During the kinetic study of the reaction , `2A + B to C+ D ,` following results were obtained

Based on the above date which one of the following is correct ?

Options

A. `Rate =k[A]^(2)[B]`
B. `Rate =K[A][B}`
C. `Rate k [A]^(2) [B]^(2)`
D. `Rate =k [A][B]^(2)`

Answer

D

Explanation

Let the of reaction with respect to A is x and with respect to B is Y thus ,
rate `=k|a|^(X)|B|^(y)`
( x and y are stoichiometric coefficient ) for the given cases ,
`I, Rate=K(0,1)^(X)(0,1)^(y) =6.0xx10^(-3)`
`II. rate =K (0,3)^(X)(0.2)^(y)=7.2xx10^(-2)`
`III. rate =K(0.3)^(X)(0.40)^(y)=2.88xx10^(-1)`
`IV, rate = K(0,4)^(X) (0.1) ^(y) =2.40xx10^(-2)`
dividing Eq. (i) by Eq.(iv) we get
`((0.1)/(0.4))^(X)((0.1)/(0.1))^(Y)=(6.0xx10^(-3))/(2.4xx10^(-2))`
`or ((1)/(4))^(x)=((1)/(4))^(1)`
` therefore x=1`
On dividing Eq.(II) by Eq.(ii) we get
`((0.3)/(0.3))^(x)((0.2)/(0.4))^(y)=(7.2xx10^(-2))/(2.88xx10^(-1))`
`or ((1)/(2))^(y)=(1)/(4)`
`or ((1)/(2))^(y) =((1)/(2))^(2)`
`therefore y=2`
thus rata law is ,
rate = `K[A]^(1) [B]^(2)`
`=k|A|[B]^(2)`