Unit of K for third order reaction is

Options

A. `(("litre")/("mole")) sec`
B. `(("mole")/("litre")) sec`
C. `(("litre")/("mole"))^(-1) sec^(-1)`
D. `(("mole")/("litre"))^(-1) sec^(-1) `

Explanation

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

### Step-by-Step Solution:

1. **Understand the General Formula for Rate Constant (k)**:
The unit of the rate constant \( k \) can be derived from the general formula:
\[ \text{Unit of } k = \text{(mole/L)}^{1-n} \cdot \text{(time)}^{-1} \]
where \( n \) is the order of the reaction.

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

3. **Substitute the Value of n into the Formula**:
Substitute \( n = 3 \) into the formula:
\[ \text{Unit of } k = \text{(mole/L)}^{1-3} \cdot \text{(time)}^{-1} \]
This simplifies to:
\[ \text{Unit of } k = \text{(mole/L)}^{-2} \cdot \text{(time)}^{-1} \]

4. **Express the Units Clearly**:
The unit can be expressed as:
\[ \text{Unit of } k = \frac{1}{\text{(mole/L)}^{2} \cdot \text{(time)}} \]
If we take time as seconds (s), the unit becomes:
\[ \text{Unit of } k = \frac{1}{\text{mol}^{2}/\text{L}^{2} \cdot \text{s}} = \frac{\text{L}^{2}}{\text{mol}^{2} \cdot \text{s}} \]

5. **Final Answer**:
Therefore, the unit of the rate constant \( k \) for a third-order reaction is:
\[ \text{L}^{2} \cdot \text{mol}^{-2} \cdot \text{s}^{-1} \]