Chemical Kinetics and Nuclear ChemistryHard

Question

During the kinetic study of the reaction, 2A + B → C + D, following results were obtained

Based on the above data which one of the following is correct ?

Options

A.rate = k [A]2[B]
B.rate = k [A] [B]
C.rate = k [A]2[B]2
D.rate = k [A] [B]2

Solution

Let the order of reaction with respect to A is x and with respect to B is y. Thus,
      rate = k [A]x [B]y
For the given cases,
(i) rate = k (0.1)x (0.1)y = 6.0 × 10-3
(ii) rate = k (0.3)x (0.2)y = 7.2 × 10-2
(iii) rate = k (0.3)x (0.40)y = 2.88 × 10-1
(iv) rate = k (0.4)x (0.1)y = 2.40 ×10-2
On dividing eq. (i) by (iv), we get
       
or                
∴                   x = 1
On dividing Eq. (ii) by (iii), we get

or     
∴           y = 2
Thus, rate law is,
rate = k [A]1 [B]2 or
= k [A] [B]2

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