Reactant 'A' (initial concentration, a) reacts according to zero order kinetics, the time taken for the completion of the reaction is

Options

A. `a/k`
B. `a/(2k)`
C. `k/a`
D. `(2k)/a`

Answer

To find the time taken for the completion of a zero-order reaction involving reactant 'A' with an initial concentration of 'a', we can follow these steps:

### Step-by-Step Solution:

1. **Understand Zero-Order Reaction Kinetics**:
- For a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. The rate equation can be expressed as:
\[ [A]_0 - [A]_t = kt \]
where \([A]_0\) is the initial concentration, \([A]_t\) is the concentration at time \(t\), \(k\) is the rate constant, and \(t\) is the time.

2. **Determine Completion of Reaction**:
- The reaction is considered complete when the concentration of reactant 'A' reaches zero, i.e., \([A]_t = 0\). Therefore, we can rewrite the equation as:
\[ [A]_0 - 0 = kt_{\text{completion}} \]
This simplifies to:
\[ [A]_0 = kt_{\text{completion}} \]

3. **Substitute Initial Concentration**:
- Given that the initial concentration \([A]_0\) is 'a', we substitute this into the equation:
\[ a = kt_{\text{completion}} \]

4. **Solve for Time of Completion**:
- Rearranging the equation to solve for \(t_{\text{completion}}\) gives:
\[ t_{\text{completion}} = \frac{a}{k} \]

5. **Final Answer**:
- The time taken for the completion of the reaction is:
\[ t_{\text{completion}} = \frac{a}{k} \]

### Conclusion:
The time taken for the completion of the zero-order reaction is \(\frac{a}{k}\).

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