For the reaction `A + B to` products, what will be the order of reaction with respect to A and B?
`{:("Exp",[A](mol L^(-1)),[B](mol L^(-1)),"Initial rate (mol L^(-1) s^(-1))),(1,2.5 xx 10^(-4), 3 xx 10^(-5), 5 xx 10^(-4)),(2,5 xx 10^(-4),6 xx 10^(-5), 4 xx 10^(-3)),(3, 1xx 10^(-3), 6 xx 10^(-5), 1.6 xx 10^(-2)):}`

Options

A. 1 with respect to A and 2 with respect to B
B. 2 with respect to A and 1 with respect to B
C. 1 with respect to A and 1 with respect to B
D. 2 with respect to A and 2 with respect to B

Answer

B

Explanation

Rate `= k [A]^(x) [B]^(y)`
From exp.(1), `5 xx 10^(-4) = k (2.5 xx 10^(-4))^(x (3 xx 10^(-5))^(y)`
Frox exp. (2), `4 xx 10^(-3) = k (5 xx 10^(-4))^(x) (6 xx 10^(-5))^(y)`….(ii)
Dividing (ii) by (i), `(4 xx 10^(-3))/(5 xx 10^(-4))`
From exp. (3) `1.6 xx 10^(-2) = k (1 xx 10^(-3))^(x) (6 xx 10^(-5)^(-6))^(y)`...(iii)
Dividing (iii) by (ii), `(1.6 xx 10^(-2))/(4 xx 10^(-3)) = 2^(x) = 4`
or x = 2, y = 1
Hence order with respect to A is 2 and with respect to B is 1.