The half life for the zero order reaction will be

Options

A. `t_(1//2)prop(conc.)^0`
B. `t_(1//2)prop(conc.)^1`
C. `t_(1//2)prop(conc.)^-1`
D. `t_(1//2)prop(conc.)^2`

Answer

To determine the half-life of a zero-order reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Half-Life**:
The half-life (T_half) is the time required for the concentration of a reactant to decrease to half of its initial concentration.

2. **General Expression for Half-Life**:
The general expression for the half-life of a reaction of order n is given by:
\[ T_{half} = \frac{2[A_0]^{n-1}}{n \cdot k} \]
where:
- \( A_0 \) = initial concentration of the reactant
- \( n \) = order of the reaction
- \( k \) = rate constant of the reaction

3. **Identify the Order of the Reaction**:
For a zero-order reaction, \( n = 0 \).

4. **Substitute into the Half-Life Formula**:
Plugging \( n = 0 \) into the half-life formula gives:
\[ T_{half} = \frac{2[A_0]^{0-1}}{0 \cdot k} \]
This simplifies to:
\[ T_{half} = \frac{2[A_0]^{-1}}{0 \cdot k} \]
Since \( [A_0]^{-1} \) is equivalent to \( \frac{1}{[A_0]} \), we can rewrite it as:
\[ T_{half} = \frac{2}{k} \]

5. **Conclusion**:
The half-life of a zero-order reaction is independent of the initial concentration and is given by:
\[ T_{half} = \frac{[A_0]}{2k} \]

### Final Answer:
The half-life for a zero-order reaction is given by:
\[ T_{half} = \frac{[A_0]}{2k} \]