Acertain first-order reaction (a→products) has a rate constant of 8.10×10−3 s−1 at 45 ∘c. how many minutes does it take for the concentration of the reactant, [a], to drop to 6.25% of the original concentration? express your answer with the appropriate units.

The answer is 5.7 minutes

Explanation:

A first-order reaction follow the law of . Where [A] is the concentration of the reactant at any t time of the reaction, is the concentration of the reactant at the beginning of the reaction and k is the rate constant.

Dropping the concentration of the reactant to 6.25% means the concentration of A at the end of the reaction has to be . And the rate constant (k) is 8.10×10−3 s−1

Replacing the equation of the law:

Clearing the equation:

Considering the property of logarithms:

Using the property:

Clearing t and solving:

The answer is in the unit of seconds, but every minute contains 60 seconds, converting the units: