For the reaction A+Bto Products, the following initial rates were obtained at various given initial concentrations. ltrbgt Write rate law and find the rate constant for the above reaction.

For the reaction A+Bto Products, the following initial rates were obta

1.	For the reaction A+Bto Products, the following initial rates were obtained at various given initial concentrations. ltrbgt Write rate law and find the rate constant for the above reaction.
Answer» Solution :The RATE law equation may be expressed as: Rate = `k[A]^(p)[B]^(q)` ltrbgt COMPARING experiments, 1 and 2, `(Rate)_(1)=k[0.1]^(p)[0.1]^(q)=0.05` `(Rate)_(2) = k[0.2]^(p)[0.1]^(q)=0.10` Dividing eqn. (ii) by eqn. (i), `(Rate)_(2)/(Rate)_(1) = (k[0.2]^(p)[0.1]^(q))/(k[0.1]^(p)[0.1]^(q)) = 0.10/0.05 = 2:[2]^(p) = [2]^(1)` or p=1 Comparing experiments 1 and 3, `(Rate_(1)) = k[0.1]^(p)[0.1]^(q)=0.05` `(Rate)_(3) = k[0.1]^(p)[0.2]^(q)=0.05` Dividing eqn. (iii) by eqn. (i), `(Rate_(3))/(Rate_(1)) = (k[0.1]^(p)[0.2]^(q))/(k[0.1]^(p)[0.1]^(q)) = 0.05/0.05 = 1 , [2]^(1) = 1=[2]^(0) or q=0` Rate law for the reaction, rate = `k[A]^(1)[B]^(0)` Rate constant (k) for the reaction may be CALCULATED as follows: `k[0.1]^(p)[0.1]^(q)=0.05 , k[0.1]^(1)[0.1]^(0)=0.05` , `k=(0.05)/0.1=0.5`