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

A=A_0e^{-kt},

where A is the concentration at time t, the initial concentration is A_0, and k is the rate constant.

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

A=0.2\cdot A_0 when t=81.1

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