Chapter Questions
$$\begin{array}{|c|c|c|c|}\hline {\text { Experimental Data for } \mathrm{H}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{HCl}} \\\hline \text { Time (s) } & {\left[\mathrm{H}_{2}\right](\mathrm{M})} & {\left[\mathrm{Cl}_{2}\right](M)} & {[\mathrm{HCl}](M)} \\\hline 0.00 & 0.030 & 0.050 & 0.000 \\\hline 4.00 & 0.020 & 0.040 & \\\hline\end{array}$$Calculate the average reaction rate expressed in moles $\mathrm{H}_{2}$ consumed per liter per second.
Calculate the average reaction rate expressed in moles $\mathrm{Cl}_{2}$ consumed per liter per second.
Challenge If the average reaction rate for the reaction, expressed in moles of HClformed, is 0.0050 mol/L.s, what concentration of HCl would be present after 4.00 s?
MAIN Idea Relate collision theory to reaction rate.
Explain what the reaction rate indicates about a particular chemical reaction.
Compare the concentrations of the reactants and products during the course ofa chemical reaction (assuming no additional reactants are added).
Explain why the average rate of a reaction depends on the length of the timeinterval over which the rate is measured.
Describe the relationship between activation energy and the rate of a reaction.
Summarize what happens during the brief existence of an activated complex.
Apply collision theory to explain why collisions between two reacting particlesdo not always result in the formation of a product.
Interpret how the speed of a chemical reaction is related to the spontaneity ofthe reaction.
Calculate the average rate of a reaction between hypothetical molecules $A$and $B$ if the concentration of $A$ changes from 1.00$M$ to 0.50$M$ in 2.00 s.
MAIN Idea Explain why magnesium metal reacts with hydrochloric acid (HCl)at a faster rate than iron does
Explain how collision theory accounts for the effect of concentration onreaction rate.
Explain the difference between a catalyst and an inhibitor.
Describe the effect on the rate of a reaction if one of the reactants is ground toa powder rather than used as a single chunk.
Infer If increasing the temperature of a reaction by 10 K approximatelydoubles the reaction rate, what would be the effect of increasing thetemperature by 20 K?
Research how catalysts are used in industry, in agriculture, or in the treatmentof contaminated soil, waste, or water. Write a short report summarizing yourfindings about the role of a catalyst in one of these applications.
Write the rate law for the reaction $a A \rightarrow b B$ if the reaction is thirdorder in $A$ . $[B]$ is not part of the rate law.
The rate law for the reaction $2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}] \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})$ is first orderin $\mathrm{O}_{2}$ and third order overall. What is the rate law for the reaction?
Given the experimental data below, use the method of initial rates to determine the rate law for the reaction $a \mathrm{~A}+b \mathrm{~B} \rightarrow$ products. (Hint: Any number to the zero power equals one. For example, $(0.22)^{0}=1$ and $(55.6)^{0}=1.5$ $(0.22)^{0}=1$ and $(55.6)^{\circ}=1 )$
Challenge The rate law for the reaction $\mathrm{CH}_{3} \mathrm{CHO}(\mathrm{g}) \rightarrow \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CO}(\mathrm{g})$is Rate $=k\left[\mathrm{CH}_{3} \mathrm{CHO}\right]^{2} .$ Use this information to fill in the missingexperimental data below.
MAIN Idea Explain what the rate law for a chemical reaction tells you aboutthe reaction.
Apply the rate-law equations to show the difference between a first-order reaction with a single reactant and a second-order reaction with a single reactant.
Explain the function of the specific rate constant in a rate-law equation.
Explain Under what circumstance is the specific rate constant (k), not a constant. What does the size of $k$ indicate about the rate of a reaction?
Suggest a reason why, when given the rate of a chemical reaction, it is important to know that the reaction rate is an average reaction rate.
Explain how the exponents in the rate equation for a chemical reaction relate tothe coefficients in the chemical equation.
Determine the overall reaction order for a reaction between $A$ and $B$ for whichthe rate law is rate $=k[A]^{2}[B]^{2}$ .
Design an Experiment Explain how you would design an experiment todetermine the rate law for the general reaction $a A+b B \rightarrow$ products using themethod of initial rates.
Use the rate law in Example Problem 16.2 and the concentrations given in Practice Problems 31 and 32 to calculate the instantaneous rate for the reaction between NO and $\mathrm{H}_{2}$.$[\mathrm{NO}]=0.00500 \mathrm{M}$ and $\left[\mathrm{H}_{2}\right]=0.00200 \mathrm{M}$
$[\mathrm{NO}]=0.0100 M$ and $\left[\mathrm{H}_{2}\right]=0.00125 \mathrm{M}$
if the rate is $9.00 \times 10^{-5} \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s})$ and $\left[\mathrm{H}_{2}\right]$ is $0.00300 \mathrm{M}$
MAIN Idea Compare and contrast an elementary chemical reaction with acomplex chemical reaction.
Explain how the rate law for a chemical reaction is used to determine theinstantaneous rate of the reaction.
Define a reaction mechanism and an intermediate
Distinguish between an intermediate and an activated complex.
Relate the size of the activation energy of an elementary step in a complexreaction to the rate of that step.
Calculate A reaction between $A$ and $B$ to form AB is first order in $A$ and firstorder in B. The rate constant, $k,$ equals 0.500 $\mathrm{mol} /(\mathrm{L} \cdot \mathrm{s}) .$ What is the rate of the reaction when $[\mathrm{A}]=2.00 \times 10^{-2} M$ and $[\mathrm{B}]=1.50 \times 10^{-2} \mathrm{M?}$
What happens to the concentrations of the reactants andproducts during the course of a chemical reaction?
Explain what is meant by the average rate of a reaction.
How would you express the rate of the chemical reaction$\mathrm{A} \rightarrow \mathrm{B}$ based on the concentration of Reactant $\mathrm{A}$ ? Howwould that rate compare with the reaction rate based onthe Product B?
What is the role of the activated complex in a chemicalreaction?
Suppose two molecules that can react collide. Underwhat circumstances do the colliding molecules not react?
Figure 16.21 is an energy level diagram for a reaction.Match the appropriate number with the quantity itrepresents.\begin{equation}\begin{array}{l}{\text { a. reactants }} \\ {\text { b. activated complex }} \\ {\text { c. products }} \\ {\text { d. activation energy }}\end{array}\end{equation}
In the gas-phase reaction, $\mathrm{I}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{ICl},\left[\mathrm{I}_{2}\right]$ changesfrom 0.400 $\mathrm{M}$ at 0.00 min to 0.300 $\mathrm{M}$ at 4.00 $\mathrm{min.}$Calculate the average reaction rate in moles of $\mathrm{I} 2 \mathrm{con}$ .sumed per liter per minute.
In the gas-phase reaction, $\mathrm{I}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{ICl},\left[\mathrm{I}_{2}\right]$ changesfrom 0.400 $\mathrm{M}$ at 0.00 $\mathrm{min}$ to 0.300 $\mathrm{M}$ at 4.00 $\mathrm{min.}$Calculate the average reaction rate in moles of 12 con-sumed per liter per minute.
In a reaction $\mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{MgCl}_{2}(\mathrm{aq}),$6.00 $\mathrm{g}$ of Mg was present at 0.00 $\mathrm{min}$ . After 3.00 $\mathrm{min}$ , 4.50 gof Mg remained. Express the average rate as molMg consumed/min.
If a chemical reaction occurs at the rate of $2.25 \times 10^{-2}$moles per liter per second at 322 $\mathrm{K}$ , what is the rateexpressed in moles per liter per minute?
What role does the reactivity of the reactants play indetermining the rate of a chemical reaction?
In general, what is the relationship between reaction rateand reactant concentration?
Apply collision theory to explain why increasing theconcentration of a reactant usually increases the reaction rate.
Explain why a crushed solid reacts with a gas morequickly than a large chunk of the same solid.
Food Preservation Apply collision theory to explainwhy foods usually spoil more slowly when refrigeratedthan at room temperature.
Apply collision theory to explain why powdered zincreacts to form hydrogen gas faster than large pieces ofzinc when both are placed in hydrochloric acid solution.
Hydrogen peroxide decomposes to water and oxygengas more rapidly when manganese dioxide is added.The manganese dioxide is not consumed in the reaction.Explain the role of the manganese dioxide.
Examine Figure $16.22,$ which relates relative reactionrate and temperature. Approximately how does thereaction rate change for each increase of 10 $\mathrm{K} ?$
Suppose that a large volume of 3$\%$ hydrogen peroxidedecomposes to produce 12 $\mathrm{mL}$ of oxygen gas in 100 $\mathrm{s}$at 298 $\mathrm{K}$ . Estimate how much oxygen gas would beproduced by an identical solution in 100 $\mathrm{s}$ at 308 $\mathrm{K}$ .
Using the information in Question 58 estimate howmuch oxygen gas would be produced in an identicalsolution in 100 seconds at 318 $\mathrm{K}$ . Estimate the timeneeded to produce 12 $\mathrm{mL}$ of oxygen gas at 288 $\mathrm{K}$ .
In the method of initial rates used to determine the ratelaw for a chemical reaction, what is the significance ofthe word initial?
Why must the rate law for a chemical reaction be basedon experimental evidence rather than the balancedequation for the reaction?
Consider the generic chemical reaction: $A+B \rightarrow A B$ .Based on experimental data, the reaction is second orderin Reactant A. If the concentration of $\mathrm{A}$ is halved, andall other conditions remain unchanged, how does thereaction rate change?
The instantaneous rate data in Table 16.3 were obtainecfor the reaction $\mathrm{H}_{2}(\mathrm{g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{N}_{2} \mathrm{O}(\mathrm{g})$at a given temperature and concentration of $\mathrm{NO}$ . Howdoes the instantaneous rate of this reaction change asthe initial concentration of $\mathrm{H}_{2}$ is changed? Based on thedata, is $\left[\mathrm{H}_{2}\right]$ part of the rate law? Explain.
Suppose that a generic chemical reaction has the ratelaw of rate $=[A]^{2}[B]^{3}$ and that the reaction rate under agiven set of conditions is $4.5 \times 10^{-4} \mathrm{mol} /(\mathrm{L} \cdot \min ) .$ If theconcentrations of both $\mathrm{A}$ and $\mathrm{B}$ are doubled and allother reaction conditions remain constant, how will thereaction rate change?
The experimental data in Table 16.4 were obtained forthe decomposition of azomethane $\left(\mathrm{CH}_{3} \mathrm{N}_{2} \mathrm{CH}_{3}\right)$ ata particular temperature according to the equation$\mathrm{CH}_{3} \mathrm{N}_{2} \mathrm{CH}_{3}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})+\mathrm{N}_{2}(\mathrm{g}) .$ Use the data todetermine the reaction's experimental rate law.
Use the data in Table 16.4 to calculate the value of the specific rate constant, $k$.$$\begin{array}{|c|c|c|}\hline \begin{array}{c}\text { Experiment } \\\text { Number }\end{array} & \begin{array}{c}\text { Initial } \\{\left[\mathrm{CH}_{3} \mathrm{~N}_{2} \mathrm{CH}_{3}\right]}\end{array} & \begin{array}{c}\text { Initial } \\\text { Reaction Rate }\end{array} \\\hline 1 & 0.012 M & 2.5 \times 10^{-6} \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) \\\hline 2 & 0.024 M & 5.0 \times 10^{-6} \mathrm{~mol} /(\mathrm{L} \cdot \mathrm{s}) \\\hline\end{array}$$
At the same temperature, predict the reaction rate whenthe initial concentration of $\mathrm{CH}_{3} \mathrm{N}_{2} \mathrm{CH}_{3}$ is 0.048 $\mathrm{M}$ . Usethe data in Table $16.4 .$
Distinguish between a complex reaction, a reactionmechanism, and an elementary step.
Suppose that a chemical reaction takes place in a two-step mechanism.Step $1($ fast $) A+B \rightarrow C$Step $2($ slow $) C+D \rightarrow E$Which step in the reaction mechanism is the rate-determining step? Explain.
In the reaction described in Question $70,$ what are Steps 1 and 2 called? What is substance C called?(IMAGE CAN'T COPY)
In Figure $16.23,$ identify each of the labels $1,2,3,4,5,$and 6 as one of the following activated complex, intermediate, reactants, or products.
Dinitrogen pentoxide decomposes in chloroform at arate of $2.48 \times 10^{-4} \mathrm{mol} /(\mathrm{L} \cdot \mathrm{min})$ at a particular tempera-ture according to the equation $2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$The reaction is first order in $\mathrm{N}_{2} \mathrm{O}_{5}$ . Given an initialconcentration $0.400 \mathrm{mol} / \mathrm{L},$ what is the rate constant forthe reaction? What is the approximate $\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]$ after thereaction proceeds for 1.30 $\mathrm{h} ?$
Radioactive decay is first order in the decaying isotope.For example, strontium-90 contained in fallout fromnuclear explosions decays to yttrium-90 and a beta particle. Write the rate law for the decay of strontium-90.
Evaluate the validity of this statement: You can determine the rate law for a chemical reaction by examiningthe mole ratio of reactants in the balanced equation.Explain your answer.
The concentration of Reactant A decreases from0.400 mol/L at 0.00 min to 0.384 moll at 4.00 min.Calculate the average reaction rate during this timeperiod. Express the rate in mol/(L.min).
The mass of a sample of magnesium is obtained andthe sample is placed in a container of hydrochloric acid.A chemical reaction occurs according to the equation$\mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{MgCl}_{2}(\mathrm{aq}) .$ Use thedata in Table 16.5 to calculate the volume of hydrogengas produced at STP during the 3.00 -min reaction?(Hint: 1 mol of an ideal gas occupies 22.4 at STP)
If the concentration of a reaction product increases from0.0882 $\mathrm{mol} / \mathrm{L}$ to 0.1446 $\mathrm{mol} / \mathrm{L}$ in 12.0 minutes, what isthe average reaction rate during the time interval?
A two-step mechanism has been proposed for thedecomposition of nitryl chloride $\left(\mathrm{NO}_{2} \mathrm{CL}\right) .$\begin{equation}\begin{array}{l}{\text { Step } 1 : \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})} \\ {\text { Step } 2 : \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g})+\mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})}\end{array}\end{equation}What is the overall reaction? Identify any intermediatesin the reaction sequence, and explain why they arecalled intermediates.
Compare and contrast the reaction energy diagramsfor the overall decomposition of nitryl chloride by themechanism in Problem 79 under two assumptions:$A-$ that the first step is slower; $B-$ that the secondstep is slower.
Automobile Engine The following reaction takes placein an automobile's engine and exhaust system.$$\quad \mathrm{NO}_{2}(\mathrm{g})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{NO}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})$$The reaction's rate law at a particular temperature is Rate$=0.50 \mathrm{L} /(\mathrm{mol} \cdot \mathrm{s})\left[\mathrm{NO}_{2}\right]^{2}$ . What is the reaction's initial,instantaneous rate when $\left[\mathrm{NO}_{2}\right]=0.0048 \mathrm{mol} / \mathrm{L} ?$
The concentrations in a chemical reaction are expressedin moles per liter and time is expressed in seconds. If theoverall rate law is third-order, what are the units for therate and the rate constant?
Visualize the reaction energy diagram for a one-step,endothermic chemical reaction. Compare the heightsof the activation energies for the forward and reversereactions.
Differentiate between the shaded areas in Figure 16.24at temperatures $T_{1}$ and $T_{2}$ on the basis of the number ofcollisions per unit time that might occur with energyequal to or greater than the activation energy.
Apply the method of initial rates to determine the orderof a chemical reaction with respect to Reactant $\mathrm{X}$ . Createa set of hypothetical experimental data that would leadyou to conclude that the reaction is second order in X.
Formulate a rationale to explain how a complex chemical reaction might have more than one rate-determining elementary step.
Construct a diagram that shows all of the possible collision combinations between two molecules of Reactant Aand two molecules of Reactant B. Now, increase thenumber of molecules of A from two to four and sketcheach possible $A$ -B collision combination. By what factordid the number of collision combinations increase?What does this tell you about the reaction rate?
Apply collision theory to explain two reasons whyincreasing the temperature of a reaction by 10 K oftendoubles the reaction rate
Create a table of concentrations, starting with 0.100$M$concentrations of all reactants, that you would proposein order to establish the rate law for the reaction$a \mathrm{A}+b \mathrm{B}+\mathrm{cD} \rightarrow$ products using the method ofinitial rates.
Hydrocarbons Heating cyclopropane $\left(\mathrm{C}_{3} \mathrm{H}_{6}\right)$ convertsit to propene $\left(\mathrm{CH}_{2}=\mathrm{CHCH}_{3}\right) .$ The rate law is first orderin cyclopropane. If the rate constant at a particulartemperature is $6.22 \times 10^{-4} \mathrm{s}^{1}$ and the concentrationof cyclopropane is held at $0.0300 \mathrm{mol} / \mathrm{L},$ what mass ofpropene is produced in 10.0 $\mathrm{min}$ in a volume of 2.50 $\mathrm{L}$ ?
For the following categories of elements, state the possible number(s) of electrons in their outermost orbitals inthe ground state? (Chapter 5$)$\begin{equation}\begin{array}{l}{\text { a. p-block elements }} \\ {\text { b. nitrogen-group elements }} \\ {\text { c. d-block elements }} \\ {\text { d. noble-gas elements }} \\ {\text { e. s-block elements }}\end{array}\end{equation}
Classify each of the following elements as a metal,nonmetal, or metalloid. (Chapter 6$)$\begin{equation}\begin{array}{l}{\text { a. molybdenum }} \\ {\text { b. bromine }} \\ {\text { c. arsenic }} \\ {\text { d. neon }} \\ {\text { e. cerium }}\end{array}\end{equation}
Using Figure $16.25,$ determine how many sigma and pibonds are contained in a single ethene molecule.(Chapter 8$)$
Balance the following equations. (Chapter 9)\begin{equation}\begin{array}{l}{\text { a. } \mathrm{Sn}(\mathrm{s})+\mathrm{NaOH}(\mathrm{aq}) \rightarrow \mathrm{Na}_{2} \mathrm{SnO}_{2}+\mathrm{H}_{2}} \\ {\text { b. } \mathrm{C}_{8} \mathrm{H}_{18}(1)+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1)} \\ {\text { c. } \mathrm{Al}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})}\end{array}\end{equation}
What mass of iron(III) chloride is needed to prepare1.00 L of a 0.255$M$ solution? (Chapter 14)
What information must you know to calculate the boiling point elevation of a solution of hexane in benzene?(Chapter 14)
$\Delta H$ for a reaction is negative. Compare the energy ofthe products and the reactants. Is the reaction endother-mic or exothermic? (Chapter 15$)$
Pharmaceuticals Imagine that your nation is experiencing an influenza epidemic. Fortunately, scientistshave recently discovered a new catalyst that increasesthe rate of production of an effective flu medicine.Write a newspaper article describing how the catalystworks. Include a reaction energy diagram and anexplanation detailing the importance of the discovery.
Lawn Care Write an advertisement that explains thatCompany A's fertilizer works better than Company B'sfertilizer because it has smaller sized granules.Include applicable diagrams.
What is the average rate of the reaction in the first22.3 s expressed in moles of phenolphthalein con-sumed per liter per second?
What is the average rate of the reaction as the phenol-phthalein concentration decreases from 0.00050$M$ to0.00015$M$ ?
The rate law is rate $=k[$ phenolphthalein]. If the rateconstant for the reaction is $1.0 \times 10^{-2} \mathrm{s}^{-1}$ , what is theinstantaneous rate of reaction when the concentra-tion of phenolphthalein is 0.0025$M ?$