Consider the following statements The rate law for the acid catalysed hydrolosis of an ester being given as Rate `=k[H^(+)]["ester"]=k'["ester"]`. If the acid concentration is doubled at constant ester concentration
1. The second order rate constant, k is doubled
2. The pseudo first order rate constant, k is doubled
3. The rate of the reaction is doubled Which of the above statements are correct

Options

A. 1 and 2
B. 2 and 3
C. 1 and 3
D. 1,2 and 3

Answer

To solve the problem, we need to analyze the given rate law for the acid-catalyzed hydrolysis of an ester and determine the effects of doubling the concentration of the acid on the rate constant and the rate of the reaction.

### Step-by-Step Solution:

1. **Understanding the Rate Law**:
The rate law is given as:
\[ \text{Rate} = k[H^+][\text{ester}] \]
This indicates that the rate of the reaction depends on the concentration of hydrogen ions \([H^+]\) and the concentration of the ester.

2. **Identifying the Order of the Reaction**:
The reaction is second order overall because it depends on the first power of \([H^+]\) and the first power of the ester concentration. Thus, the overall order is:
\[ 1 + 1 = 2 \quad (\text{second order}) \]

3. **Pseudo First Order Reaction**:
When the concentration of the ester is much greater than that of the acid, we can treat the reaction as pseudo first order with respect to the ester. The pseudo first order rate constant \(k'\) is defined as:
\[ k' = k[H^+] \]
In this case, the rate law simplifies to:
\[ \text{Rate} = k'[\text{ester}] \]

4. **Effect of Doubling the Acid Concentration**:
If the concentration of \([H^+]\) is doubled:
\[ [H^+] \rightarrow 2[H^+] \]
The new rate becomes:
\[ \text{New Rate} = k(2[H^+])[\text{ester}] = 2k[H^+][\text{ester}] = 2 \times \text{Rate} \]
This indicates that the rate of the reaction is doubled.

5. **Impact on the Pseudo First Order Rate Constant**:
The new pseudo first order rate constant becomes:
\[ k'_{\text{new}} = k(2[H^+]) = 2k[H^+] = 2k' \]
Thus, the pseudo first order rate constant is also doubled.

6. **Conclusion on the Statements**:
- **Statement 1**: The second order rate constant \(k\) is doubled. (Incorrect, \(k\) remains constant.)
- **Statement 2**: The pseudo first order rate constant \(k'\) is doubled. (Correct.)
- **Statement 3**: The rate of the reaction is doubled. (Correct.)

### Final Answer:
The correct statements are **2 and 3**.