For the reaction :
`2A + B to A_2B` , the rate = `K[A][B]^2` with `K = 2.0 xx 10^(-6) mol^(-1) lit^(2) sec^(-1)`. Initial concentration of A and B are 0.2 mol/lt and 0.4 mol/lit respectively. Calculate the rate of reaction after [A] is reduced to 0.12 mol/lit

Options

A. ` 3.11 xx 10 ^( - 8 ) `
B. ` 8.6 xx 10 ^( -8) `
C. ` 5.21 xx 10 ^( -6 ) `
D. None of these

Answer

A

Explanation

` 2 A + B to A _ 2 B `
` t = 0 , 0.2 M 0.4 M" " 0 `
` t = t , ( 0.2 - 2 x ) ( 0.4 - x ) " " x `
`[A] = 0 .12 ` (given )
` 0.20 - 2x = 0.12 rArr 2 x = 0.08 `
` x = 0 .04 `
` [A] = ( 0.2 - 2 x ) = ( 0 .2 - 0 .04 xx 2 ) = 0 .12 M `
` [B] = ( 0 .4 - 0.04 ) = 0 .36 M `
` r = K[A][B]^2 = 2 xx 10 ^( - 6 ) xx (0 .12 ) xx ( 0 .36 ) ^2 `
` r = 3.11 xx 10 ^( - 8) `