A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is

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: 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 10-2 This is a first order process. Question 1 Calculate the half-life for the antibiotic. The units should be in days and should be calculated to three significant figures. question 2 If you start with a 1.0 M solution, how long would it take for 53 % of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures.

Explanation / Answer

follow this IF(!) the data is acurate slope = dy/dx = (1.24E-2 - 0.37E-2) / (0-40) = 0.87E-2moles/liter / day = 0.87E-2 mole/liter / day * 1 day / 24h*60min/h = 6.04E-6 mole/liter/min Q1) t-1/2 = (1.24E-2 moles/liter / 2) / (6.04E-6 moles/liter / min) = ?? min (about 22 days) Q2) (1/2)^(t/t-1/2) * 1.0 M = ((100-61)/100) * 1.0M SOLVE for t (about 30 days)

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