For the reaction, `2A +B to A_(2) B`,
The rate `=k[A][B]^(2)` with `k= 2.0 xx 10^(-6)" mol"^(-2)" L"^(2)" s"^(-1)`
Calculate the initial rate of reaction when `[A]=0.1"mol L"^(-1), [B] = 0.2" mol L"^(-1)`. Calculate the rate of reaction after [A] is reduced to `0.06 "mol L"^(-1)`.

Explanation

(a) Case I Initial rate `=k[A][B]^(2)` (Given)
`=(2.0xx10^(-6)"mol"^(-2)L^(2)s^(-1)) xx (0.1"mol L"^(-1)) xx (0.2 "mol L"^(-1))^(2)`
`=8.0xx10^(-9)"mol L"^(-1)s^(-1)`
(b) Case Il Concentration of A at a particular time
`=0.06 "mol L"^(-1)`
Amount of A reacted `=(0.1 -0.06)`
`=0.04" mol L"^(-1)`
Amount of B reacted
`=(1)/(2) xx 0.04"mol L"^(-1) =0.02 "mol L"^(-1)`
Concentration of B at a particular time
`=(0.2 -0.02) "mol L"^(-1)=0.18"mol L"^(-1)`
Rate `=k[A][B]^(2)=(2.0xx10^(-6)"mol"^(-2)L^(2)s^(-1))xx (0.06 "mol L"^(-1)) xx (0.18 "mol L"^(-1))^(2)`
`=3.89xx10^(-9)"mol L"^(-1)s^(-1)`