The rate constant of a reaction has the units as that of rate of reaction . The reaction order is

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine the order of a reaction when the rate constant has the same units as the rate of reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Rate Law**: The rate of a reaction can be expressed using the rate law equation:
\[ r = k [A]^x [B]^y \]
where \( r \) is the rate of the reaction, \( k \) is the rate constant, and \( [A] \) and \( [B] \) are the concentrations of the reactants raised to their respective powers \( x \) and \( y \).

2. **Identify Units of Rate**: The rate of a reaction (r) is typically expressed in terms of concentration per unit time. For example, in mol/L/s (moles per liter per second).

3. **Identify Units of Rate Constant**: The units of the rate constant \( k \) depend on the overall order of the reaction. The general formula for the units of the rate constant is:
\[ \text{Units of } k = \frac{\text{Units of rate}}{(\text{Units of concentration})^{\text{order}}} \]
For a reaction of order \( n \), the units of \( k \) can be expressed as:
\[ k = \frac{\text{mol L}^{-1} s^{-1}}{(\text{mol L}^{-1})^n} = \text{mol L}^{-1} s^{-1} \cdot \text{mol}^{n} L^{n} \]
Simplifying this gives:
\[ k = \text{mol}^{1-n} L^{n-1} s^{-1} \]

4. **Set Units of Rate Equal to Units of k**: Since we are given that the units of the rate constant \( k \) are the same as the units of the rate \( r \), we can set them equal:
\[ \text{mol L}^{-1} s^{-1} = \text{mol}^{1-n} L^{n-1} s^{-1} \]

5. **Equate the Exponents**: By equating the exponents of each unit, we get:
- For moles: \( 1 = 1 - n \) → \( n = 0 \)
- For liters: \( -1 = n - 1 \) → \( n = 0 \)
- For time: Both sides already match as \( -1 \).

6. **Conclusion**: The only solution that satisfies both equations is \( n = 0 \). Therefore, the reaction is a zero-order reaction.

### Final Answer:
The reaction order is **0**.