If it takes 81.1 min for the concentration of a reactant to drop to 20% of its initial value in a first-order reaction, what is the rate constant for the reaction in the units min-1?

In a first-order equation, the concentration as a function of time can be written as

,

where is the concentration at time , the initial concentration is , and is the rate constant.

In this case, we know that after 81.1 min, the concentration is only 20% of it's initial value. Hence

when

So just plug in those values in the equation and solve for . That's it.