The rate constant of a reaction has same dimensions as rate of reaction The reaction is of

Options

A. zero order
B. first order
C. second order
D. None of these

Explanation

To solve the question, "The rate constant of a reaction has the same dimensions as the rate of reaction. The reaction is of:", we will analyze the relationship between the rate of reaction and the rate constant for different orders of reactions.

### Step-by-Step Solution:

1. **Understanding Rate of Reaction**:
- The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. The units for rate can be expressed as:
\[ \text{Rate} = \frac{\Delta [\text{Concentration}]}{\Delta t} \]
- The standard unit of concentration is moles per liter (mol/L), and the unit of time is seconds (s). Therefore, the units for rate are:
\[ \text{Units of Rate} = \frac{\text{mol/L}}{\text{s}} = \text{mol L}^{-1} \text{s}^{-1} \]

2. **Rate Constant for Different Orders**:
- The rate constant (k) has different units depending on the order of the reaction:
- **Zero Order Reaction**:
- Rate equation: \( R = k \)
- Units of k: Same as rate = mol L\(^{-1}\) s\(^{-1}\)
- **First Order Reaction**:
- Rate equation: \( R = k[A] \)
- Rearranging gives: \( k = \frac{R}{[A]} \)
- Units of k: \( \frac{\text{mol L}^{-1} \text{s}^{-1}}{\text{mol L}^{-1}} = \text{s}^{-1} \)
- **Second Order Reaction**:
- Rate equation: \( R = k[A]^2 \)
- Rearranging gives: \( k = \frac{R}{[A]^2} \)
- Units of k: \( \frac{\text{mol L}^{-1} \text{s}^{-1}}{(\text{mol L}^{-1})^2} = \text{mol}^{-1} \text{L}^{1} \text{s}^{-1} \)

3. **Comparing Units**:
- From the analysis:
- For **Zero Order**: Units of k = mol L\(^{-1}\) s\(^{-1}\) (same as rate)
- For **First Order**: Units of k = s\(^{-1}\) (not the same as rate)
- For **Second Order**: Units of k = mol\(^{-1}\) L s\(^{-1}\) (not the same as rate)

4. **Conclusion**:
- The only case where the rate constant (k) has the same dimensions as the rate of reaction is for a **zero order reaction**.

Thus, the correct answer is **Zero Order Reaction**.