Question

Suppose that the half-life of steroids taken by an athlete is 42.0 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for 15.0% of steroids to remain in the athlete’s body?

Answer 1

Answer

115 days

Explanation

(1/2)ⁿ = x

where,

n = number of half life elapsed

x = fraction of reactant remaining n half life

(1/2)ⁿ = 0.15

take log on both side

nlog(0.5) = log(0.15)

-n0.3010 = - 0.8239

n = 2.737

Time required = n × t_{1/2 = 2.737 × 42.0days = 115 days}