Rate constant has the unit `"mol"^(-2)L^(-2)s^(-1)` , then order of reaction is

Options

A. zero order, t= 7.5 sec
B. first
C. second
D. third

Explanation

To determine the order of a reaction given that the rate constant has the unit of \( \text{mol}^{-2} \text{L}^2 \text{s}^{-1} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between rate, rate constant, and concentration**:
The rate of a reaction can be expressed as:
\[ \text{Rate} = k \times [A]^n \]
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 unit of rate is typically expressed as concentration per time. In SI units, this can be written as:
\[ \text{Rate} = \frac{\text{mol}}{\text{L} \cdot \text{s}} \]

3. **Express the unit of the rate constant \( k \)**:
Given that the unit of \( k \) is \( \text{mol}^{-2} \text{L}^2 \text{s}^{-1} \), we can express this in terms of the concentration unit:
\[ k = \text{mol}^{-2} \text{L}^2 \text{s}^{-1} \]

4. **Relate the units of \( k \) to the order of the reaction**:
From the equation of the rate, we can rearrange it to find the units of \( k \):
\[ k = \frac{\text{Rate}}{[A]^n} \]
Substituting the units:
\[ k = \frac{\frac{\text{mol}}{\text{L} \cdot \text{s}}}{\left(\frac{\text{mol}}{\text{L}}\right)^n} \]
This simplifies to:
\[ k = \frac{\frac{\text{mol}}{\text{L} \cdot \text{s}}}{\frac{\text{mol}^n}{\text{L}^n}} = \frac{\text{mol}^{1-n}}{\text{L}^{1-n} \cdot \text{s}} \]

5. **Set the units equal**:
Now we can set the units of \( k \) equal to the given units:
\[ \frac{\text{mol}^{1-n}}{\text{L}^{1-n} \cdot \text{s}} = \text{mol}^{-2} \text{L}^2 \text{s}^{-1} \]

6. **Compare the exponents**:
From the left side:
- For \( \text{mol} \): \( 1 - n = -2 \) → \( n = 3 \)
- For \( \text{L} \): \( -(1-n) = 2 \) → \( n - 1 = -2 \) → \( n = 3 \)
- For \( \text{s} \): \( -1 = -1 \) (this is consistent)

7. **Conclusion**:
The order of the reaction is \( n = 3 \).

### Final Answer:
The order of the reaction is **3**.