The second order rate constant is usually expressed as

Options

A. `Mol L s^(-1)`
B. `Mol^(-1) L^(-1) s^(-1)`
C. `Mol L^(-1) s^(-1)`
D. `Mol^(-1) L s^(-1)`

Answer

To determine the units of the second order rate constant, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rate Law**:
For a second order reaction, the rate law can be expressed as:
\[ \text{Rate} = k [A]^2 \]
where \( k \) is the rate constant and \([A]\) is the concentration of the reactant.

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

3. **Substitute the Units into the Rate Law**:
From the rate law, we can rearrange it to find \( k \):
\[ k = \frac{\text{Rate}}{[A]^2} \]

4. **Substitute the Units for Rate and Concentration**:
- The units of the rate are \( \text{mol L}^{-1} \text{s}^{-1} \).
- The concentration \([A]\) has units of \( \text{mol L}^{-1} \). Since it is squared for a second order reaction, the units become:
\[ [A]^2 = (\text{mol L}^{-1})^2 = \text{mol}^2 \text{L}^{-2} \]

5. **Calculate the Units of \( k \)**:
Now substituting the units into the equation for \( k \):
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2 \text{L}^{-2}} = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2 \text{L}^{-2}} = \frac{1}{\text{mol L}^{-1} \cdot \text{s}} = \text{mol}^{-1} \text{L} \text{s}^{-1} \]

6. **Final Units of the Second Order Rate Constant**:
Thus, the units of the second order rate constant \( k \) are:
\[ k = \text{mol}^{-1} \text{L} \text{s}^{-1} \]

### Conclusion:
The second order rate constant is expressed in the units of \( \text{mol}^{-1} \text{L} \text{s}^{-1} \).

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