Hydrolysis of ester in catalysed by acid. Rates of hydrolysis of ester were obtained initially and after `50%` ester has been hydrolused as `R_(0)` and `R_(50)` then (same temp.)

Options

A. `R_(0)=R_(50)`
B. `R_(0) lt R_(50)`
C. `R_(0) gt R_(50)`
D. Cannot be determined

Answer

To solve the problem regarding the hydrolysis of an ester catalyzed by acid, we need to analyze the rates of the reaction at two different points: initially (R₀) and after 50% of the ester has been hydrolyzed (R₅₀).

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The hydrolysis of an ester in the presence of an acid can be represented as:
\[ \text{Ester} + \text{Water} \xrightarrow{\text{H}^+} \text{Carboxylic Acid} + \text{Alcohol} \]
In this reaction, the ester reacts with water to form a carboxylic acid and an alcohol, facilitated by the presence of an acid catalyst (H⁺).

2. **Identifying the Reaction Order**:
The reaction is classified as a pseudo-first-order reaction because the concentration of water is in excess. Therefore, the rate of the reaction primarily depends on the concentration of the ester.

3. **Rates of Reaction**:
- At the initial stage, the rate of hydrolysis is denoted as R₀.
- After 50% of the ester has been hydrolyzed, the rate is denoted as R₅₀.

4. **Effect of Product Formation**:
As the reaction proceeds, the concentration of the ester decreases. However, since the reaction is pseudo-first-order, the rate is proportional to the concentration of the ester. When 50% of the ester has been hydrolyzed, the concentration of the ester is reduced, which would typically suggest a decrease in the rate of reaction.

5. **Catalyst Regeneration**:
Importantly, the acid catalyst (H⁺) is regenerated during the reaction. This means that as the reaction proceeds, the effective concentration of the catalyst remains constant, and thus the reaction can continue at a relatively high rate.

6. **Comparison of Rates**:
Initially, when the concentration of the ester is at its maximum, the rate R₀ will be higher than R₅₀ because R₅₀ is measured after 50% of the ester has reacted. However, the presence of the acid catalyst helps maintain a significant rate of reaction even after some ester has been converted.

7. **Conclusion**:
Therefore, we conclude that:
\[ R₀ > R₅₀ \]
The correct answer to the question is that the initial rate (R₀) is greater than the rate after 50% hydrolysis (R₅₀).

### Final Answer:
The correct option is **R₀ > R₅₀**.