Question

Acid hydrolysis of ester is first order reaction and rate constant is given by \[ k = \frac{2.303}{t} \log \frac{V_0 - V}{V_0 - V_t} \] where \( V_0 \), \( V_t \), and \( V_\infty \) are the volume of standard NaOH required to neutralise acid present at a given time, if ester is 50% neutralised then

• A. \( V_t = V_0 \)
• B. \( V_t = 2V_0 \)
• C. \( V_\infty = V_t \)
• D. \( V_\infty = 2V_t \)

Hint:

For first order reactions, the volume of NaOH required to neutralise the acid can be used to determine the rate of reaction.

Answer 1

The Correct Option is C

Step 1: Using the equation for hydrolysis.
For first order reactions, the rate constant \( k \) is related to the change in volume of NaOH required to neutralise the acid. If the ester is 50% neutralised, then the final volume \( V_\infty \) is equal to \( V_t \), the volume at time \( t \).

Step 2: Conclusion.
The correct relationship is \( V_\infty = V_t \), corresponding to option (3).