Q: A drug has an initial concentration of $$5.0 \times 10$$^{-3}$$\ \text{g}\cdot\text{cm}^{-3} in $$aqueous solution. After 24 months, the concentration drops to $$3.48 \times 10$$^{-3}$$\ \text{g}\cdot\text{cm}^{-3}. $$The degradation process follows first-order kinetics. What is the rate constant for this reaction?

$$1.5 \times 10$$^{-2}$$\ \text{month}^{-1}$$

Question 1

Which of the following best describes a zero-order reaction in pharmaceutical drug degradation?

Accepted Answer

The degradation rate is independent of the reactant concentration.

Question 2

A drug suspension decomposes by zero-order kinetics with a rate constant of $$2\ 	ext{mg}\cdot	ext{mL}^{-1}\cdot	ext{month}^{-1}. If $$the initial concentration is $$100\ 	ext{mg}\cdot	ext{mL}^{-1}$$, what is the shelf life ($$t_{0.9}$$)?

Accepted Answer

5 months

Question 3

Which equation correctly represents the integrated rate law for a first-order reaction?

Accepted Answer

$$[A]_t = [A]_0 e$$^{-kt}$$

Question 4

A tablet has remained in storage for 2 years since manufacture. The decomposition rate constant ($$k) is$$ $$6 	imes 10$$^{-2}$$\ 	ext{year}^{-1}$$ and the reaction is first-order. What percentage of the original drug remains after 2 years?

Accepted Answer

89%

Question 5

Which of the following is true regarding second-order kinetic processes?

Accepted Answer

The half-life may be represented by $$t_{0.5} = \frac{[A]_0}{2k}.$$

Question 6

When the results of a drug degradation study are plotted as the logarithm of the amount of API remaining against time and yield a straight line, which of the following is true?

Accepted Answer

The half-life may be represented by $$t_{1/2} = 0.693/k.$$

Question 7

A drug has an initial concentration of $$5.0 	imes 10$$^{-3}$$\ 	ext{g}\cdot	ext{cm}^{-3} in $$aqueous solution. After 24 months, the concentration drops to $$3.48 	imes 10$$^{-3}$$\ 	ext{g}\cdot	ext{cm}^{-3}. $$The degradation process follows first-order kinetics. What is the rate constant for this reaction?

Accepted Answer

$$1.5 	imes 10$$^{-2}$$\ 	ext{month}^{-1}$$

Question 8

Which of the following represents the relationship between rate constant, $$k$$, and absolute temperature, $$T$$, as predicted by the Arrhenius equation?

Accepted Answer

A plot of $$\ln k$$ against $$1/T$$ will be linear.

Question 9

The rate constant for a reaction is $$2.7 	imes 10$$^{-4}$$\ 	ext{L}\cdot	ext{mol}^{-1}\cdot	ext{s}^{-1} at 600K $$and $$3.5 	imes 10$$^{-3}$$\ 	ext{L}\cdot	ext{mol}^{-1}\cdot	ext{s}^{-1} at 650K. $$Calculate $$k at 700K.$$

Accepted Answer

0.032 L.mol$$^{-1}.s$^{-1}$$

Question 10

Which of the following is the correct integrated rate law for a zero-order reaction?

Accepted Answer

$$[A]_t = [A]_0 - kt$$

Question 11

In a reversible reaction $$A \rightleftharpoons B$$, at equilibrium, which expression correctly relates the equilibrium constant $$K_{eq} to $$the rate constants?

Accepted Answer

$$K_{eq} = \frac{k_1$}{k_{-1}}$$

Question 12

Which factor does NOT generally increase the rate of a chemical reaction?

Accepted Answer

Decreasing the surface area of a solid reactant

Question 13

For a first-order reaction, which plot will yield a straight line?

Accepted Answer

Logarithm of concentration vs. time

Question 14

Which of the following is the correct expression for the half-life ($$t_{1/2}) of a $$first-order reaction?

Accepted Answer

$$t_{1/2} = \frac{0.693}{k}$$

Question 15

Which of the following is a characteristic of pseudo first-order reactions?

Accepted Answer

The rate law simplifies to $$R = k'[A]$$ because one reactant is in large excess.

Question 16

Which of the following is the correct form of the Arrhenius equation?

Accepted Answer

$$k = Ae$$^{-Ea/RT}$$

Question 17

What is the unit of the gas constant $$R$$ when used in the Arrhenius equation with energy in J and temperature in K?

Accepted Answer

J$$\cdotK$^{-1}\cdot$$mol$$^{-1}$$

Question 18

Which plot confirms a second-order reaction when analyzing drug decomposition data?

Accepted Answer

Inverse concentration vs. time

Elementary Chemical Kinetics: Principles, Rate Laws, and Applications

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