What is the overall order of the reaction which has the following rate expression? Rate = k[A]$^\frac{1}{2}$[B]$^\frac{3}{2}$
- One
- Two
- Zero
- Three
The Correct Option is D
Approach Solution - 1
The overall order of a reaction is determined by summing the exponents of the concentration terms in the rate expression. Given the rate expression: Rate = k[A]$^\frac{1}{2}$[B]$^\frac{3}{2}$, we identify the exponents for each concentration:
The exponent of [A] is $\frac{1}{2}$.
The exponent of [B] is $\frac{3}{2}$.
To find the overall order, add these exponents:
Overall order = $\frac{1}{2}$ + $\frac{3}{2}$ = 2
Approach Solution -2
The rate expression for a given reaction is:
Rate = k[A]1/2[B]3/2
The order of the reaction with respect to A is 1/2, and with respect to B is 3/2.
The overall order of the reaction is obtained by summing the exponents of the concentration terms in the rate expression. Thus, the overall order is:
\( \frac{1}{2} + \frac{3}{2} = 2 \).
Therefore, the overall order of the reaction is 2, which indicates the reaction is second-order overall.
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