The experimentally derived mathematical expression which gives a relation between rate of reaction and concentration of reactants is known as rate law or rate equation. The rate law is established by the kinetic study of a reaction experimentally.

Let us consider a general reaction

mA + nB → pC + qD

\(\frac{dx}{dt}\) α [A]^p x [B]^q 

or, \(\frac{dx}{dt}\) = k [A]^p x [B]^q 

The reaction is said to be of 'p' order with respect to reactant 'A' and of 'q' order with respect to reactant 'B'.

The overall order of the reaction is (p + q).

Thus rate law is given by experimental observation. However, for elementary or simple reactions rate law is written according to the law of mass action.

At 1000 K, the following data were obtained in a homogeneous reaction.

2A(g) + 2B(g) → C(g) + 2D(g)

What is the order of reaction with respect to A?

First order

Let the rate of reaction be given as, r = k[A]^x[B]^y 

3 x 10^-5 = k[5 x 10^-3]^x[2.5 x 10^-3]^y         ......(1)

9 x 10^-5 = k[15 x 10^-3]^x[2.5 x 10^-3]^y         ......(2)

Dividing (1) by (2), we get

\(\frac{3 × 10^{-5}}{9 × 10^{-5}}\) = (\(\frac{5 × 10^{-3}}{15 × 10^{-3}}\))^x

 (\(\frac{1}{3}\))¹ =  (\(\frac{1}{3}\))^x

x = 1