Elimination of the pharmaceutical IV antibiotic gentamicin follows first-order kinetics. If the half-life of gentamicin is 1.5 hours for an adolescent. What fraction of the original reactant concentration will remain after 8 hours if the original concentration was 8.4 x 10-5 M.

Explanation:

The given data is:

The half-life of gentamicin is 1.5 hrs.

The reaction follows first-order kinetics.

The initial concentration of the reactants is 8.4 x 10-5 M.

The concentration of reactant after 8 hrs can be calculated as shown below:

The formula of the half-life of the first-order reaction is:

Where k = rate constant

t1/2=half-life

So, the rate constant k value is:

The expression for the rate constant is :

Substitute the given values and the k value in this formula to get the concentration of the reactant after time 8 hrs is shown below:

The concentration of reactant remains after 8 hours is 2.09x10^-6M.