For a reaction whose rate expression is rate `(dx)/(dt)=k[A]^(1//2) [B]^(3//2)` the overall order of the reaction will be:

Options

A. `3//2`
B. `3//4`
C. 2
D. 1

Answer

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

### Step-by-Step Solution:

1. **Identify the Rate Expression**:
The rate expression provided is:
\[ \frac{dx}{dt} = k[A]^{1/2}[B]^{3/2} \]
Here, \(k\) is the rate constant, and \([A]\) and \([B]\) are the concentrations of reactants A and B, respectively.

2. **Determine the Order with Respect to Each Reactant**:
- The order with respect to reactant A is the exponent of \([A]\) in the rate expression, which is \(1/2\).
- The order with respect to reactant B is the exponent of \([B]\) in the rate expression, which is \(3/2\).

3. **Calculate the Overall Order of the Reaction**:
The overall order of the reaction is the sum of the individual orders with respect to each reactant:
\[ \text{Overall Order} = \text{Order with respect to A} + \text{Order with respect to B} \]
Substituting the values we found:
\[ \text{Overall Order} = \frac{1}{2} + \frac{3}{2} \]

4. **Perform the Addition**:
To add the fractions:
\[ \frac{1}{2} + \frac{3}{2} = \frac{1 + 3}{2} = \frac{4}{2} = 2 \]

5. **Conclusion**:
Thus, the overall order of the reaction is \(2\).

### Final Answer:
The overall order of the reaction is **2**.

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