Pseudo First Order Reactions - Kinetics

A RThe first-order reversible liquid reaction takes place in a batch reactor. After 8 minutes, conversion ofA is 33.3% while equilibrium conversion is 66.7%. Find the rate equation for this reaction.

SOLVED:Consider the reversible, first-order interconversion of two molecules A and B: A krki⇌ B where kf=3.0 ×10^-3  s^-1 is the rate constant for the forward reaction and kr=1.0 ×10^-3  s^-1 is the rate constant for the reverse reaction. We'll see in the next chapter that a reaction does not go to completion, but instead reaches a state of equilibrium with comparable concentrations of reactants and products if the rate constants kf and kr have comparable values. (a) What are the rate laws for t