Aseries of experiments were performed to determine the mechanism of the reaction 2a + b → c + d. given the following data, which of the following proposed mechanisms is/are most likely correct?
experiment [a] [b] plot that gave straight line
#1 1.0 m 1 x 10-4 m 1n[b] vs time
#2 1 x 10-4m 1.0 m 1/[a] vs time
a. a + b < = > e (fast)
e + b --> c + d (slow)
b. a + b < = > e (fast)
e + a --> c + d (slow)
c. a + a --> e (slow)
e + b --> c + d (fast)

1) as we are getting a straight line on plotting ln[b] v/s time so this is first order with respect to [b].
2) as we are getting a straight line on plotting 1/[a] v/s time so this second order with respect to [a]
as per results both the reactants are affecting the rate of reaction so these two should be in the rate determining slow step
let us check: remember rate depends on the slowest step
mechanism i:
rate = )
however, e is an intermediate, so we will use equilibrium reaction of step (1)
k = [e] / [a] [ b]
[e] = k [a][b]
[e] = k*)
put (ii) in (i) to remove the intermediate from the rate law expression
rate = k2 k*[a][b][b]
rate = k2 k[a][b]2
here the rate is directly proportional to [a] and [b]2, which is not consistent
mechanism ii:
rate = k2 [e][a] )
again, e is an intermediate. we will eliminate it .
we will use 1st step
k = [e]/[a][b]
[e] = k*)
put (ii) in (i)
so,
rate = k2 k[a][a][b]
rate = k2 k*[a]2[b]
hence this is the correct mechanims
mechanism iii:
rate = k2 [a][a]
rate = k2 [a]2
again this is not in agreement with the experiment results
hope this ♡