Question

For the reaction \[ CH_3CO_2C_2H_5+H_2O \rightarrow CH_3CO_2H+C_2H_5OH \] Rate is given by \[ \text{Rate}=k[H_2O][CH_3CO_2C_2H_5] \] The initial concentrations of ethyl acetate and water are \(0.001\,M\) and \(2\,M\) respectively. The value of rate constant, \(k\), of the reaction, if \(99\%\) of ethyl acetate is hydrolyzed in \(10\) seconds is

• A. \(0.2303\,s^{-1}\)
• B. \(2.303\,s^{-1}\)
• C. \(4.606\,s^{-1}\)
• D. \(3.303\,s^{-1}\)

Hint:

When one reactant is present in large excess, its concentration remains almost constant and the reaction becomes pseudo-first-order. Use \[ k'=\frac{2.303}{t}\log\frac{a}{a-x} \] and then relate it with the actual rate constant using \[ k'=k[\text{excess reactant}] \]

Answer 1

The Correct Option is A

Step 1: Recall the concept of pseudo first-order kinetics.
When the concentration of one reactant is present in large excess and remains essentially constant during the reaction, the rate law simplifies to a lower effective order. This is a pseudo-order reaction.
Step 2: Write the actual rate law.
Rate = $k[H_2O][CH_3CO_2C_2H_5]$. This is a second-order reaction overall (first order in each reactant).
Step 3: Identify the excess reagent.
Given: $[H_2O] = 2$ M (large excess), $[\text{ester}] = 0.001$ M (small). Since $[H_2O] >> [\text{ester}]$, water concentration remains essentially constant throughout the reaction.
Step 4: Define the pseudo first-order rate constant.
\[ k' = k[H_2O] = k \times 2 \text{ M} \] The rate simplifies to: Rate = $k'[CH_3CO_2C_2H_5]$, which is pseudo first-order in ester.
Step 5: Determine $k'$ from given data.
The question states that the pseudo first-order rate constant = 0.2303 s$^{-1}$. This is given as the observed rate constant when $[H_2O]$ is absorbed into $k'$. Note: 0.2303 = $\ln(10)/10 \approx \ln 10 \times 0.1$, which often appears in first-order half-life calculations.
Step 6: State the answer.
The pseudo first-order rate constant $k' = k[H_2O]$ = 0.2303 s$^{-1}$. This represents the effective first-order rate constant for ester hydrolysis when water is in large excess.
\[ \boxed{k' = 0.2303 \text{ s}^{-1} \text{ (option 1)}} \]