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

(i) Case I Initial rate`=k[A][B]^(2)" "`(Given)
`= (2.0 xx 10^(-6)" mol"^(-2)" L"^(2)" s"^(-1) ) xx (0.1" mol L"^(-1) ) xx (0.2" mol L"^(-1) )^(2)`
`= 8.0 xx 10^(-9)" mol L"^(-1) " s"^(-1)" "(1)`
(ii) Case II 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) = (2.0 xx 10^(-6)" mol"^(-2)" L"^(2)" s"^(-1) )xx(0.06" mol L"^(-1) ) xx (0.18" mol L"^(-1) )^(2)`
`= 3.89 xx 10^(-9)" mol L"^(-1)" s"^(-1)" "(1)`