Rate constant of two reactions are given below. Identifying their order of reaction
`k = 5.3 xx 10^(-2) L mol^(-1) s^(-1)`
`k = 3.8 xx 10^(-4) s^(-1)`

Options

A. (i) second order, (ii) first order
B. (i) first order, second order
C. (i) zero order, (ii) first order
D. (i) second order, (ii) zero order

Explanation

To identify the order of the reactions based on the given rate constants, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Units of Rate Constant (k)**:
The units of the rate constant (k) can be expressed as:
\[ k = \text{(mole)}^{1-n} \cdot \text{(liter)}^{n-1} \cdot \text{(second)}^{-1} \]
where \( n \) is the order of the reaction.

2. **Analyze the First Rate Constant**:
The first rate constant is given as:
\[ k_1 = 5.3 \times 10^{-2} \, \text{L mol}^{-1} \text{s}^{-1} \]
- Here, the units are \( \text{L mol}^{-1} \text{s}^{-1} \).
- Comparing with the general form, we have:
- \( 1 - n = -1 \) (from the unit of seconds)
- \( n - 1 = 1 \) (from the unit of liters)
- Solving \( 1 - n = -1 \) gives:
\[ n = 2 \]
- Thus, the first reaction is a **second-order reaction**.

3. **Analyze the Second Rate Constant**:
The second rate constant is given as:
\[ k_2 = 3.8 \times 10^{-4} \, \text{s}^{-1} \]
- Here, the units are \( \text{s}^{-1} \).
- Comparing with the general form, we have:
- \( 1 - n = 0 \) (from the unit of seconds)
- Solving \( 1 - n = 0 \) gives:
\[ n = 1 \]
- Thus, the second reaction is a **first-order reaction**.

4. **Conclusion**:
- The first reaction (with \( k_1 \)) is a **second-order reaction**.
- The second reaction (with \( k_2 \)) is a **first-order reaction**.

### Final Answer:
- The first reaction is of second order, and the second reaction is of first order.