The following results have been obtained during the kinetic studies of reaction :

The rate law is

Options

A. `(-d[NO])/(dt)=k[NO]^2[H_2]`
B. `(-d[NO])/(dt)=k[NO]^2[H_2]^(1/2)`
C. `(-d[NO])/(dt)=k[NO][H_2]^(2)`
D. `(-d[NO])/(dt)=k[NO][H_2]`

Answer

A

Explanation

For the reaction :
`2NO+2H_2rarrN_2+2H_2O`
`(-d[NO])/(dt)=[NO]^x[H_2]^y` From the gicen set (1) and (2), and `4.8xx10^(-5)=[1xx10^(-2)]^x[1xx10^(-3)]^y`......(ii)
Dividing (i) by (ii)
`43.2/4.8=[3/1]^x1`
i.e. `9=(3)^x` `x=2`
Hence order of [NO] = 2
Similarly, from set (2) and (3)
`(86.4xx10^(-5))/(43.2xx10^(-5))=[(2xx10^(-3))/(1xx10^(-3))]^y`
`2^1=(2)^y`
Hence, order of `[H-2]` = 1
`"hence, "-(d[NO])/(dt)=k[NO]^2[H_2]^1`
and option (a) is the correct option