The unit of second order reaction rate constant is

Options

A. `lit^(-1).mol^(-1).sec^(-1)`
B. `lit^(2).mol^(2).sec^(-1)`
C. `lit.mol^(-1).sec^(-1)`
D. `sec^(-1)`

Explanation

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

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

### Step 2: Identify the Units of Rate
The rate of a reaction is typically expressed in terms of concentration change over time. The unit of rate is:
\[ \text{Rate} = \frac{\text{moles}}{\text{liter} \cdot \text{second}} = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 3: Identify the Units of Concentration
The concentration \( [A] \) is expressed in moles per liter (mol/L), which can also be written as:
\[ [A] = \text{mol L}^{-1} \]

### Step 4: Substitute Units into the Rate Law
Substituting the units into the rate law expression:
\[ \text{Rate} = k [A]^2 \]
This can be rewritten in terms of units:
\[ \text{mol L}^{-1} \text{s}^{-1} = k \cdot (\text{mol L}^{-1})^2 \]

### Step 5: Simplify the Equation
Now, simplify the right side:
\[ \text{mol L}^{-1} \text{s}^{-1} = k \cdot \text{mol}^2 \text{L}^{-2} \]
To isolate \( k \), we rearrange the equation:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2 \text{L}^{-2}} \]

### Step 6: Calculate the Units of k
Now, we can simplify the units:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2 \text{L}^{-2}} = \frac{1}{\text{mol} \cdot \text{L}^{-1}} \cdot \text{s}^{-1} = \text{L mol}^{-1} \text{s}^{-1} \]

### Conclusion
Thus, the unit of the second-order reaction rate constant \( k \) is:
\[ \text{L mol}^{-1} \text{s}^{-1} \]