For a zero-order reaction, with the initial reactant concentration a, the time for completion of the reaction is

Options

A. k/a
B. a/k
C. 2k/a
D. a/2k

Answer

To determine the time for the completion of a zero-order reaction with an initial reactant concentration \( a \), we can follow these steps:

### Step-by-Step Solution:

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

2. **Defining the Change in Concentration**:
- Let \( [A]_0 \) be the initial concentration of the reactant \( A \) and \( [A] \) be the concentration at time \( t \).
- The change in concentration \( X \) can be defined as:
\[ X = [A]_0 - [A] \]
- For a complete reaction, \( [A] \) becomes 0, so \( X = [A]_0 \).

3. **Using the Zero-Order Kinetics Equation**:
- For zero-order reactions, the relationship between the change in concentration and time is given by:
\[ X = kt \]
- Substituting \( X = [A]_0 \) into the equation gives:
\[ [A]_0 = kt \]

4. **Solving for Time**:
- Rearranging the equation to solve for time \( t \):
\[ t = \frac{[A]_0}{k} \]
- Since we are given the initial concentration as \( a \), we can replace \( [A]_0 \) with \( a \):
\[ t = \frac{a}{k} \]

5. **Conclusion**:
- Therefore, the time for completion of the reaction for a zero-order reaction with initial reactant concentration \( a \) is:
\[ t = \frac{a}{k} \]

### Final Answer:
The time for completion of a zero-order reaction with initial reactant concentration \( a \) is \( t = \frac{a}{k} \).