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Question:

Mechanism of a hypothetical reaction X2 + Y2 → 2XY is given below:
(i) X2 ⇌ X + X (fast)
(ii) X + Y2 → XY + Y (slow)
(iii) X + Y → XY (fast)
The overall order of the reaction will be:

0

2

1.5

1

Solution:

Take reaction (i) and (iii) to be equilibrium reaction where value of kf >>> kb
Therefore, [X]²/[X2] = K'e ⇌ [X] = K'e⁰·⁵ × [X2]⁰·⁵ − (A)
Since reaction (ii) is the slowest step, so the rate of this reaction will be reaction rate for the main reaction.
⇌ r = Ke[X][Y2] − (B)
Substituting equation(A) in equation(B)
We get r = Ke × K'e⁰·⁵[X2]⁰·⁵[Y2]
Let Ke × K'e = K
⇌ r = K[X2]⁰·⁵[Y2]
Hence, order of reaction is 1 + 0.5 = 1.5