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Question
For a hypothetical reaction \[\ce{A + B -> C}\], it is found that doubling the concentration of A increases the rate by 8 times and doubling the concentration of B increases the rate by 4 times. The overall order of the reaction is ____________.
Options
4
2
3
5
Solution
For a hypothetical reaction \[\ce{A + B -> C}\], it is found that doubling the concentration of A increases the rate by 8 times and doubling the concentration of B increases the rate by 4 times. The overall order of the reaction is 5.
Explanation:
Let the rate of given reaction be:
(rate)1 = k [A]x [B]y
Doubling the concentration of A increases the rate by 8.
∴ (rate)2 = k [2A]x [B]y = 2x k [A]x [B]y
∴ (rate)2 = 2x × (rate)1
`("rate")_2/("rate")_1` = 2x
8 = 2x
∴ x = 3
Doubling the concentration of B increases the rate by 4.
(rate)3 = k [A]x [2B]y
(rate)3 = 2y k [A]x [B]y
∴ (rate)3 = 2y (rate)1
`("rate")_3/("rate")_1` = 2y
4 = 2y
∴ y = 2
∴ Overall order = x + y = 3 + 2 = 5
