A flask contains a mixture of two compounds AB and XY. Both of these decompose on heating by first order reaction. If the half-life of AB is 30 min and that of XY is 10 min, how long will it take for the concentration of AB to be four times that of XY ? Assume that the initial concentration of both AB and XY to be same.

A flask contains a mixture of two compounds AB and XY. Both of these d

1.	A flask contains a mixture of two compounds AB and XY. Both of these decompose on heating by first order reaction. If the half-life of AB is 30 min and that of XY is 10 min, how long will it take for the concentration of AB to be four times that of XY ? Assume that the initial concentration of both AB and XY to be same.
Answer» Solution :SUPPOSE time taken for [AB] to be EQUAL to 4 [XY] is t min. Half-lives of AB in t min `=(t)/(30)` Amount of AB LEFT after `t//30` half-lives `=((1)/(2))^(t//30)[AB]_(0)` Half-lives of XY in t min `=(t)/(10)` Amount of XY left after `t//10` half-lives `=((1)/(2))^(t//10)[XY]_(0)` But `[AB]=4[XY]:.((1)/(2))^(t//30)[AB]_(0)=4XX((1)/(2))^(t//10)[XY]_(0)` But `[AB]_(0)=[XY]_(0)("Given")` `:.((1)/(2))^(t//30)=4xx((1)/(2))^(t//10)" or "((1)/(2))^(t//30-t//10)=4" or "2^((t//10-t//30))=2^(2)" or "(t)/(10)-(t)/(30)=2` or `20t=600"or"t=30" min"`