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 (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 (r) is proportional to the square of the concentration of the reactant. The general form of the rate law can be expressed as:
\[ r = k[A]^2 \]
where:
- \( r \) = rate of the reaction
- \( k \) = rate constant
- \( [A] \) = concentration of the reactant

### Step 2: Identify the Units of Rate
The rate of a reaction is defined as the change in concentration per unit time. Therefore, the units of rate (r) can be expressed as:
\[ \text{Units of } r = \frac{\text{moles}}{\text{liter} \cdot \text{second}} = \text{mol L}^{-1} \text{s}^{-1} \]

### Step 3: Identify the Units of Concentration
The concentration of a reactant is expressed in terms of moles per liter:
\[ \text{Units of concentration} = \text{mol L}^{-1} \]

### Step 4: Determine the Units of the Rate Constant (k)
From the rate law, we can rearrange to find the units of the rate constant (k):
\[ k = \frac{r}{[A]^2} \]
Substituting the units we identified:
\[ k = \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^2} \]

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

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

### Conclusion
The dimensions of the rate constant of a second-order reaction involve both concentration and time.

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