In the routine acid-catalyzed hydrolysis of an ester, the overall reaction's progress is experimenta — Chemical Kinetics Chemistry Question
Question
In the routine acid-catalyzed hydrolysis of an ester, the overall reaction's progress is experimentally gauged by titrating a constant fixed volume of the mixture sequentially against standard NaOH. If $V_0$, $V_t$, and $V_\infty$ dictate the distinct volumes of NaOH fully consumed at $t=0$, $t=t$, and $t=\infty$ respectively, what will be the robust algebraic expression exactly holding true when the ester is verifiably 50% hydrolyzed?
💡 Solution & Explanation
The concentration of unreacted ester at time $t$ is proportional to $(V_\infty - V_t)$. The initial ester concentration is proportional to $(V_\infty - V_0)$. At exactly 50% completion, the unreacted ester matches half the initial ester. Hence, $(V_\infty - V_t) = 0.5(V_\infty - V_0)$. Multiplying by 2 yields $2V_\infty - 2V_t = V_\infty - V_0$, which algebraically rearranges definitively to $V_\infty = 2V_t - V_0$.