k for a zero order reaction is `2xx10^(-2)` mol . `L^(-1)s^(-1)` . If the concentration of the reactant changed into the product .Now if the same reaction is carried out with an initial concentration of 5 moles per litre . The percentage of the reactant changing to the product is .

Options

A. `0.5` M
B. `1.25` M
C. `12.5` M
D. `1.0` M

Answer

To solve the problem, we need to determine the percentage of the reactant that changes into the product in a zero-order reaction given the rate constant (k) and the initial concentration of the reactant.

### Step-by-Step Solution:

1. **Understanding Zero-Order Reaction**:
In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

2. **Given Data**:
- Rate constant \( k = 2 \times 10^{-2} \, \text{mol} \, \text{L}^{-1} \, \text{s}^{-1} \)
- Initial concentration of the reactant \( [A]_0 = 5 \, \text{mol} \, \text{L}^{-1} \)

3. **Calculating the Time for Complete Reaction**:
For a zero-order reaction, the concentration of the reactant decreases linearly over time. The integrated rate law for a zero-order reaction is given by:
\[ [A] = [A]_0 - kt \]
To find the time required for the reactant to completely convert to product, we set \( [A] = 0 \):
\[ 0 = 5 - (2 \times 10^{-2})t \]
Rearranging gives:
\[ (2 \times 10^{-2})t = 5 \]
\[ t = \frac{5}{2 \times 10^{-2}} = 250 \, \text{s} \]

4. **Percentage of Reactant Converted**:
Since the reaction is zero-order, the entire concentration of the reactant will convert to product over the time calculated. Therefore, the percentage of the reactant that changes to product is:
\[ \text{Percentage} = \left( \frac{\text{Amount converted}}{\text{Initial amount}} \right) \times 100 \]
Here, the amount converted is equal to the initial amount:
\[ \text{Percentage} = \left( \frac{5}{5} \right) \times 100 = 100\% \]

### Final Answer:
The percentage of the reactant that changes to the product is **100%**.