12.4 Integrated rate laws  (Page 5/7)

Describe how graphical methods can be used to determine the order of a reaction and its rate constant from a series of data that includes the concentration of A at varying times.

Use the data provided to graphically determine the order and rate constant of the following reaction: ${\text{SO}}_2{\text{Cl}}_2⟶{\text{SO}}_2+{\text{Cl}}_2$

Use the data provided in a graphical method to determine the order and rate constant of the following reaction:
$2P⟶Q+W$

Pure ozone decomposes slowly to oxygen, ${\text{2O}}_3(g)⟶{\text{3O}}_2(g).$ Use the data provided in a graphical method and determine the order and rate constant of the reaction.

From the given data, use a graphical method to determine the order and rate constant of the following reaction:
$2X⟶Y+Z$

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

What is the half-life for the first-order decay of carbon-14? $({}_6^{14}\text{C}⟶{}_7^{14}\text{N}+{\text{e}}^{-})$ The rate constant for the decay is 1.21 $\times$ 10 ⁻⁴ year ⁻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/s.

What is the half-life for the decomposition of O ₃ when the concentration of O ₃ is 2.35 $\times$ 10 ⁻⁶ M ? The rate constant for this second-order reaction is 50.4 L/mol/h.

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/s. If the initial concentration is 0.500 mol/L, what is the value of t _1/2 ?

The half-life of a reaction of compound A to give compounds D and E is 8.50 min when the initial concentration of A is 0.150 mol/L. How long will it take for the concentration to drop to 0.0300 mol/L if the reaction is (a) first order with respect to A or (b) second order with respect to A ?

Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of 3 $\times$ 10 ⁴ 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 equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 µg (0.15 $\times$ 10 ⁻⁶ g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.

Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected heart problems. The half-lives are 6 h and 73 h, respectively. What percent of the radioactivity would remain for each of the isotopes after 2 days (48 h)?

There are two molecules with the formula C ₃ H ₆ . Propene, ${\text{CH}}_3\text{CH}={\text{CH}}_2,$ is the monomer of the polymer polypropylene, which is used for indoor-outdoor carpets. Cyclopropane is used as an anesthetic:

When heated to 499 °C, cyclopropane rearranges (isomerizes) and forms propene with a rate constant of
5.95 $\times$ 10 ⁻⁴ s ⁻¹ . What is the half-life of this reaction? What fraction of the cyclopropane remains after 0.75 h at 499.5 °C?

Fluorine-18 is a radioactive isotope that decays by positron emission to form oxygen-18 with a half-life of 109.7 min. (A positron is a particle with the mass of an electron and a single unit of positive charge; the equation is ${}_{518}^9\text{F}⟶{}_{18}^8\text{O}+{\text{e}}^{-}.)$ Physicians use ¹⁸ F to study the brain by injecting a quantity of fluoro-substituted glucose into the blood of a patient. The glucose accumulates in the regions where the brain is active and needs nourishment.

(a) What is the rate constant for the decomposition of fluorine-18?

(b) If a sample of glucose containing radioactive fluorine-18 is injected into the blood, what percent of the radioactivity will remain after 5.59 h?

(c) How long does it take for 99.99% of the ¹⁸ F to decay?

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?

Recently, the skeleton of King Richard III was found under a parking lot in England. If tissue samples from the skeleton contain about 93.79% of the carbon-14 expected in living tissue, what year did King Richard III die? The half-life for carbon-14 is 5730 years.

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:

For the past 10 years, the unsaturated hydrocarbon 1,3-butadiene $({\text{CH}}_{\text{2}}=\text{CH}–\text{CH}={\text{CH}}_2)$ has ranked 38th among the top 50 industrial chemicals. It is used primarily for the manufacture of synthetic rubber. An isomer exists also as cyclobutene:

The isomerization of cyclobutene to butadiene is first-order and the rate constant has been measured as 2.0 $\times$ 10 ⁻⁴ s ⁻¹ at 150 °C in a 0.53-L flask. Determine the partial pressure of cyclobutene and its concentration after 30.0 minutes if an isomerization reaction is carried out at 150 °C with an initial pressure of 55 torr.