Question

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for of the initial dose to remain in the athlete’s body?

Answer 1

To determine how long it would take for ⅛ of the initial dose to remain in the athlete's body, we can use the concept of half-life.

Step-by-step explanation:

To determine how long it would take for ⅛ of the initial dose to remain in the athlete's body, we can use the concept of half-life. The half-life of the steroids is given as 42 days. In a first-order process, the rate constant can be calculated using the formula:

r = ln(2) / t1/2

where r is the rate constant and t1/2 is the half-life. Substituting the given value, we find:

r = ln(2) / 42

Once we have the rate constant, we can use it to determine the time it takes for ⅛ of the initial dose to remain. The equation for this is:

t = (ln(8) / r) * t1/2

Substituting the values, we get:

t = (ln(8) / (ln(2) / 42)) * 42

Simplifying the expression gives an approximate value of t = 119.7 days.

Answer 2

2.4 × 10² days

Step-by-step explanation:

There is some info missing. I think this is the original question.

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for 1/64 of the initial dose to remain in the athlete’s body?

First, we will calculate the rate constant (k) for this process.

k = ln 2/ (t1/2) = ln 2 / 42 d = 0.017 d⁻¹

We can find the time t so that the concentration of the steroids [A] = 1/64 [A]₀ using the following expression.

`ln[A]/[A]_(0)=-k.t\\t = (ln[A]/[A]_(0))/(-k) \\t = (ln1/64)/(-0.017d^(-1) )\\t=2.4* 10^(2) d`