Question

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.

Answer 1

Step-by-step 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:

`k=(0.693)/(t_1_/_2)`

Where k = rate constant

t1/2=half-life

So, the rate constant k value is:

`k=(0.693)/(1.5 hrs)`

The expression for the rate constant is :

`k=(2.303)/(t) log (initial concentration)/(concentration after time`

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:

`(0.693)/(1.5 hrs) =(2.303)/(8 hrs) x log (8.4x10^-^5)/(y) \\ log (8.4x10^-^5)/(y) =1.604\\(8.4x10^-^5)/(y)=10^1^.^6^0^4\\(8.4x10^-^5)/(y)=40.18\\y=(8.4x10^-^5)/(40.18) \\=>y=2.09x10^-^6`

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