An acid base indicator which is a weak acid has a value . At what concentration ratio of sodium acet — Ionic Equilibrium Chemistry Question
Question
An acid base indicator which is a weak acid has a $pK_a$ value $= 5.5$. At what concentration ratio of sodium acetate to acetic acid would the indicator show a colour half way between those of its acid and conjugate base forms? $pK_a$ of acetic acid $= 4.75$. $[\text{Antilog } (0.75) = 5.62, \text{Antilog } (0.69) = 4.93]$
💡 Solution & Explanation
The indicator is halfway between its forms when $[\text{HIn}] = [\text{In}^-]$, meaning the solution $\text{pH} = pK_a(\text{indicator}) = 5.5$. To achieve this pH, the acetic acid buffer must satisfy the Henderson-Hasselbalch equation: $\text{pH} = pK_a(\text{acid}) + \log(\frac{[\text{Salt}]}{[\text{Acid}]})$. Thus, $5.5 = 4.75 + \log(\text{Ratio})$. Solving for the ratio gives $\log(\text{Ratio}) = 5.5 - 4.75 = 0.75$. The ratio is the antilog of 0.75, which is given as 5.62. Thus, the ratio is 5.62:1. Therefore, correct answer is C.