A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is
ID: 507380 • Letter: A
Question
A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is stored as a solid and a fresh solution must be prepared for the patient. The antibiotic is unstable in solution and decomposes according to the following data:
This is a first order process.
If you start with a 1.0 M solution, how long would it take for 41 % of the antibiotic to decompose?
The answer should be in days and should be calculated to three significant figures.
Time (days) [Antibiotic] (mol/L) 0 1.24 x 10-2 10. 0.92 x 10-2 20. 0.68 x 10-2 30. 0.50 x 10-2 40. 0.37 x 10-2Explanation / Answer
Integrated form of first-order rate law to get the rate constant:
ln A = -kt + ln Ao
=> ln 0.0037 = - (k) (40 day) + ln 0.0124
=> -5.59942 = - (k) (40 day) - 4.39005
=>1.20937 = k x 40 day
=>k = 1.20937/40 day-1
=>k =0.03023425 day-1
We could use any of the other intervals.
Integrated form of first-order rate law to get the time:
ln A = -kt + ln Ao
=>ln 0.59 = - (0.03023425 day-1) (t) + ln 1.00
=>-0.5276327 = - (0.03023425 day-1) (t) + 0
=> t=0.5276327 /0.03023425
=> t = 17.45 day
41% of the antibiotic decomposed which means that 59% remained. A is the amount on-hand at the end of the time, which is why I used 0.59.
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