The following results have been obtained during the kinetic studies of the reaction: 2A + B rarr C + D
Determine the rate law and the rate constant for the reaction.

Explanation

(i) Suppoe order of reaction with respect to reactant A is m and w.r.t. B is n. Then the rate law will be Rate `= K [ A] ^(m) [B]^(n)`
`implies (("Rate") "expt I")/( ("Rate") "expt "IV)= ( 6. 0 xx 10 ^(-3))/( 2. 4 xx 10 ^(-2)) = (K (0.1 ) ^( m ) ( 0. 1 ) ^(m))/( K ( 0.4) ^(m) (0.1) ^(n)) = (1)/(4) = ((0. 1 ) ^(m))/( (0.4) ^(m)) = ((1)/(4)) ^(m)`
`(("Rate") "expt II")/( ("Rate")"expt III") = ( 7. 2 xx 10 ^(-2))/( 2. 88 xx 10 ^(-1)) = (K (0. 3) ^(m) ( 0.2) ^(n))/( K ( 0. 3) ^( m) ( 0. 4) ^( n)) = (1)/(4) = ((0.2 ) ^( n ))/( (0.4) ^( n)) = ((1)/(2)) ^( n) = ((1)/(2)) ^(n)`
`implies n = 2`
Rate law expression is given by Rate `= K [A] [B] ^(2)`
(ii) Order of reaction w.r.t. A = 10
Order of reaction w.r.t. B =2
Overall order of reaction `= 1 + 2 = 3`
`K = (( "Rate"))/([A][B] ^(2) ) = ( 6. 0 xx 10 ^(-3) mol L ^(-1) min ^(-1))/( (0.1 mol L ^(-1) ) ( 0.1 mol L ^(-1))) = 6. 0 mol ^(-1) L ^(2) min ^(-1)`