During the kinetic study of the reaction, 2 ~A + B C + D , following results were obtained ( array |c|c|c|c| Run & [A] / mol~ L ⁻¹ & [B] / mol~ L ⁻¹ & array cc Initial rate of formation of D / mol~ L ⁻¹ ~min ⁻¹ array I & 0.1 & 0.1 & 6.0 10⁻³ II & 0.3 & 0.2 & 7.2 10⁻² III & 0.3 & 0.4 & 2.88 10⁻¹ IV & 0.4 & 0.1 & 2.40 10⁻² array ) Based on the above data which one of the following is correct?

Step-by-step solution

Let the order of reaction with respect to A is x and with respect to B is y . Thus, rate = k [ A ]^ x [ B ]^ y For the given cases, (I) rate = k (0.1)^ x (0.1)^ y =6.0 10⁻³ (II) rate = k (0.3)^ x (0.2)^ y =7.2 10⁻² (III) rate = k (0.3)^ x (0.40)^ y =2.88 10⁻¹ (IV) rate = k (0.4)^ x (0.1)^ y =2.40 10⁻² On dividing Eq. (I) by (IV), we get ( 0.1 0.4 )^x ( 0.1 0.1 )^y= 6.0 10⁻³ 2.4 10⁻² or ( 1 4 )^x= ( 1 4 )^1 x =1 On dividing Eq. (II) by (III), we get aligned & & ( 0.3 0.3 )^x ( 0.2 0.4 )^y & = 7.2 10⁻² 2.88 10⁻¹ or &