For the reaction: `2A+BrarrA_(2)B` the rate `k[A][B]^(2) " with "k=2.0xx10^(-6)"mol"^(-2).L^(2).s^(-1)` . Calculate the initial rate of the reaction when `[A]=0.1"mol.L"^(-1) , [B]=0.02"mol".L^(-1)` . Calculate the rate of reaction after [A] is reduced to `0.06"mol.L"^(-1)` .

Explanation

Given , initial rate `=k[A][B]^(2)`
Initial concentration : `[A]=0.1"mol.L"^(-1),[B]=0.2"mol.L"^(-1),and k=2.0xx10^(-6)"mol"^(-2).L^(2),and k = 2.0xx10^(-6)"mol"^(-2).L^(2).s^(-1)`
`therefore` Initial rate `=(2xx10^(-6))xx(0.1)xx(0.2)^(2)`
`=8xx10^(-9)"mol"^(-1).s^(-1)`
and final concentration of `[A]=0.06"mol"^(-1)`
`therefore` Decrease in concentration of [A] = (0.1 - 0.06)
`=0.04"mol.L"^(-1)`
From the reaction , 2mol of A react with 1 mol of B.
`therefore` 0.04 mol of A will react with `(0.04)/(2)=0.02"mol".L^(-1)of B`
`therefore` Concentration of unreacted `B=0.2-0.02=0.18"mol.L^(-1)`
`therefore" The final rate"=(2.0xx10^(-6))xx(0.06)xx(0.18)^(2)`
`=3.89xx10^(-9)"mol.L"^(-1).s^(-1)`