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: Write the general form of a second-order reaction
A second-order reaction can be represented as:
\[ \text{A} \rightarrow \text{Products} \]
with the rate law given by:
\[ \text{Rate} = k[\text{A}]^2 \]

### Step 2: Define the rate of reaction
The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. The unit of rate can be expressed as:
\[ \text{Rate} = \frac{\Delta [\text{A}]}{\Delta t} \]
The unit of concentration \([\text{A}]\) is typically expressed in moles per liter (mol/L), and time is measured in seconds (s). Therefore, the unit of rate is:
\[ \text{Rate} = \frac{\text{mol/L}}{\text{s}} = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 3: Rearrange the rate law to solve for k
From the rate law:
\[ \text{Rate} = k[\text{A}]^2 \]
we can rearrange this to solve for k:
\[ k = \frac{\text{Rate}}{[\text{A}]^2} \]

### Step 4: Substitute the units into the equation
Substituting the units into the equation for k:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^2} \]

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

### Step 6: Final dimensions of k
Thus, the dimensions of the rate constant k for a second-order reaction are:
\[ k = \text{L mol}^{-1} \text{s}^{-1} \]

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