(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
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 3 (Option B)
(Show the work for these questions) 35. What is the half-life of a medication for which...
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