Mechanism of a hypothetical reaction
`X_2+Y_2rarr2XY`, is given below :
(i) `X_2rarrX+X(fast)`
(ii) `X+Y_2=XY+Y`(slow)
(iii) X+Y`rarr`XY(fast)
The overall order of the reaction will be

Options

A. 2
B. 0
C. 1.5
D. 1

Answer

C

Explanation

Correct the reactions given in question as
`X_2hArrX+X` (fast)
`X+YrarrXY+Y` (slow)
Slow step is the rate determining step, Rate =k[X]`[Y_2]`
Equilibrium constant for fast step, `K=([X]^2)/([X_2])[X]=sqrt(K[X_2])`
By substituting [X] in equation (i), we get
Rate=`ksqrt(K[X_2])[Y_2]=k.[X_2]^(1//2)[Y_2]`
`therefore` Order of reaction =`1/2+1=3/2=1.5`