# A pharmacist must calculate the shelf life for an antibiotic. The antibiotic is stored as a solid...

## 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 data in the table below.

{eq}\begin{array}{|c|c|} \hline \text{Time (days)} & \text{[Antibiotic] (Mol/L)} \\ \hline \text{0} & 1.24 \times 10^{-2} \\ \hline \text{10.} & 0.92 \times 10^{-2} \\ \hline \text{20.} & 0.68 \times 10^{-2} \\ \hline \text{30.} & 0.50 \times 10^{-2} \\ \hline \text{40.} & 0.37 \times 10^{-2} \\ \hline \end{array} {/eq}

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 77% of the antibiotic to decompose? The answer should be in days and should be calculated to three significant figures.

## First Order Kinetics

For first order kinetics, natural log of reactant concentration plotted against time should yield a straight line. The fitted line corresponds to the integrated rate law equation

$$ln [A]_t = -kt + ln [A]_o $$

which allows one to extrac the rate constant (k) of the reaction.

## Answer and Explanation: 1

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View this answer**Part : {eq}t_{1/2} = 22.9\;day
{/eq}
**

**Part 2: {eq}36.6\;days
{/eq}**

Part 1

Plotting {eq}ln [antibiotic] \;vs\; t {/eq} is shown below.

From...

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Chapter 19 / Lesson 6In chemistry, first-order reactions are linear and depend on just one reactant. Explore the definition and mathematical representation of first-order reactions, and review reaction rates, differential rate law, integrated rate law, half-life, and a sample problem to gain understanding.