R3.1 Proton transfer reactions

For a weak acid indicator, the Henderson–Hasselbalch equation relates pH to the ratio of conjugate base to acid: $\text{pH}=\text{p}{K}_a+{\log }_{10}\frac{[{\text{X}}^{-}]}{[\text{HX}]}$

The ratio $[{\text{X}}^{-}]/[\text{HX}]=10$, so ${\log }_{10}(10)=1$. Therefore: $\text{pH}=4.20+1=5.20$

The pH is $5.20$. This makes sense: when the conjugate base concentration exceeds the acid form, pH is above $\text{p}{K}_a$, which is consistent with a pH of $5.20>4.20$.

We need $\text{pH}=\text{p}{K}_a+{\log }_{10}([{\text{X}}^{-}]/[\text{HX}])$. With $\text{p}{K}_a=4.20$ and the ratio equal to $10$, pH must be $4.20+1=5.20$.

A pH of $3.20$ would require ${\log }_{10}([{\text{X}}^{-}]/[\text{HX}])=3.20-4.20=-1$, meaning $[\text{HX}]$ is 10 times $[{\text{X}}^{-}]$. This contradicts the given condition, so $3.20$ is incorrect.

A pH of $4.20$ would mean ${\log }_{10}([{\text{X}}^{-}]/[\text{HX}])=0$, i.e. equal concentrations. The question states $[{\text{X}}^{-}]=10[\text{HX}]$, so $4.20$ is incorrect.

A pH of $6.20$ would require ${\log }_{10}([{\text{X}}^{-}]/[\text{HX}])=2$, i.e. $[{\text{X}}^{-}]=100[\text{HX}]$. The given ratio is only $10$, so $6.20$ is incorrect.

Only $5.20$ satisfies $\text{pH}=4.20+{\log }_{10}(10)=4.20+1=5.20$.

Ethanoic acid is a weak acid and sodium hydroxide is a strong base. In a weak acid–strong base titration, the salt formed (${\text{CH}}_3{\text{COO}}^{-}{\text{Na}}^{+}$) undergoes hydrolysis, producing a basic solution at the equivalence point.

Because the acetate ion (${\text{CH}}_3{\text{COO}}^{-}$) is a weak base that accepts protons from water, the equivalence point lies above pH 7, typically around pH 8–9 for this system.

Phenolphthalein has a colour-change range of pH 8.3–10.0, which falls within the steep portion of the pH curve for a weak acid–strong base titration. It will change colour sharply at the equivalence point, making it the most suitable indicator.

Weak acid + strong base titration → equivalence point is above pH 7 (approximately pH 8–9). The ideal indicator must have its transition range within this region.

Methyl orange changes colour between pH 3.1–4.4, well below the equivalence point pH. It would change colour prematurely, long before the equivalence point is reached.

Bromocresol purple (pH 5.2–6.8) also transitions below the equivalence point of pH ~8–9, so it would not accurately signal the equivalence point.

Alizarin yellow changes between pH 10.1–12.0, which is beyond the equivalence point. Excess NaOH would be required before any colour change is observed, giving an inaccurate result.

Phenolphthalein (pH 8.3–10.0) aligns with the equivalence point pH for a weak acid–strong base titration. It is the correct choice.