The rate equation for the hydrolysis of an ester in presence of NaOH is, rate=K [ester] [NaOH]. If the concentration of NaOH is increased by 100 times than that of ester, the order of the reaction will be

Options

A. 1
B. 2
C. 0
D. 3

Explanation

To determine the order of the reaction for the hydrolysis of an ester in the presence of NaOH when the concentration of NaOH is increased by 100 times that of the ester, we can follow these steps:

### Step 1: Write the Rate Equation
The given rate equation for the hydrolysis of the ester is:
\[ \text{Rate} = k [\text{ester}] [\text{NaOH}] \]
Here, \( k \) is the rate constant, and the reaction depends on the concentrations of both the ester and NaOH.

### Step 2: Identify the Initial Order of the Reaction
From the rate equation, we can see that:
- The order with respect to the ester is 1 (since it is raised to the power of 1).
- The order with respect to NaOH is also 1 (since it is raised to the power of 1).

Thus, the total order of the reaction initially is:
\[ \text{Total Order} = 1 + 1 = 2 \]

### Step 3: Analyze the Change in Concentration of NaOH
Now, we are told that the concentration of NaOH is increased to 100 times that of the ester. If we denote the concentration of the ester as \( [\text{ester}] = x \), then:
\[ [\text{NaOH}] = 100x \]

### Step 4: Substitute the New Concentration into the Rate Equation
The new rate equation can be expressed as:
\[ \text{Rate} = k [\text{ester}] [\text{NaOH}] = k x (100x) = 100k x^2 \]

### Step 5: Determine the Effect of Excess NaOH
Since NaOH is now in excess (100 times the concentration of the ester), the rate of the reaction becomes independent of the concentration of NaOH. In this case, the order with respect to NaOH effectively becomes 0.

### Step 6: Calculate the New Total Order of the Reaction
Now, the total order of the reaction will be:
\[ \text{Total Order} = \text{Order with respect to ester} + \text{Order with respect to NaOH} = 1 + 0 = 1 \]

### Conclusion
Therefore, the order of the reaction when the concentration of NaOH is increased by 100 times that of the ester is **1**.

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