During the kinetic study of the reaction `2A +B rarr C + D` following results were obtained.
`{:(, Run[A],[B] i n M,"Initial rate of fo rmation of D in "m s^(-1),),(I,0.1,0.1,6.0 xx 10^(-3),),(II,0.3,0.2,7.2xx10^(-2),),(III,0.3,0.4,2.88xx10^(-1),),(IV,0.4,0.1,2.40xx10^(-2),):}`
On the basis of above data which one is correct ?

Options

A. rate `=k[A][B]^(2)`
B. rate `=[A]^(2)[B]`
C. rate `=k[A][B]`
D. rate `=k[A]^(2)[B]^(2)`

Answer

A

Explanation

Rate, `r = k[A]^(a)[B]^(b)`
Run I : `6.0 xx 10^(-3)k(0.1)^(a)(0.1)^(b)`….(i)
Run II. `7.2 xx 10^(-2) = k(0.3)^(a)(0.2)^(b)`…(ii)
Run III : `2.88 xx 10^(-1)=k(0.3)^(a)(0.4)^(b)`
Run IV : `2.40 xx 10^(-2) = k(0.4)^(a)(0.1)^(b)`….(iv)
From (ii) and (iii)
`4 = 2^(b)rArr b =2`
From (i) and (iv)
`4 = 4^(a)rArr a=1`
`:.` rate, `r = k [A][B]^(2)` .