Question

For antibiotics (with half-life of 4 hr), doctor asks the patient to take a double-dose initially at hr 0, then a regular-dose every 4 hr, what is the amount of drug in the body at 24-hr (6 half-lives later)? show work

time	0 hr	4 hr	8 hr	12 hr	16 hr	20 hr	24 hr
drug administered	200 mg	100 mg	100 mg	100 mg	100 mg	100 mg	100 mg
drug remaining	200 mg	?	?	?	?	?	?

Answer 1

for first order reactions amount of reactant remained after 'n' half lives = Initial amount / 2ⁿ.

Hence after 6 half lives (24hours) drug remained = 100 / 2⁶ = 100 / 64 = 1.5625 mg.

(OR)

Intial amount = 100 mg.

Since half life time = 4 hr.

Amount after 4 hr = 100 / 2 = 50 mg.

amount fter 8 hr = 50 / 2 = 25 mg.

amount after 12 hr = 25 / 2 = 12.5 mg.

amount after 16 hr = 12.5 / 2 = 6.25 mg.

amount after 20 hr = 6.25 / 2 = 3.125 mg.

Then, amount after 24 hr = 3.125 / 2 = 1.5625 mg.