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The rate expression for a reaction is ra...

The rate expression for a reaction is rate `=k[A]^(3//2)[B]^(-1)`, the order of reaction is

A

`0`

B

`1//2`

C

`3//2`

D

`5//2`

Text Solution

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The correct Answer is:
To determine the order of the reaction from the given rate expression, we follow these steps: ### Step-by-Step Solution: 1. **Identify the Rate Expression**: The rate expression provided is: \[ \text{rate} = k[A]^{\frac{3}{2}}[B]^{-1} \] 2. **Understand the Order of Reaction**: The order of a reaction is defined as the sum of the powers of the concentration terms in the rate law. 3. **Extract the Powers from the Rate Expression**: - The power of [A] is \(\frac{3}{2}\). - The power of [B] is \(-1\). 4. **Calculate the Total Order**: To find the total order of the reaction, we sum the powers: \[ \text{Total Order} = \frac{3}{2} + (-1) \] 5. **Perform the Calculation**: - Convert \(-1\) to a fraction for easy addition: \[ -1 = -\frac{2}{2} \] - Now, add the fractions: \[ \text{Total Order} = \frac{3}{2} - \frac{2}{2} = \frac{1}{2} \] 6. **Conclusion**: The order of the reaction is \(\frac{1}{2}\), indicating that it is a half-order reaction. ### Final Answer: The order of the reaction is \(\frac{1}{2}\). ---
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