For a reaction of order n, the unit of the constant is :

Options

A. `mol^(1-n) L^(1-n)s`
B. `mol^(1-n)L^(2n)s^(-1)`
C. `mol^(-1) L^(n-1)s^(-1)`
D. `mol^(1-n) L^(1-n)s^(-1)`

Answer

To determine the unit of the rate constant (k) for a reaction of order n, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rate of Reaction**:
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. **Define the Units of Rate**:
The rate of reaction is generally expressed in terms of concentration change per unit time. The units for rate are:
\[ \text{Rate} = \frac{\text{moles}}{\text{liter} \cdot \text{second}} = \text{mol L}^{-1} \text{s}^{-1} \]

3. **Express Concentration in Terms of Units**:
The concentration \( [A] \) is measured in moles per liter (mol/L). Therefore, the units of concentration are:
\[ [A] = \text{mol L}^{-1} \]

4. **Substitute Units into the Rate Equation**:
Rearranging the rate equation for \( k \):
\[ k = \frac{\text{Rate}}{[A]^n} \]
Substituting the units:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^n} \]

5. **Simplify the Units**:
The denominator becomes:
\[ (\text{mol L}^{-1})^n = \text{mol}^n \text{L}^{-n} \]
Therefore, substituting back into the equation for \( k \):
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^n \text{L}^{-n}} = \text{mol}^{1-n} \text{L}^{n-1} \text{s}^{-1} \]

6. **Final Expression for Units of Rate Constant**:
Thus, the unit of the rate constant \( k \) for a reaction of order \( n \) is:
\[ k = \text{mol}^{1-n} \text{L}^{n-1} \text{s}^{-1} \]

### Conclusion:
The unit of the rate constant for a reaction of order \( n \) is:
\[ \text{mol}^{1-n} \text{L}^{n-1} \text{s}^{-1} \]