# . In a reaction between A and B the initial rate of reaction

In a reaction between A and B the initial rate of reaction (r0) was measured for different intial concnetration of A and B as given below.

 A/mol L-1 0.20 0.20 0.40 B/mol L-1 0.30 0.10 0.05 r0 /mol L-1 s-1 5.07 x 10-5 5.07 x 10-5 1.43 x 10-5

What is the order to the raction with respect to A and B?

Hint: (i) Rate of reaction = k[A]x [B]y; Order = x (with respect to A) and y (with respect to B)

(ii) Make three equations for the three experiments by putting the value of [A][B] and r0 and solve them to find the value of x and y

Rate law states that

Rate = k[A]x[B]y

(Rate)1 = k[0.20]x[0.30]y = 5.07 x 10-5 ......(i)

(Rate)2= k[0.20]x[0.10]y= 5.07 x 10-5​ ......(ii)

(Rate)3= k[0.40]x[0.05]y= 1.43 x 10-4​ ......(iii)

Dividing equation (i) by equation (ii)

(Rate)1/(Rate)2 = k[0.20]x[0.30]y/k[0.20]x[0.10]y = 5.07 x 10-5​ /5.07 x 10-5​ = 1

y =0= 1; y = 0

Now dividing equation (ii) by (iii)

(Rate)2/(Rate)3= k[0.20]x[0.10]0/k[0.40]x[0.05]0= 5.07 x 10-5​ /1.43 x 10-4

[1/2]x = 1/2.82

2x = 2.82

x log 2 = log 2.82

x = 1.4957 = 1.5

Order with respect to A = 1.5

Order with respect to B = 0