The following results have been obtained during the kinetic studies of the reaction,
`2A + B to C +D`.

Determine the rate law and the rate constant for the reaction.

Explanation

Rate law may be expressed as
Rate `= k [A]^(x) [B]^(y)`
`("Rate")_1 = 6.0 xx 10^(-3) = k (0.1)^(x) (0.1)^(y)" "...(i)`
`("Rate")_2 = 7.2 xx 10^(-2) = k (0.3)^(x) (0.2)^(y) " "...(ii)`
`("Rate")_4 = 2.88 xx 10^(-1) = k (0.3)^(x) = (0.4)^(y) " "...(iii)`
`("Rate")_4 = 2.40 xx 10^(-2) = k (0.4)^(x) (0.1)^(y)" "...(iv)`
`(("Rate")_1)/(("Rate")_4) = (6.0 xx 10^(-3) )/( 2.40 xx 10^(-2) ) = (k(0.1)^(x) (0.1)^(y))/( k(0.4)^(x) (0.1)^(y))`
or `(1)/(4) = ((0.1)^(x) )/( (0.4)^(x) ) = ((1)/(4))^(x) " "therefore x =1`
`(("Rate")_2)/(("Rate")_3) = (7.2 xx 10^(-2) )/( 2.88 xx 10^(-1) ) = (k(0.3)^(x) (0.2)^(y) )/( k(0.3)^(x) (0.4)^(y) )`
or `(1)/(4) ((0.2)^(y) )/( (0.4)^(y) ) = ((1)/(2))^(y) " "therefore y=2`
Now, rate law expression is given by
Rate `= k[A][B]^2`