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 find the half-life for a zero-order reaction, we can follow these steps:

### Step 1: Understand the zero-order reaction rate law
For 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:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

### Step 2: Write the integrated rate equation for a zero-order reaction
The integrated rate equation for a zero-order reaction is given by:
\[ [A] = [A_0] - kt \]
where:
- \( [A] \) is the concentration at time \( t \),
- \( [A_0] \) is the initial concentration,
- \( k \) is the rate constant,
- \( t \) is the time.

### Step 3: Define the half-life
The half-life (\( t_{1/2} \)) of a reaction is the time required for the concentration of a reactant to decrease to half of its initial concentration. Therefore, at half-life:
\[ [A] = \frac{[A_0]}{2} \]

### Step 4: Substitute into the integrated rate equation
Substituting this into the integrated rate equation:
\[ \frac{[A_0]}{2} = [A_0] - kt_{1/2} \]

### Step 5: Rearrange the equation
Rearranging the equation gives:
\[ kt_{1/2} = [A_0] - \frac{[A_0]}{2} \]
\[ kt_{1/2} = \frac{[A_0]}{2} \]

### Step 6: Solve for half-life
Now, we can solve for \( t_{1/2} \):
\[ t_{1/2} = \frac{[A_0]}{2k} \]

### Step 7: Conclusion
Thus, the half-life for a zero-order reaction is given by:
\[ t_{1/2} = \frac{[A_0]}{2k} \]