12.4 Integrated Rate Laws

What is the half-life for the first-order decay of phosphorus-32? $\left(_{15}^{32} \text{P} \rightarrow _{16}^{32} \text{S} + \text{e}^{-}\right)$ The rate constant for the decay is 4.85 $\times$ 10⁻² day⁻¹.

What is the half-life for the decomposition of NOCl when the concentration of NOCl is 0.15 M? The rate constant for this second-order reaction is 8.0 $\times$ 10⁻⁸ L mol⁻¹ s⁻¹.

The reaction of compound  A to give compounds  C and  D was found to be second-order in  A. The rate constant for the reaction was determined to be 2.42 L mol⁻¹ s⁻¹. If the initial concentration is 0.500 mol/L, what is the value of t_1/2?

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of 3 $\times$ 10⁴ g/mol that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalyzed reactions can be complex, at low concentrations this reaction can be described by a rate law that is first order in the catalyst (penicillinase) and that also invol…

Suppose that the half-life of steroids taken by an athlete is 42 days. Assuming that the steroids biodegrade by a first-order process, how long would it take for $\frac{1}{64}$ of the initial dose to remain in the athlete’s body?

Nitroglycerine is an extremely sensitive explosive. In a series of carefully controlled experiments, samples of the explosive were heated to 160 °C and their first-order decomposition studied. Determine the average rate constants for each experiment using the following data: