The rate of reaction, 2NO + `Cl_(2) to 2NOCl` is doubled when concentration of `Cl_(2)` is doubled and becomes eight times when concentration of both NO and `Cl_(2)` are doubled. Determine the order of the reaction.

Explanation

Rate( r) = `k[NO]^(x)[Cl_(2)]^(y)` ………….(i)
Rate (2r) = `k[NO]^(x)[2Cl_(2)]^(y)`……………(ii)
Rate (8r) = `k[2NO]^(x)[2Cl_(2)]^(y)`……………….(iii)
Divide eqn. (iii) by eqn. (ii), `(8r)/(2r) = k[2NO]^(x)[2Cl_(2)]^(y)` or `4=[2]^(x)` or `[2]^(x)` or x=2
Divide eqn. (ii) by eqn. (i), `(2r)/r=(k[NO]^(x)[2Cl_(2)]^(y))/(k[NO]^(x)[Cl_(2)]^(y))` or `2=[2]^(y)` or `[2]^(1)` or y=2
The reaction rate (r) = `k[NO]^(1)[Cl_(2)]^(2)` : Order = 2+1 = 3