A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is
ID: 1049531 • 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. Calculate the half-life for the antibiotic. The units should be in days and should be calculated to three significant figures. If you start with a 1.0 M solution, how long would it take for 39 % of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures.Explanation / Answer
For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
Mo = initial concentration = 1.24x10-2 mol/L OR M
M= concentration after time t = 0.92x10-2 mol/L OR M
t = time = 10 days
Plug the values we get k = 0.0298 day-1
Half-life , t1/2 = 0.693 / k
= 0.693 / 0.0298
= 23.2 days
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For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
Mo = initial concentration = 1.0 M
M= concentration after time t = Mo - (39% Mo) = 61% of Mo = 0.61Mo = 0.61x1.0 = 0.61 M
t = time = ?( days)
Plug the values we get t= 16.6 days
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