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 determine the dimensions of the rate constant for a second-order reaction, we can follow these steps:

### Step-by-Step Solution:

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

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

3. **Substitute the Units into the Rate Law:**
From the rate law, we can rearrange to find the units of the rate constant \( k \):
\[ k = \frac{\text{Rate}}{[A]^2} \]
Substituting the units of rate and concentration:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^2} \]

4. **Simplify the Units:**
Simplifying the expression for \( k \):
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2 \text{L}^{-2}} = \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol}^2} \cdot \text{L}^2 = \frac{\text{L}}{\text{mol} \cdot \text{s}} \]

5. **Express the Dimensions:**
The dimensions of the rate constant \( k \) can be expressed as:
\[ [k] = \text{L} \cdot \text{mol}^{-1} \cdot \text{s}^{-1} \]

6. **Identify the Involved Dimensions:**
From the final expression, we can see that the dimensions of the rate constant involve:
- Concentration (mol)
- Time (s)

### Final Answer:
The dimensions of the rate constant of a second-order reaction involve time and concentration.

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