Chapter 17: KineticsContent check — Chemistry: Atoms First, Chapter 17: Kinetics

Write the equations that relate the rates of consumption of the reactants and the rates of formation of the products.

has been determined to be rate = k[NO]²[H₂]. What are the orders with respect to each reactant, and what is the overall order of the reaction?

Determine the rate law and the rate constant for the reaction from the following experimental data:

Determine the rate law expression and the value of the rate constant k with appropriate units for this reaction.

The decay is first-order with a rate constant of 0.138 d⁻¹. How many days will it take for 90% of the iodine−131 in a 0.500 M solution of this substance to decay to Xe-131?

Assuming the kinetics of this reaction are consistent with the Arrhenius equation, calculate the activation energy for this decomposition.

Derive the equation relating atomic fluorine concentration to molecular fluorine concentration.

A study of the rate of the reaction represented as $2A⟶B$ gave the following data:

(a) Determine the average rate of disappearance of A between 0.0 s and 10.0 s, and between 10.0 s and 20.0 s.

(b) Estimate the instantaneous rate of disappearance of A at 15.0 s from a graph of time versus [A]. What are the units of this rate?

(c) Use the rates found in parts (a) and (b) to determine the average rate of formation of B between 0.00 s and 10.0 s, and the instantaneous rate of formation of B at 15.0 s.

Go to the PhET Reactions & Rates interactive. Use the Single Collision tab to represent how the collision between monatomic oxygen (O) and carbon monoxide (CO) results in the breaking of one bond and the formation of another. Pull back on the red plunger to release the atom and observe the results. Then, click on “Reload Launcher” and change to “Angled shot” to see the difference.

(a) What happens when the angle of the collision is changed?

(b) Explain how this is relevant to rate of reaction.

In the PhET Reactions & Rates interactive, on the Many Collisions tab, set up a simulation with 15 molecules of A and 10 molecules of BC. Select “Show Bonds” under Options.

(a) Leave the Initial Temperature at the default setting. Observe the reaction. Is the rate of reaction fast or slow?

(b) Click “Pause” and then “Reset All,” and then enter 15 molecules of A and 10 molecules of BC once again. Select “Show Bonds” under Options. This time, increase the initial temperature until, on the graph, the total average energy line is completely above the potential energy curve. Describe what happens to the reaction.

Doubling the concentration of a reactant increases the rate of a reaction four times. With this knowledge, answer the following questions:

(a) What is the order of the reaction with respect to that reactant?

(b) Tripling the concentration of a different reactant increases the rate of a reaction three times. What is the order of the reaction with respect to that reactant?

How will the rate of reaction change for the process: $\text{CO(}g)+$ ${\text{NO}}_2(g)⟶$ ${\text{CO}}_2(g)+$ $\text{NO(}g)$ if the rate law for the reaction is $\text{rate}=$ $k{\left[{\text{NO}}_2\right]}^2?$

(a) Decreasing the pressure of NO₂ from 0.50 atm to 0.250 atm.

(b) Increasing the concentration of CO from 0.01 M to 0.03 M.

The rate constant for the radioactive decay of ¹⁴C is 1.21 $\times$ 10⁻⁴ year⁻¹. The products of the decay are nitrogen atoms and electrons (beta particles):
${}_6^{14}\text{C}⟶$ ${}_7^{14}\text{N}+$ ${\text{e}}^{-}$
$\text{rate}=$ $k\left[{}_6^{14}\text{C}\right]$

What is the instantaneous rate of production of N atoms in a sample with a carbon-14 content of 6.5 $\times$ 10⁻⁹ M?

Alcohol is removed from the bloodstream by a series of metabolic reactions. The first reaction produces acetaldehyde; then other products are formed. The following data have been determined for the rate at which alcohol is removed from the blood of an average male, although individual rates can vary by 25–30%. Women metabolize alcohol a little more slowly than men:

Determine the rate law, the rate constant, and the overall order for this reaction.

Nitrosyl chloride, NOCl, decomposes to NO and Cl₂.
$\text{2NOCl(}g)⟶$ $\text{2NO(}g)+$ ${\text{Cl}}_2(g)$

Determine the rate law, the rate constant, and the overall order for this reaction from the following data:

Nitrogen monoxide reacts with chlorine according to the equation:
$\text{2NO(}g)+$ ${\text{Cl}}_2(g)⟶$ $\text{2NOCl(}g)$

The following initial rates of reaction have been observed for certain reactant concentrations:

What is the rate law that describes the rate’s dependence on the concentrations of NO and Cl₂? What is the rate constant? What are the orders with respect to each reactant?

For the reaction $A⟶B+C,$ the following data were obtained at 30 °C:

(a) What is the order of the reaction with respect to [A], and what is the rate law?

(b) What is the rate constant?

The rate constant for the first-order decomposition at 45 °C of dinitrogen pentoxide, N₂O₅, dissolved in chloroform, CHCl₃, is 6.2 $\times$ 10⁻⁴ min⁻¹.
${\text{2N}}_2{\text{O}}_5⟶$ ${\text{4NO}}_2+$ ${\text{O}}_2$

What is the rate of the reaction when [N₂O₅] = 0.40 M?

The following data have been determined for the reaction:
${\text{I}}^{\text{−}}+$ ${\text{OCl}}^{\text{−}}⟶$ ${\text{IO}}^{\text{−}}+$ ${\text{Cl}}^{\text{−}}$

Determine the rate law and the rate constant for this reaction.

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

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.

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 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.

There are two molecules with the formula C₃H₆. 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 °C?

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:

The rate of a certain reaction doubles for every 10 °C rise in temperature.

(a) How much faster does the reaction proceed at 45 °C than at 25 °C?

(b) How much faster does the reaction proceed at 95 °C than at 25 °C?

Hydrogen iodide, HI, decomposes in the gas phase to produce hydrogen, H₂, and iodine, I₂. The value of the rate constant, k, for the reaction was measured at several different temperatures and the data are shown here:

What is the value of the activation energy (in kJ/mol) for this reaction?

The hydrolysis of the sugar sucrose to the sugars glucose and fructose,
${\text{C}}_{12}{\text{H}}_{22}{\text{O}}_{11}+$ ${\text{H}}_2\text{O}⟶$ ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6+$ ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$

follows a first-order rate law for the disappearance of sucrose: rate = k[C₁₂H₂₂O₁₁] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)

(a) In neutral solution, k = 2.1 $\times$ 10⁻¹¹ s⁻¹ at 27 °C and 8.5 $\times$ 10⁻¹¹ s⁻¹ at 37 °C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 °C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature).

(b) When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is 1.65 $\times$ 10⁻⁷ M. How long will it take the solution to reach equilibrium at 27 °C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible.

(c) Why does assuming that the reaction is irreversible simplify the calculation in part (b)?

Write the rate law for each of the following elementary reactions:

(a) ${\text{O}}_3\stackrel{\text{sunlight}}{\to }{\text{O}}_2+$ $\text{O}$

(b) ${\text{O}}_3+$ $\text{Cl}⟶$ ${\text{O}}_2+$ $\text{ClO}$

(c) $\text{ClO}+\text{O}⟶\text{Cl}+{\text{O}}_2$

(d) ${\text{O}}_3+$ $\text{NO}⟶$ ${\text{NO}}_2+$ ${\text{O}}_2$

(e) ${\text{NO}}_2+\text{O}⟶\text{NO}+{\text{O}}_2$

Experiments were conducted to study the rate of the reaction represented by this equation.³
$\text{2NO}(g)+$ $2{\text{H}}_2(g)⟶$ ${\text{N}}_2(g)+$ $2{\text{H}}_2\text{O}(g)$

Initial concentrations and rates of reaction are given here.

Consider the following questions:

(a) Determine the order for each of the reactants, NO and H₂, from the data given and show your reasoning.

(b) Write the overall rate law for the reaction.

(c) Calculate the value of the rate constant, k, for the reaction. Include units.

(d) For experiment 2, calculate the concentration of NO remaining when exactly one-half of the original amount of H₂ had been consumed.

(e) The following sequence of elementary steps is a proposed mechanism for the reaction.

Step 1: $\text{NO}+\text{NO}\rightleftharpoons {\text{N}}_2{\text{O}}_2$

Step 2: ${\text{N}}_2{\text{O}}_2+$ ${\text{H}}_2\rightleftharpoons$ ${\text{H}}_2\text{O}+$ ${\text{N}}_2\text{O}$

Step 3: ${\text{N}}_2\text{O}+$ ${\text{H}}_2\rightleftharpoons$ ${\text{N}}_2+$ ${\text{H}}_2\text{O}$

Based on the data presented, which of these is the rate determining step? Show that the mechanism is consistent with the observed rate law for the reaction and the overall stoichiometry of the reaction.

Consider this scenario and answer the following questions: Chlorine atoms resulting from decomposition of chlorofluoromethanes, such as CCl₂F₂, catalyze the decomposition of ozone in the atmosphere. One simplified mechanism for the decomposition is:
$$\begin{array}{}\\ \\ {\text{O}}_3\stackrel{\text{sunlight}}{\to }{\text{O}}_2+\text{O}\\ {\text{O}}_3+\text{Cl}⟶{\text{O}}_2+\text{ClO}\\ \text{ClO}+\text{O}⟶\text{Cl}+{\text{O}}_2\end{array}$$

(a) Explain why chlorine atoms are catalysts in the gas-phase transformation:
$2{\text{O}}_3⟶3{\text{O}}_2$

(b) Nitric oxide is also involved in the decomposition of ozone by the mechanism:
$$\begin{array}{}\\ {\text{O}}_3\stackrel{\text{sunlight}}{\to }{\text{O}}_2+\text{O}\\ {\text{O}}_3+\text{NO}⟶{\text{NO}}_2+{\text{O}}_2\\ {\text{NO}}_2+\text{O}⟶\text{NO}+{\text{O}}_2\end{array}$$

Is NO a catalyst for the decomposition? Explain your answer.

For each of the following pairs of reaction diagrams, identify which of the pairs is catalyzed:

(a)

(b)

For each of the following reaction diagrams, estimate the activation energy (E_a) of the reaction:

(a)

(b)