The dimensions of rate constant of a second order reaction involves :

Options

A. time and concentration
B. neither time nor concentration
C. time only
D. concentration only

Explanation

To find the dimensions of the rate constant \( k \) for a second-order reaction, we can follow these steps:

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

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

### Step 3: Define the Units of Concentration
The concentration \( [A] \) is expressed in moles per liter:
\[ [A] = \frac{\text{moles}}{\text{liter}} = \text{mol L}^{-1} \]

### Step 4: Substitute the Units into the Rate Law
Substituting the units into the rate law gives:
\[ \text{mol L}^{-1} \text{s}^{-1} = k \cdot (\text{mol L}^{-1})^2 \]

### Step 5: Simplify the Equation
This can be rewritten as:
\[ \text{mol L}^{-1} \text{s}^{-1} = k \cdot \text{mol}^2 \text{L}^{-2} \]

### Step 6: Rearranging for \( k \)
To find the units of \( k \), we can rearrange the equation:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2 \text{L}^{-2}} = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2} \cdot \text{L}^2 \]
This simplifies to:
\[ k = \frac{\text{L}^2}{\text{mol} \cdot \text{s}} \]

### Step 7: Write the Dimensions of \( k \)
Thus, the dimensions of the rate constant \( k \) for a second-order reaction are:
\[ k \sim \text{L}^2 \text{mol}^{-1} \text{s}^{-1} \]

### Summary
The dimensions of the rate constant \( k \) for a second-order reaction involve:
- Length (L)
- Amount of substance (mol)
- Time (s)