Question

A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives are 59.00 min for A and 12.00 min for B. If the concentrations of A and B are equal initially, how long will it take for the concentration of A to be four times that of B?

Answer 1

for first order reaction

CA/CAO= e^{(-KA*t) (1)}

CB/CBO = e^{-(KB*t)   (2)}

CA, CB = concentrations of A and B at any time, CAO, CBO =intial concentrations of A and B

for first order reaction Rate constant = 0.693/ half life

KA= Rate constant for A = 0.693/ half life of A= 0.693/59 =0.011746 min-1

KB= Rate constnat for B= 0.693/12 =0.05775

taking ratio of Eq.1 and Eq.2 and noting that CAO=CBO

gives CA/CB =e^-(KA-KB)*t

given CA/CB= 4, -(KA-KB)= KB-KA= 0.05775-0.011746=0.046

4= e^0.046t

t= ln4/0.046=30.13 minutes

4= e