Compounds A and B react according to the following chemical equation.

A(g) + 2B(g)  2C(g)

The concentration of either A or B was changed keeping the concentrations of one of the reactants constant and rates were measured as a function of initial concentration. The following results were obtained. Choose the correct option for the rate equations for this reaction.

Experiment Initial
concentration of
[A]/mol L–1
Initial
concentration of
[B]/moI L–1
Initial
rate (mol L–1 s–1)
1.
2.
3.
0.30
0.30
0.60
0.30
0.60
0.30
0.10
0.40
0.20
1. Rate = kA2B
2. Rate = kAB2
3. Rate = kAB
4. Rate = kA2B0

HINT: Find out the effect of change in rate by changing concentrations of reactant.

Step 1:

The rate of reaction is the change in concentration of reactant with respect to time.

r=k[A]x[B]γ Rate of exp.1 Rate of exp.2=[0.30]x[0.30]y[0.30]x[0.60]y0.100.40=[0.30]γ[0.60]y14=[12]γ[12]2=[12]γy=2

Step 2: 

 Rate of exp.1 Rate ofexp.3=[0.30]x[0.30]y[0.60]x[0.30]y0.100.20=[0.300.60]x[0.300.30]y12=[12]x[1]y12=[12]xi.e.,                     x=1∴                Rate =k[A]x[B]y Rate =k[A]1[B]2