33) The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.13 M. it takes __ min for it to decrease to 0.085 M. A) 12 B) 10. C) 8.0 D) 11 E) 7.0 Answer: C

The half-life of a first-order reaction is the time it takes for the concentration of the reactant to decrease to half of its initial concentration. In this case, the half-life is given as 13 minutes. The question asks how long it takes for the concentration to decrease from 0.13 M to 0.085 M.To solve this, we can use the formula for first-order kinetics: Where:- is the final concentration- is the initial concentration- is the rate constant- is the timeFirst, we need to find the rate constant . We can use the half-life formula for a first-order reaction: Given that minutes, we can solve for : Now, we can use the first-order kinetics formula to find the time it takes for the concentration to decrease to 0.085 M: Solving for , we get: Therefore, the correct answer is C) 8.0 minutes.