Question

(Show the work for these questions)

35. What is the half-life of a medication for which only 12.5% remains after 24 hours?

A. 4 hours

B. 8 hours

C. 16 hours

D. None of the above

36. What is the half-life of an orally administered medicated syrup if its level is down to 61⁄4 % after 12 hours?

A. 6 hours

B. 4 hours

C. 3 hours

D. 2 hours

37. When a 500-mg medical dosage has degenerated to approximately 63 mg of its original, how many half-lives have passed?

A. 4

B. 3

C. 2

D. None of the above

Answer 1

1) Let us consider initial amount, Ao = 100

Final amount, At= 12.5

t = 24 hrs

ln [A]t = -kt + ln [A]o

ln 12.5 = -24k + ln 100

2.526 = -24k + 4.605

2.526-4.605 = -24k

-2.079/-24 = k

rate constant, k = 0.0866 /hr

Half life is [A]t = 50

t0.5 = half life = 0.693/k = 0.693/0.0866 = 8 hrs (option B)

2)

Let us consider initial amount, Ao = 100

Final amount, At= 6 (1/4) = 25/4 = 6.25

t = 12 hrs

ln [A]t = -kt + ln [A]o

ln 6.25 = -12k + ln 100

1.8326 = -12k + 4.605

1.8326-4.605 = -12k

-2.7724/-12 = k

rate constant, k = 0.231 /hr

Half life is [A]t = 50

t0.5 = half life = 0.693/k = 0.693/0.231 = 3 hrs (option C)

3) [A]0 = 500 mg

[A]t = 63 mg

A(t) = Ao(0.5)^t/t0.5

number of half lives = t/t0.5

63 mg = 500 (0.5)ⁿ

63/500 = 0.5ⁿ

0.126 = 0.5ⁿ

Apply log₁₀ on both sides

log 0.126 = n log 0.5

-0.8996 = n x -0.3010

n = 0.8996/0.3010 = 2.99 $\approx$ 3 (Option B)