What is the order of a reaction which has a rate expression rate = `K[A]^(3//2)[B]^(-1)`

Options

A. `3//2`
B. `1//2`
C. 0
D. None of these

Answer

To determine the order of the reaction from the given rate expression, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Rate Expression**: The given rate expression is:
\[ \text{rate} = K[A]^{\frac{3}{2}}[B]^{-1} \]

2. **General Form of Rate Expression**: The general form of a rate expression can be written as:
\[ \text{rate} = K[A]^x[B]^y \]
where \(x\) and \(y\) are the orders of the reaction with respect to reactants A and B, respectively.

3. **Compare the Exponents**: From the given rate expression, we can identify:
- \(x = \frac{3}{2}\) (the exponent of [A])
- \(y = -1\) (the exponent of [B])

4. **Calculate the Overall Order**: The overall order of the reaction is the sum of the individual orders:
\[ \text{Order} = x + y \]
Substituting the values of \(x\) and \(y\):
\[ \text{Order} = \frac{3}{2} + (-1) \]

5. **Perform the Calculation**:
\[ \text{Order} = \frac{3}{2} - 1 = \frac{3}{2} - \frac{2}{2} = \frac{1}{2} \]

6. **Conclusion**: The order of the reaction is:
\[ \text{Order} = \frac{1}{2} \]

### Final Answer:
The order of the reaction is \( \frac{1}{2} \).

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