The pH range of a basic indicator (InOH) is . Determine the ratio , above which the solution appears — Ionic Equilibrium Chemistry Question
Question
The pH range of a basic indicator (InOH) is $3.4 – 4.6$. Determine the ratio $[\text{In}^+]/[\text{InOH}]$, above which the solution appears only in the colour of $\text{In}^+$?
💡 Solution & Explanation
The indicator's pH range spans $3.4$ to $4.6$, meaning the middle is $\text{pH} = 4.0$. For a basic indicator $\text{InOH} \rightleftharpoons \text{In}^+ + \text{OH}^-$, $\text{pOH} = pK_b + \log([\text{In}^+]/[\text{InOH}])$. At the midpoint (ratio=1), $\text{pH} = 4.0 \implies \text{pOH} = 10.0$, making $pK_b = 10.0$. The colour of $\text{In}^+$ dominates at the lower pH bound (more acidic). At $\text{pH} = 3.4$, $\text{pOH} = 10.6$. Substituting this in: $10.6 = 10.0 + \log([\text{In}^+]/[\text{InOH}]) \implies \log([\text{In}^+]/[\text{InOH}]) = 0.6$. The required ratio is $10^{0.6} \approx 3.98$, which rounds to 4. Therefore, correct answer is 4.