Q: Given the reaction $$AB \rightarrow A + B is $$first order in $$AB$$, and $$k = 0.25\ \text{min}^{-1}$$, what is the half-life ($$t_{1/2}) of $$the reaction?

$$t_{1/2} = \frac{0.693}{0.25} = 2.77\ \text{min}$$

Q: If the initial concentration of a reactant is $$0.80\ \text{M}$$ and after $$30$$ minutes it is $$0.20\ \text{M} in a $$first-order reaction, what is the rate constant $$k$$?

$$k = \frac{1}{30} \ln\left(\frac{0.20}{0.80}\right) = 0.0462\ \text{min}^{-1}$$

Question 1

Which of the following best describes the difference between a differential rate law and an integrated rate law?

Accepted Answer

A differential rate law expresses the rate of change of concentration over time, while an integrated rate law expresses the concentration of a reactant as a function of time.

Question 2

For a first-order reaction, which of the following equations correctly represents the integrated rate law?

Accepted Answer

$$\ln [A]_t = -kt + \ln [A]_0$$

Question 3

A reaction is found to have a rate constant with units of $$	ext{M}^{-1}	ext{s}^{-1}. $$What is the order of the reaction?

Accepted Answer

Second order

Question 4

If the half-life of a reaction is independent of the initial concentration, what is the order of the reaction?

Accepted Answer

First order

Question 5

Given the reaction $$AB ightarrow A + B is $$first order in $$AB$$, and $$k = 0.25\ 	ext{min}^{-1}$$, what is the half-life ($$t_{1/2}) of $$the reaction?

Accepted Answer

$$t_{1/2} = \frac{0.693}{0.25} = 2.77\ 	ext{min}$$

Question 6

Which graph would be linear for a first-order reaction when plotted versus time?

Accepted Answer

$$\ln [A] vs. $$time

Question 7

A student observes that plotting $$\frac{1}{[A]}$$ versus time yields a straight line. What is the order of the reaction with respect to $$A$$?

Accepted Answer

Second order

Question 8

For a zero-order reaction, which of the following is true about the half-life as the reaction proceeds?

Accepted Answer

The half-life increases as the concentration decreases.

Question 9

If the initial concentration of a reactant is $$0.80\ 	ext{M}$$ and after $$30$$ minutes it is $$0.20\ 	ext{M} in a $$first-order reaction, what is the rate constant $$k$$?

Accepted Answer

$$k = \frac{1}{30} \ln\left(\frac{0.20}{0.80}ight) = 0.0462\ 	ext{min}^{-1}$$

Question 10

Which of the following statements is true regarding the use of integrated rate laws?

Accepted Answer

They allow calculation of reactant concentration at any time if the rate constant and initial concentration are known.

Question 11

A radioactive isotope decays by a first-order process with a half-life of $$10$$ hours. How long will it take for the sample to decay to $$12.5\% of $$its original amount?

Accepted Answer

$$30$$ hours

Question 12

Which of the following is a diagnostic tool for identifying a first-order reaction?

Accepted Answer

The half-life is independent of the initial concentration.

Question 13

For a reaction with the integrated rate law $$[A]_t = [A]_0 - kt$$, what is the order of the reaction?

Accepted Answer

Zero order

Question 14

A chemist determines that the rate constant for a reaction is $$0.015\ 	ext{M}^{-1}	ext{s}^{-1}. $$Which integrated rate law should be used to calculate the concentration of reactant at time $$t$$?

Accepted Answer

$$\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$$

Question 15

Which of the following best explains why integrated rate laws are useful in chemical kinetics?

Accepted Answer

They provide a direct relationship between concentration and time, enabling prediction of reactant or product concentrations at any moment.

Integrated Rate Laws, Reaction Order, and Half-Lives in Chemical Kinetics

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