
Initially, the basic buffer solution contains:
[Salt] = [NH4^+] = 0.10 mol, [Base] = [NH3] = 0.10 mol$$[\text{Salt}] = [\text{NH}4^+] = 0.10\text{ mol}, \quad [\text{Base}] = [\text{NH}3] = 0.10\text{ mol} $$
pOHinitial = 4.745 + (0.10)/(0.10) = 4.745$$\text{pOH}{\text{initial}} = 4.745 + \log \frac{0.10}{0.10} = 4.745 $$
When 0.05 mol$0.05\text{ mol}$ of strong acid HCl$\text{HCl}$ is introduced, it reacts stoichiometrically with the weak base NH₃$\text{NH}_3$: [cite: 1049, 1050]
arrayrcccc & NH3 & + & H^+ & arrow & NH4^+ Initial (mol): & 0.10 & & 0.05 & & 0.10 Final (mol): & 0.05 & & 0 & & 0.15 array$$\begin{array}{rcccc}
& \text{NH}3 & + & \text{H}^+ & \rightarrow & \text{NH}4^+ \
\text{Initial (mol):} & 0.10 & & 0.05 & & 0.10 \
\text{Final (mol):} & 0.05 & & 0 & & 0.15
\end{array}$$
Step 1: Computing Post-Acid pOH and pH
Recalculating via Henderson's equation:
pOHfinal = 4.745 + (0.15)/(0.05) = 4.745 + 3$$\text{pOH}{\text{final}} = 4.745 + \log \frac{0.15}{0.05} = 4.745 + \log 3 $$
The total shift value follows as:
Δ pOH = pOHfinal - pOHinitial = 3 = 0.477$$\Delta \text{pOH} = \text{pOH}{\text{final}} - \text{pOH}{\text{initial}} = \log 3 = 0.477 $$
Since pH = 14 - pOH$\text{pH} = 14 - \text{pOH}$:
Δ pH = -Δ pOH = -0.477$$\Delta \text{pH} = -\Delta \text{pOH} = -0.477 $$
Expressing the structural magnitude in scientific notation format:
|Δ pH| = 0.477 = 47.7 × 10⁻² ≈ 48 × 10⁻²$$|\Delta \text{pH}| = 0.477 = 47.7 \times 10^{-2} \approx 48 \times 10^{-2} $$
Pattern Recognition
Buffer shifting rule: Adding an acid consumes base and builds salt. The base drops from 0.1$0.1$ to 0.05$0.05$ (halved), while salt grows from 0.1$0.1$ to 0.15$0.15$ (tripled). The ratio flips to 3, introducing a clean 3$\log 3$ change factor into the solution.
Chapter Mix
Class 11 Chemistry: Ionic Equilibrium