If concentration are measured in moles/lit and time in minutes, the unit for the rate constant of a `3^(rd)` order reaction are

Options

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

Answer

To determine the unit for the rate constant (k) of a third-order reaction when concentrations are measured in moles per liter (mol/L) and time is measured in minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Order of Reaction**:
The order of the reaction (n) is given as 3 for a third-order reaction.

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

3. **Express the Rate**:
The rate of the reaction has units of concentration per unit time. Since concentration is in moles per liter (mol/L) and time is in minutes, the units of rate can be expressed as:
\[ \text{Rate} = \frac{\text{mol}}{\text{L} \cdot \text{min}} \]

4. **Substitute the Order of Reaction**:
For a third-order reaction (n = 3), we can express the rate as:
\[ \text{Rate} = k [A]^3 \]
Rearranging gives us:
\[ k = \frac{\text{Rate}}{[A]^3} \]

5. **Substituting Units**:
Substitute the units of rate and concentration into the equation:
\[ k = \frac{\frac{\text{mol}}{\text{L} \cdot \text{min}}}{\left(\frac{\text{mol}}{\text{L}}\right)^3} \]

6. **Simplifying the Units**:
When we simplify this expression, we get:
\[ k = \frac{\frac{\text{mol}}{\text{L} \cdot \text{min}}}{\frac{\text{mol}^3}{\text{L}^3}} = \frac{\text{mol} \cdot \text{L}^3}{\text{L} \cdot \text{min} \cdot \text{mol}^3} \]
This simplifies to:
\[ k = \frac{\text{L}^2}{\text{mol}^2 \cdot \text{min}} \]

7. **Final Unit of k**:
Therefore, the unit for the rate constant (k) of a third-order reaction is:
\[ k = \frac{\text{L}^2}{\text{mol}^2 \cdot \text{min}} \]

### Conclusion:
The correct unit for the rate constant of a third-order reaction, when concentrations are in moles per liter and time is in minutes, is \(\frac{\text{L}^2}{\text{mol}^2 \cdot \text{min}}\).