We will continue our look at the rate equation today by examining the graphs that are generated by reaction concentration over time. In addition, we will consider the concept of half-life of a reaction and how that also connects to the rate data and graphs.

**Learning Objectives**

- Apply the integrated form of a rate law to determine the concentration of a reactant at a given time. (14.4)
- Apply the relationship between the rate constant of a first-order reaction and its half-life. (14.4)

To become familiar with the topics presented in this mission, view the slides below and take note of the key ideas. These are from section 14.4 of your text.

Now work through the practice problems, and post your work to OneNote.

**14.87 **The reaction 2NO_{2} → 2 NO + O_{2} has the rate constant k = 0.63 M^{–1} s^{–1}.

(a) Based on the units for k, is the reaction first or second order in NO_{2}?

(b) If the initial concentration of NO_{2} is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

**14.90** Americium-241 is used in smoke detectors. It has a first–order rate constant for radioactive decay of k = 1.6 × 10^{–3} yr^{–1}. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day ^{–1}.

(a) What are the half-lives of these two isotopes?

(b) Which one decays at a faster rate?

(c) How much of a 1.00-mg sample of each isotope remains after 3 half-lives?

(d) How much of a 1.00-mg sample of each isotope remains after 4 days?

**2005 FRQ#3**

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