Units for the rate constant of first order reaction is

Options

A. `Sec^(-1)`
B. `mol.lit^(-1)`
C. `lit.mol^(-1)`
D. `mol^(3).lit^(-1).sec^(-1)`

Explanation

To determine the units for the rate constant of a first-order reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rate Law**:
The rate of a reaction can be expressed as:
\[ \text{Rate} = k [A]^n \]
where \( k \) is the rate constant, \([A]\) is the concentration of the reactant, and \( n \) is the order of the reaction.

2. **Identify the Units of Rate**:
The rate of a reaction is typically expressed in terms of concentration per unit time. Therefore, the units of rate can be written as:
\[ \text{Rate} = \frac{\text{moles}}{\text{liter} \cdot \text{seconds}} = \text{mol L}^{-1} \text{s}^{-1} \]

3. **Identify the Units of Concentration**:
The concentration \([A]\) is expressed in moles per liter:
\[ [A] = \text{mol L}^{-1} \]

4. **Substituting into the Rate Law**:
For a first-order reaction, \( n = 1 \). Therefore, we can rewrite the rate law as:
\[ \text{Rate} = k [A]^1 \]

5. **Rearranging for the Rate Constant \( k \)**:
Rearranging the equation gives us:
\[ k = \frac{\text{Rate}}{[A]} \]

6. **Substituting Units into the Equation**:
Now substituting the units into the equation for \( k \):
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol L}^{-1}} = \text{s}^{-1} \]

7. **Conclusion**:
Thus, the units for the rate constant \( k \) for a first-order reaction is:
\[ \text{Units of } k = \text{s}^{-1} \]

### Final Answer:
The unit for the rate constant of a first-order reaction is \( \text{s}^{-1} \).