If reaction between A and B to give C shows first order kinetics in A and second order in B, the rate equation can be written as

Options

A. Rate = k[A]`[B]^(1//2)`
B. Rate = `[A]^(1//2)[B]`
C. Rate `=k[A][B]^2`
D. Rate `=k[A]^2[B]`

Answer

To derive the rate equation for the reaction between A and B to give C, we need to consider the order of the reaction with respect to each reactant.

### Step-by-Step Solution:

1. **Identify the Reaction**: The reaction is given as:
\[ A + B \rightarrow C \]

2. **Determine the Order of Reaction**:
- The problem states that the reaction is **first order** in A. This means that the rate of the reaction is directly proportional to the concentration of A raised to the power of 1.
- The reaction is **second order** in B. This means that the rate of the reaction is directly proportional to the concentration of B raised to the power of 2.

3. **Write the Rate Law Expression**:
The rate law expression can be written as:
\[ \text{Rate} = k [A]^m [B]^n \]
where \( m \) is the order with respect to A and \( n \) is the order with respect to B.

4. **Substitute the Orders**:
Given that \( m = 1 \) (first order in A) and \( n = 2 \) (second order in B), we can substitute these values into the rate law expression:
\[ \text{Rate} = k [A]^1 [B]^2 \]

5. **Simplify the Rate Law**:
The expression can be simplified to:
\[ \text{Rate} = k [A] [B]^2 \]

6. **Conclusion**:
Therefore, the rate equation for the reaction is:
\[ \text{Rate} = k [A] [B]^2 \]