Assuming the theoretical hydrolysis of an ester occurs cleanly without integrating an external stron — Chemical Kinetics Chemistry Question
Question
Assuming the theoretical hydrolysis of an ester occurs cleanly without integrating an external strong acid catalyst ($H^+$), meaning the initial volume $V_0$ at $t=0$ required for blank neutralization is identically zero. The resultant mathematical formula describing the kinetic rate constant $k$ for this simplified first-order pseudo-process, deploying solely $V_t$ and $V_\infty$, will be:
💡 Solution & Explanation
The universally complete rate constant equation for acid-catalyzed ester hydrolysis is $k = \frac{2.303}{t} \log \left(\frac{V_\infty - V_0}{V_\infty - V_t}\right)$. In the specific absence of any initial catalyst, $V_0 = 0$. Plugging $V_0=0$ into the numerator of the log term immediately collapses the integrated expression to $k = \frac{2.303}{t} \log \left(\frac{V_\infty}{V_\infty - V_t}\right)$.