The rate of reaction
2NO + Cl₂ → 2NOCl
is double when concentration of Cl₂ is doubled and it becomes 8 times when concentrations of both NO and Cl₂ are doubled. Deduce the order of this reaction.

{Rate}_{1} = k [NO]^{x} [{Cl}_{2}]^{y} . . . (i) 2 \times {Rate}_{1} = k [NO]^{x} [2 {Cl}_{2}]^{y} . . . (ii)

Dividing (ii) by (i), we get

\frac{2}{1} = \frac{(2)^{y}}{1} y = 1

8 \times {Rate}_{1} = k [2 NO]^{x} [2 {Cl}_{2}]^{y}

...(iii)

Dividing (iii) by (ii) we get

4 = \frac{{[2 NO]}^{x}}{[NO]^{x}} = 2^{x} 2^{x} = 2^{2} \Rightarrow x = 2

Order of reaction is 2 + 1 = 3.

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