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 30 % of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures.
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For a first-order reaction, the rate equation is: \[ \ln \left( \frac{[A]_0}{[A]} \right) = kt \] where \([A]_0\) is the initial concentration, \([A]\) is the concentration at time \(t\), and \(k\) is the rate constant. Show more…
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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 55 % of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures.
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