Chapter 17: Reaction Rates - Neshaminy School District · 2009-08-27 · 528 Chapter 17 Reaction...
Transcript of Chapter 17: Reaction Rates - Neshaminy School District · 2009-08-27 · 528 Chapter 17 Reaction...
528 Chapter 17
Reaction Rates
CHAPTER 17
What Yoursquoll LearnYou will investigate amodel describing howchemical reactions occur asa result of collisions
You will compare the ratesof chemical reactions undervarying conditions
You will calculate the ratesof chemical reactions
Why Itrsquos ImportantPerhaps someday yoursquoll beinvolved with the space pro-gram Rockets along withtheir crews and cargo arepropelled into space by theresult of a chemical reactionAn understanding of reactionrates is the tool that allows usto control chemical reactionsand use them effectively
This launch of the MarsExploration Rover Spirit in June2003 propelled the robot to itssuccessful touchdown on Marsin January 2004
Visit the Chemistry Web site atchemistrymccom to find linksabout reaction rates
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171 A Model for Reaction Rates 529
DISCOVERY LAB
Materials
hydrogen peroxidebeaker or cupbakerrsquos yeasttoothpicks
Speeding Reactions
Many chemical reactions occur so slowly that you donrsquot even knowthey are happening For some reactions it is possible to alter the
reaction speed using another substance
Safety Precautions
Always use safety goggles and an apron in thelab
Procedure1 Create a ldquobefore and afterrdquo table and record your observations2 Pour about 10 mL of hydrogen peroxide into a small beaker or
cup Observe the hydrogen peroxide
3 Add a ldquopinchrdquo (18 tsp) of yeast to the hydrogen peroxide Stirgently with a toothpick and observe the mixture again
AnalysisInto what two products does hydrogen peroxide decompose Whyarenrsquot bubbles produced in step 1 What is the function of the yeast
Objectivesbull Calculate average rates of
chemical reactions fromexperimental data
bull Relate rates of chemicalreactions to collisionsbetween reacting particles
Vocabularyreaction ratecollision theoryactivated complextransition stateactivation energy
Section 171 A Model for Reaction Rates
One of the most spectacular chemical reactions the one between liquidhydrogen and liquid oxygen provides the energy to launch rockets intospace as shown on the opposite page This reaction is fast and exothermicYet other reactions and processes yoursquore familiar with such as the hardeningof concrete or the formation of fossil fuels occur at considerably slowerrates The DISCOVERY LAB for this chapter emphasized that the speed atwhich a reaction occurs can vary if other substances are introduced into thereaction In this section yoursquoll learn about a model that scientists use todescribe and calculate the rates at which chemical reactions occur
Expressing Reaction RatesAs you know some chemical reactions are fast and others are slow howev-er fast and slow are inexact relative terms Chemists engineers medicalresearchers and others often need to be more specific
Think about how you express speed or rate in the situations shown inFigure 17-1 on the next page The speed of the sprinter on the track teammay be expressed as meters per second The speed at which the hiker movesmight be expressed differently perhaps as meters per minute We generallydefine the average rate of an action or process to be the change in a givenquantity during a specific period of time Recall from your study of math thatthe Greek letter delta () before a quantity indicates a change in the quanti-ty In equation form average rate or speed is written as
Average rate qu
anttity
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For chemical reactions this equation defines the average rate at whichreactants produce products which is the amount of change of a reactant in agiven period of time Most often chemists are concerned with changes in themolar concentration (molL M) of a reactant or product during a reactionTherefore the reaction rate of a chemical reaction is stated as the change inconcentration of a reactant or product per unit time expressed as mol(Ls)Brackets around the formula for a substance denote the molar concentrationFor example [NO2] represents the molar concentration of NO2
Itrsquos important to understand that reaction rates are determined experimen-tally by measuring the concentrations of reactants andor products in anactual chemical reaction Reaction rates cannot be calculated from balancedequations as stoichiometric amounts can
Suppose you wish to express the average rate of the reaction
CO(g) NO2(g) 0 CO2(g) NO(g)
during the time period beginning at time t1 and ending at time t2 Calculatingthe rate at which the products of the reaction are produced results in a reac-tion rate having a positive value The rate calculation based on the produc-tion of NO will have the form
Average reaction rate [
N
tO]
For example if the concentration of NO is 000M at time t1 000 s and0010M two seconds after the reaction begins the following calculationgives the average rate of the reaction expressed as moles of NO produced perliter per second
Average reaction rate
0200100M
s 00050 mol(Ls)
Notice how the units calculate
Ms
moslL
mLol
1s (
mL
osl)
Although molL M chemists typically reserve M to express concentrationand mol(Ls) to express rate
Alternatively you can choose to state the rate of the reaction as the rate atwhich CO is consumed as shown below
Average reaction rate [
CtO]
Do you predict a positive or negative value for this reaction In this case anegative value indicates that the concentration of CO decreases as the reac-tion proceeds
Actually reaction rates must always be positive When the rate ismeasured by the consumption of a reactant scientists commonly apply anegative sign to the calculation to get a positive reaction rate Therefore thefollowing form of the average rate equation is used to calculate the rate ofconsumption
Average reaction rate qu
anttity
[CO] at time t2 [CO] at time t1t2 t1
0010M 0000M200 s 000 s
[NO] at time t2 [NO] at time t1t2 t1
530 Chapter 17 Reaction Rates
Figure 17-1
The average rate of travel forthese activities is based on thechange in distance over timeSimilarly the reaction rate isbased on the change in concen-tration over time
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[C4H9Cl] [C4H9Cl]at t 000 s at t 400 s
0220M 0100M
171 A Model for Reaction Rates 531
EXAMPLE PROBLEM 17-1
Calculating Average Reaction RatesReaction data for the reaction between butyl chloride (C4H9Cl) and water(H2O) is given in Table 17-1 Calculate the average reaction rate over thistime period expressed as moles of C4H9Cl consumed per liter per second
1 Analyze the ProblemYou are given the initial and final concentrations of C4H9Cl and theinitial and final times You can calculate the average reaction rate ofthe chemical reaction using the change in concentration of butyl chlo-ride in four seconds In this problem the reactant butyl chloride isconsumed
Known Unknown
t1 000 s Average reaction rate mol(Ls)t2 400 s[C4H9Cl] at t1 0220M[C4H9Cl] at t2 0100M
2 Solve for the UnknownWrite the equation for the average reaction rate insert the knownquantities and perform the calculation
Average reaction rate
(Substitute units)
01
42000msolL
00300 mol(Ls)
3 Evaluate the AnswerThe average reaction rate of 00300 moles C4H9Cl consumed per literper second seems reasonable based on start and end amounts Theanswer is correctly expressed in three significant figures
0100 molL 0220 molL400 s 000 s
0100M 0220M400 s 000 s
[C4H9Cl] at time t2 [C4H9Cl] at time t1t2 t1
PRACTICE PROBLEMSUse the data in the following table to calculate the average reaction rates
1 Calculate the average reaction rate expressed in moles H2 consumedper liter per second
2 Calculate the average reaction rate expressed in moles Cl2 consumedper liter per second
3 Calculate the average reaction rate expressed in moles HCl producedper liter per second
Molar Concentration of C4H9Cl
Table 17-1
Time (s) [H2] (M) [Cl2] (M) [HCl] (M)
000 0030 0050 0000
400 0020 0040 0020
Experimental Data for H2 Cl2 0 2HCl
For more practice calculating averagereaction rates go toSupplemental PracticeSupplemental Practice
Problems in Appendix A
Practice
The Collision TheoryYou have learned that reaction rates are calculated from experimental dataBut what are we actually measuring with these calculations Looking atchemical reactions from the molecular level will provide a clearer picture ofexactly what reaction rates measure
Have you ever seen a demolition derby in which the competing vehiclesare constantly colliding Each collision may result in the demolition of one ormore vehicles as shown in Figure 17-2a The reactants in a chemical reactionmust also come together in order to form products as shown in Figure 17-2bThe collision theory states that atoms ions and molecules must collide inorder to react The collision theory summarized in Table 17-2 explains whyreactions occur and how the rates of chemical reactions can be modified
Consider the reaction between hydrogen gas (H2) and oxygen gas (O2)
2H2 O2 0 2H2O
According to the collision theory H2 and O2 molecules must collide in orderto react and produce H2O Now look at the reaction between carbon monox-ide (CO) gas and nitrogen dioxide (NO2) gas at a temperature above 500 K
CO(g) NO2(g) 0 CO2(g) NO(g)
These molecules collide to produce carbon dioxide (CO2) gas and nitrogenmonoxide (NO) gas However detailed calculations of the number of molec-ular collisions per second yield a puzzling resultmdashonly a small fraction ofcollisions produce reactions In this case other factors must be considered
Orientation and the activated complex Why donrsquot the NO2 and COmolecules shown in Figure 17-3a and b react when they collide Analysisof this example indicates that in order for a collision to lead to a reaction thecarbon atom in a CO molecule must contact an oxygen atom in an NO2 mol-ecule at the instant of impact Only in that way can a temporary bondbetween the carbon atom and an oxygen atom form The collisions shown inFigure 17-3a and b do not lead to reactions because the molecules collidewith unfavorable orientations That is because a carbon atom does not con-tact an oxygen atom at the instant of impact the molecules simply rebound
When the orientation of colliding molecules is correct as Figure 17-3cillustrates a reaction occurs as an oxygen atom is transferred from an NO2molecule to a CO molecule A short-lived intermediate substance is formedThe intermediate substance in this case OCONO is called an activated com-plex An activated complex is a temporary unstable arrangement of atomsthat may form products or may break apart to re-form the reactants Becausethe activated complex is as likely to form reactants as it is to form productsit is sometimes referred to as the transition state An activated complex isthe first step leading to the resulting chemical reaction
532 Chapter 17 Reaction Rates
Figure 17-2
The product of a demolitionderby the crunch of metal isthe result of collisions betweenthe cars The product of achemical reaction is the result of collisions between atomsions and molecules Refer toTable C-1 in Appendix C for akey to atom color conventions
b
a
A2 B2 2AB
Collision Theory Summary
1 Reacting substances (atomsions or molecules) must collide
2 Reacting substances must collide with the correct orientation
3 Reacting substances must collide with sufficient energyto form the activated complex
Table 17-2
a
b
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Activation energy and reaction The collision depicted in Figure 17-3ddoes not lead to a reaction for a different reason Although the CO and NO2molecules collide with a favorable orientation no reaction occurs becausethey collide with insufficient energy to form the activated complex The min-imum amount of energy that reacting particles must have to form the acti-vated complex and lead to a reaction is called the activation energy Ea
Activation energy has a direct influence on the rate of a reaction A highEa means that relatively few collisions will have the required energy to pro-duce the activated complex and the reaction rate will be low On the otherhand a low Ea means that more collisions will have sufficient energy toreact and the reaction rate will be higher The problem-solving LAB belowemphasizes this fact It might be helpful to think of this relationship in termsof a person pushing a heavy cart up a hill If the hill is high a substantialamount of energy and effort will be required to move the cart and it will takea long time to get it to the top If the hill is low less energy will be requiredand the task will be accomplished faster
171 A Model for Reaction Rates 533
Figure 17-3
The collisions in and donot result in a reaction becausethe molecules are not in positionto form bonds The molecules in
are in the correct orientationwhen they collide and a reac-tion occurs The molecules in are also in the correct positionson collision but insufficientenergy at the point of collisionprevents a chemical reaction
d
c
ba
Incorrect orientationRebound
Incorrect orientationCollision Rebound
Correct orientationCollision
Collision
Activated complex Products
Correct orientationInsufficient energy
ReboundCollision
a b
dc
problem-solving LAB
Speed and Energy of CollisionDesigning an Experiment Controlling therate of a reaction is common in your everydayexperience Consider two of the major appliancesin your kitchen a refrigerator slows down chemi-cal processes that cause food to spoil and anoven speeds up chemical processes that causefoods to cook Petroleum and natural gasesrequire a spark to run your carrsquos engine and heatyour home
AnalysisAccording to collision theory reactants must col-lide with enough energy in order to react Recallfrom the kinetic-molecular theory that mass andvelocity determine the kinetic energy of a parti-
cle In addition temperature is a measure of theaverage kinetic energy of the particles in asample of matter According to kinetic-moleculartheory how are the frequency and energy ofcollisions between gas particles related totemperature
Thinking CriticallyHow would you design an experiment with ahandful of marbles and a shoe box lid to simu-late the range of speeds among a group of parti-cles at a given temperature How would youmodel an increase in temperature Describe howyour marble model would demonstrate the rela-tionship between temperature and the frequencyand energy of the collisions among a group ofparticles
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Figure 17-4 shows the energy diagram for the progress of the reactionbetween carbon monoxide and nitrogen dioxide Does this energy diagramlook somewhat different from those you studied in Chapter 16 Why Inaddition to the energies of the reactants and products this diagram shows theactivation energy of the reaction Activation energy can be thought of as abarrier the reactants must overcome in order to form the products In thiscase the CO and NO2 molecules collide with enough energy to overcome thebarrier and the products formed lie at a lower energy level Do you recall thatreactions that lose energy such as this example are called exothermic reactions
For many reactions the process from reactants to products is reversibleFigure 17-5 shows the reverse endothermic reaction between CO2 and NOto reform CO and NO2 In this reverse reaction the reactants which are themolecules that were formed in the exothermic forward reaction lie at a lowenergy level and must overcome a significant activation energy to reform COand NO2 This requires an input of energy If this reverse reaction isachieved CO and NO2 again lie at a high energy level
534 Chapter 17 Reaction Rates
Figure 17-4
In an exothermic reaction mole-cules collide with enough ener-gy to overcome the activationenergy barrier form an activat-ed complex then release energyand form products at a lowerenergy level
Figure 17-5
In the reverse endothermic reac-tion the reactant moleculeslying at a low energy level mustabsorb energy to overcome theactivation energy barrier andform high-energy products
Reaction progress
Reactants
Products
Activated complex
Activationenergy
CO2(g) NO(g)
CO(g) NO2(g)
Energy
releasedby reaction
Ener
gy
Reaction progress
Reactants
Products
Activatedcomplex
CO2(g) NO(g)
CO(g) NO2(g)
Ener
gy
Activationenergy Energy
absorbedby reaction
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The influence of spontaneity Recall from Chapter 16 that reaction spon-taneity is related to change in free energy G If G is negative the reac-tion is spontaneous under the conditions specified If G is positive thereaction is not spontaneous Letrsquos now consider whether spontaneity has anyeffect on reaction rates Are more spontaneous reactions faster than lessspontaneous ones
To investigate the relationship between spontaneity and reaction rate con-sider the following gas-phase reaction between hydrogen and oxygen
2H2(g) O2(g) 0 2H2O(g)
Here G 458 kJ at 298 K (25degC) and 1 atm pressure Because G isnegative the reaction is spontaneous For the same reaction H 484 kJ which means that the reaction is highly exothermic You canexamine the speed of this reaction by filling a tape-wrapped soda bottle withstoichiometric quantities of the two gasesmdashtwo volumes hydrogen and onevolume oxygen A thermometer in the stopper allows you to monitor thetemperature inside the bottle As you watch for evidence of a reaction thetemperature remains constant for hours Have the gases escaped Or havethey simply failed to react If you remove the stopper and hold a burningsplint to the mouth of the bottle a reaction occurs explosively Clearly thehydrogen and oxygen gases have not escaped from the bottle Yet they didnot react noticeably until you supplied additional energy in the form of alighted splint The example shown in Figure 17-6 illustrates this same phe-nomenon The soap bubbles you see billowing from the bowl are filled withhydrogen When the lighted splint introduces additional energy an explo-sive reaction occurs between the hydrogen that was contained in the bub-bles and oxygen in the air
As these examples show reaction spontaneity in the form of G impliesabsolutely nothing about the speed of the reaction G merely indicates thenatural tendency for a reaction or process to proceed Factors other thanspontaneity however do affect the rate of a chemical reaction These factorsare keys in controlling and using the power of chemistry
171 A Model for Reaction Rates 535
Figure 17-6
Although the reaction ofhydrogen and oxygen is sponta-neous the combination doesnot produce an obvious reactionwhen mixed
If an additional form ofenergy is introduced to the samespontaneous reaction the reac-tion rate increases significantly
b
a
Section 171 Assessment
4 What does the reaction rate indicate about a partic-ular chemical reaction
5 How is the rate of a chemical reaction usuallyexpressed
6 What is the collision theory and how does it relateto reaction rates
7 According to the collision theory what must hap-pen in order for two molecules to react
8 How is the speed of a chemical reaction related tothe spontaneity of the reaction
9 Thinking Critically How would the rate of thereaction 2H2(g) O2(g) 0 2H2O(g) stated as theconsumption of hydrogen compare with the ratestated as the consumption of oxygen
10 Interpreting Scientific Illustrations Based onyour analysis of Figures 17-4 and 5 how does Ea
for the reaction CO NO2 9 CO2 NO (thereverse reaction) compare with that of the reactionCO NO2 0 CO2 NO (the forward reaction)
a
b
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536 Chapter 17 Reaction Rates
Section 172
Factors Affecting ReactionRates
Objectivesbull Identify factors that affect
the rates of chemical reactions
bull Explain the role of a catalyst
Vocabulary catalystinhibitorheterogeneous catalysthomogeneous catalyst
According to the collision theory chemical reactions occur when moleculescollide in a particular orientation and with sufficient energy to achieve acti-vation energy You can probably identify chemical reactions that occur fastsuch as gasoline combustion and others that occur more slowly such as ironrusting But can the reaction rate of any single reaction vary or is the reac-tion rate constant regardless of the conditions In this section you will learnthat the reaction rate for almost any chemical reaction can be modified byvarying the conditions of the reaction
The Nature of ReactantsAn important factor that affects the rate of a chemical reaction is the reactivenature of the reactants As you know some substances react more readily thanothers For example calcium and sodium are both reactive metals howeverwhat happens when each metal is added to water is distinctly different Whena small piece of calcium is placed in cold water as shown in Figure 17-7athe calcium and water react slowly to form hydrogen gas and aqueous calci-um hydroxide
Ca(s) 2H2O(l) 0 H2(g) Ca(OH)2(aq)
When a small piece of sodium is placed in cold water the sodium and waterreact quickly to form hydrogen gas and aqueous sodium hydroxide as shownin Figure 17-7b
2Na(s) 2H2O(l) 0 H2(g) 2NaOH(aq)
Comparing the two equations itrsquos evident that the reactions are similarHowever the reaction between sodium and water occurs much fasterbecause sodium is more reactive with water than calcium is In fact the reac-tion releases so much heat so quickly that the hydrogen gas ignites as it isformed
Figure 17-7
The tendency of a substance toreact influences the rate of areaction involving the substanceThe more reactive a substance isthe faster the reaction rate
a b
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ConcentrationReactions speed up when the concentrations of reacting particles areincreased One of the fundamental principles of the collision theory is thatparticles must collide to react The number of particles in a reaction makes adifference in the rate at which the reaction takes place Think about a reac-tion where reactant A combines with reactant B At a given concentration ofA and B the molecules of A collide with B to produce AB at a particular rateWhat happens if the amount of B is increased Increasing the concentrationof B makes more molecules available with which A can collide Reactant Aldquofindsrdquo reactant B more easily because there are more B molecules in thearea which increases probability of collision and ultimately increases therate of reaction between A and B
Look at the two reactions shown in Figure 17-8 Steel wool is first heat-ed over a burner until it is red hot In Figure 17-8a the hot steel wool reactswith oxygen in the air How does this reaction compare with the one inFigure 17-8b in which the hot steel wool is lowered immediately into a flaskcontaining nearly 100 percent oxygenmdashapproximately five times the concen-tration of oxygen in air Applying the collision theory to this reaction thehigher concentration of oxygen increases the collision frequency betweeniron atoms and oxygen molecules which increases the rate of the reaction
If you have ever been near a person using bottled oxygen or seen an oxy-gen generator you may have noticed a sign cautioning against smoking orusing open flames Can you now explain the reason for the caution noticeThe high concentration of oxygen could cause a combustion reaction to occurat an explosive rate The CHEMLAB at the end of this chapter gives you anopportunity to further investigate the effect of concentration on reaction rates
Surface AreaNow suppose you were to lower a red-hot chunk of steel instead of steelwool into a flask of oxygen gas The oxygen would react with the steel muchmore slowly than it would with the steel wool Using what you know aboutthe collision theory can you explain why You are correct if you said thatfor the same mass of iron steel wool has much more surface area than thechunk of steel The greater surface area of the steel wool allows the oxygenmolecules to collide with many more iron atoms per unit of time
172 Factors Affecting Reaction Rates 537
Figure 17-8
The concentration of oxygenin the air surrounding the steelwool is much less than that ofthe pure oxygen in the flask
The higher oxygen concen-tration accounts for the fasterreaction
b
a
a b
LAB
See page 960 in Appendix E forSurface Area and Cooking Eggs
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Pulverizing (or grinding) a substance is one way to increase its rate ofreaction This is because for the same mass many small particles possessmore total surface area than one large particle So a spoonful of granulatedsugar placed in a cup of water dissolves faster than the same mass of sugarin a single chunk which has less surface area as shown in Figure 17-9 Thisexample illustrates that increasing the surface area of a reactant does notchange its concentration but it does increase the rate of reaction by increas-ing the collision rate between reacting particles
TemperatureGenerally increasing the temperature at which a reaction occurs increasesthe reaction rate For example you know that the reactions that cause foodsto spoil occur much faster at room temperature than when the foods arerefrigerated The graph in Figure 17-10a illustrates that increasing the tem-perature by 10 K can approximately double the rate of a reaction How cana small increase in temperature have such a significant effect
As you learned in Chapter 13 increasing the temperature of a substanceincreases the average kinetic energy of the particles that make up the sub-stance For that reason reacting particles collide more frequently at highertemperatures than at lower temperatures However that fact alone doesnrsquotaccount for the increase in reaction rate with increasing temperature To bet-ter understand how reaction rate varies with temperature examine the graphshown in Figure 17-10b This graph compares the numbers of particles hav-ing sufficient energy to react at temperatures T1 and T2 where T2 is greaterthan T1 The shaded area under each curve represents the number of colli-sions having energy equal to or greater than the activation energy The dot-ted line indicates the activation energy (Ea) for the reaction How do theshaded areas compare The number of high-energy collisions at the highertemperature T2 is much greater than at the lower temperature T1 Thereforeas the temperature increases more collisions result in a reaction
As you can see increasing the temperature of the reactants increases thereaction rate because raising the kinetic energy of the reacting particles rais-es both the collision frequency and the collision energy You can investigatethe relationship between reaction rate and temperature by performing theminiLAB for this chapter
538 Chapter 17 Reaction Rates
Figure 17-9
Increasing the surface area ofreactants provides more oppor-tunity for collisions with otherreactants thereby increasing thereaction rate
280 290 300 310 320 330
Rel
ativ
e re
acti
on
rat
e
5
0
10
15
20
25
30
35
40
Temperature (K)
Reaction Rate and Temperature
(290K2)
(310K8)
(320K16)
(330K32)
Collision energy
Nu
mb
er o
f p
arti
cles
T2 T1
T1
00
T2
Particle Energy and Temperature
Activationenergy
a b
Figure 17-10
Increasing the temperatureof a reaction increases the fre-quency of collisions and there-fore the rate of reaction
Increasing the temperaturealso raises the kinetic energy ofthe particles thus more of thecollisions at high temperatureshave enough energy to over-come the activation energy barrier and react
b
a
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CatalystsYoursquove seen that increasing the temperature andor the concentration of reac-tants can dramatically increase the rate of a reaction However an increasein temperature is not always the best (or most practical) thing to do Forexample suppose that you want to increase the rate of a reaction such as thedecomposition of glucose in a living cell Increasing the temperature andorthe concentration of reactants is not a viable alternative because it mightharm or kill the cell
It is a fact that many chemical reactions in living organisms would notoccur quickly enough to sustain life at normal living temperatures if it werenot for the presence of enzymes An enzyme is a type of catalyst a sub-stance that increases the rate of a chemical reaction without itself being con-sumed in the reaction Although catalysts are important substances in achemical reaction a catalyst does not yield more product and is not includ-ed in the product(s) of the reaction In fact catalysts are not included in thechemical equation
How does a catalyst increase the reaction rate Figure 17-11 on the nextpage shows the energy diagram for an exothermic chemical reaction The redline represents the uncatalyzed reaction pathwaymdashthe reaction pathway withno catalyst present The blue line represents the catalyzed reaction pathway
172 Factors Affecting Reaction Rates 539
Examining Reaction Rate andTemperatureRecognizing Cause and Effect Several factorsaffect the rate of a chemical reaction This laballows you to examine the effect of temperatureon a common chemical reaction
Materials small beaker thermometer hot plate250-mL beaker balance water effervescent(bicarbonate) tablet stopwatch or clock withsecond hand
Procedure1 Take a single effervescent tablet and break it
into four roughly equal pieces
2 Measure the mass of one piece of the tabletMeasure 50 mL of room-temperature water(approximately 20degC) into a small cup orbeaker Measure the temperature of the water
3 With a stopwatch ready add the piece oftablet to the water Record the amount oftime elapsed between when the tablet hits thewater and when you see that all of the pieceof tablet has dissolved in the water
4 Repeat steps 2 and 3 twice more except usewater temperatures of about 50degC and 65degCBe sure to raise the temperature gradually andmaintain the desired temperature (equilibrate)throughout the run
Analysis1 Calculate the reaction rate by finding the
masstime for each run
2 Graph the reaction rate (masstime) versustemperature for the runs
3 What is the relationship between reaction rateand temperature for this reaction
4 Using your graphed data predict the reactionrate for the reaction carried out at 40degC Heatand equilibrate the water to 40degC and use thelast piece of tablet to test your prediction
5 How did your prediction for the reaction rateat 40degC compare to the actual reaction rate
miniLAB
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Figure 17-12
Compare the amount of time itwould take this train to travelover or around the barrier withthe time it takes to travelthrough the barrier Obviouslytravel is faster through themountain with the aid of thetunnel
Note that the activation energy for the catalyzed reaction is much lower thanfor the uncatalyzed reaction The lower activation energy for the catalyzedreaction means that more collisions have sufficient energy to initiate reac-tion It might help you to visualize this relationship by thinking of the reac-tionrsquos activation energy as a mountain range to be crossed as shown inFigure 17-12 In this analogy the tunnel representing the catalyzed path-way provides an easier and therefore quicker route to the other side of themountains
Another type of substance that affects reaction rates is called an inhibitorUnlike a catalyst which speeds up reaction rates an inhibitor is a substancethat slows down or inhibits reaction rates Some inhibitors in fact actuallyprevent a reaction from happening at all
In our fast-paced world it might seem unlikely that it would be desirableto slow a reaction But if you think about your environment you can proba-bly come up with several uses for inhibitors One of the primary applicationsfor inhibitors is in the food industry where inhibitors are called preserva-tives Figure 17-13 shows how a commercially available fruit freshener
540 Chapter 17 Reaction Rates
Figure 17-11
This energy diagram shows howthe activation energy of the cat-alyzed reaction is lower andtherefore the reaction producesthe products at a faster ratethan the uncatalyzed reactiondoes
Reaction progress
Reactants
Products
Catalyzedreactionpathway
Ener
gy
Uncatalyzedreactionpathway
Activation energy with no catalyst
Activation energywith catalyst
Chem MC-540
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inhibits fruit from browning once it is cut These preservatives are safe to eatand give food a longer shelf-life Another inhibitor is the compound maleichydrazide (C4N2H4O2) which is used as a plant growth inhibitor and weedkiller Inhibitors also are important in biology For example a class ofinhibitors called monoamine oxidase inhibitors blocks a chemical reactionthat can cause depression
Heterogeneous and homogeneous catalysts In order to reduce harm-ful engine emissions automobiles manufactured today must have catalyticconverters similar to the one described in How It Works at the end of thechapter The most effective catalysts for this application are transition metaloxides and metals such as palladium and platinum These substances catalyzereactions that convert nitrogen monoxide to nitrogen and oxygen carbonmonoxide to carbon dioxide and unburned gasoline to carbon dioxide andwater Because the catalysts in a catalytic converter are solids and the reac-tions they catalyze are gaseous the catalysts are called heterogeneous cata-lysts A heterogeneous catalyst exists in a physical state different than thatof the reaction it catalyzes A catalyst that exists in the same physical state asthe reaction it catalyzes is called a homogeneous catalyst For example ifboth an enzyme and the reaction it catalyzes are in aqueous solution theenzyme is a homogeneous catalyst
172 Factors Affecting Reaction Rates 541
Figure 17-13
The preservative that wasapplied to the apple on the leftis an inhibitor that reacted withsubstances in the apple to slowthe chemical reactions thatcause the apple to brown
Section 172 Assessment
11 How do temperature concentration and surfacearea affect the rate of a chemical reaction
12 How does the collision model explain the effect ofconcentration on the reaction rate
13 How does the activation energy of an uncatalyzedreaction compare with that of the catalyzedreaction
14 Thinking Critically For a reaction of A and Bthat proceeds at a specific rate x mol(Ls) what
is the effect of decreasing the amount of one ofthe reactants
15 Using the Internet Conduct Internet researchon how catalysts are used in industry in agricul-ture or in the treatment of contaminated soilwaste or water Write a short report summarizingyour findings about one use of catalysts
chemistrymccomself_check_quiz
Topic Industrial CatalystsTo learn more about industri-al catalysts visit theChemistry Web site atchemistrymccomActivity Research how cata-lysts help reactions to occurin industry that would nototherwise be able to proceedExplain how scientists havebeen able to design materialsthat will only use catalysts ata certain time
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542 Chapter 17 Reaction Rates
Section 173 Reaction Rate Laws
Objectivesbull Express the relationship
between reaction rate andconcentration
bull Determine reaction ordersusing the method of initialrates
Vocabulary rate lawspecific rate constantreaction ordermethod of initial rates
In Section 171 you learned how to calculate the average rate of a chemicalreaction given the initial and final times and concentrations The word aver-age is important because most chemical reactions slow down as the reactantsare consumed To understand why most reaction rates slow over time recallthat the collision theory states that chemical reactions can occur only whenthe reacting particles collide and that reaction rate depends upon reactantconcentration As reactants are consumed fewer particles collide and thereaction slows Chemists use the concept of rate laws to quantify the resultsof the collision theory in terms of a mathematical relationship between therate of a chemical reaction and the reactant concentration
Reaction Rate LawsThe equation that expresses the mathematical relationship between the rateof a chemical reaction and the concentration of reactants is called a rate lawFor example the reaction A 0 B which is a one-step reaction has only oneactivated complex between reactants and products The rate law for this reac-tion is expressed as
where k is the specific rate constant or a numerical value that relates reac-tion rate and concentration of reactants at a given temperature Units for therate constant include L(mols) L2(mol2s) and sndash1 Depending on the reac-tion conditions especially temperature k is unique for every reaction
The rate law means that the reaction rate is directly proportional to the molarconcentration of A Thus doubling the concentration of A will double the reac-tion rate Increasing the concentration of A by a factor of 5 will increase thereaction rate by a factor of 5 The specific rate constant k does not change withconcentration however k does change with temperature A large value of kmeans that A reacts rapidly to form B What does a small value of k mean
Rate k[A]
Figure 17-14
Specific rate constants are deter-mined experimentally Scientistshave a number of methods attheir disposal that can be usedto establish k for a given reaction
A spectrophotometer measures the absorption of specific wavelengths oflight by a reactant or product as a reaction progresses to determine the specif-ic rate constant for the reaction
a
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Reaction order In the expression Rate k[A] it is understood that thenotation [A] means the same as [A]1 In other words for reactant A theunderstood exponent 1 is called the reaction order The reaction order for areactant defines how the rate is affected by the concentration of that reactantFor example the rate law for the decomposition of H2O2 is expressed by thefollowing equation
Rate k[H2O2]
Because the reaction rate is directly proportional to the concentration ofH2O2 raised to the first power [H2O2]
1 the decomposition of H2O2 is said tobe first order in H2O2 Because the reaction is first order in H2O2 the reac-tion rate changes in the same proportion that the concentration of H2O2changes So if the H2O2 concentration decreases to one-half its originalvalue the reaction rate is halved as well
Recall from Section 171 that reaction rates are determined from experi-mental data Because reaction order is based on reaction rates it follows thatreaction order also is determined experimentally Finally because the rateconstant describes the reaction rate k too must be determined experimen-tally Figure 17-14 illustrates two of several experimental methods that arecommonly used to measure reaction rates
Other reaction orders The overall reaction order of a chemical reactionis the sum of the orders for the individual reactants in the rate law Manychemical reactions particularly those having more than one reactant are notfirst order Consider the general form for a chemical reaction with two reac-tants In this chemical equation a and b are coefficients
aA bB 0 products
The general rate law for such a reaction is
Rate k[A]m[B]n
where m and n are the reaction orders for A and B respectively Only if thereaction between A and B occurs in a single step (and with a single activat-ed complex) does m a and n b Thatrsquos unlikely however because sin-gle-step reactions are uncommon
173 Reaction Rate Laws 543
MathHandbookMath
Handbook
Review direct and inverse rela-tionships in the Math Handbookon page 905 of this text
A manometer measures pressure changes that result from the productionof gas as a reaction progresses The reaction rate is directly proportional to therate at which the pressure increases
b
Chem MC-543
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For example the reaction between nitrogen monoxide (NO) and hydrogen(H2) is described by the following equation
2NO(g) 2H2(g) 0 N2(g) 2H2O(g)
This reaction which occurs in more than one step has the following rate law
Rate k[NO]2[H2]
This rate law was determined experimentally The data tell that the ratedepends on the concentration of the reactants as follows If [NO] doubles therate quadruples if [H2] doubles the rate doubles The reaction is describedas second order in NO first order in H2 and third order overall because thesum of the orders for the individual reactants (the sum of the exponents) is(2 1) or 3
Determining Reaction OrderOne common experimental method of evaluating reaction order is called themethod of initial rates The method of initial rates determines reactionorder by comparing the initial rates of a reaction carried out with varyingreactant concentrations To understand how this method works letrsquos use thegeneral reaction aA bB 0 products Suppose that this reaction is carriedout with varying concentrations of A and B and yields the initial reactionrates shown in Table 17-3
Recall that the general rate law for this type of reaction is
Rate k[A]m[B]n
To determine m the concentrations and reaction rates in Trials 1 and 2 arecompared As you can see from the data while the concentration of Bremains constant the concentration of A in Trial 2 is twice that of Trial 1Note that the initial rate in Trial 2 is twice that of Trial 1 Because doubling[A] doubles the rate the reaction must be first order in A That is because2m 2 m must equal 1 The same method is used to determine n only thistime Trials 2 and 3 are compared Doubling the concentration of B causes therate to increase by four times Because 2n 4 n must equal 2 This infor-mation suggests that the reaction is second order in B giving the followingoverall rate law
Rate k[A]1[B]2
The overall reaction order is third order (sum of exponents 2 1 3)
544 Chapter 17 Reaction Rates
Experimental Initial Rates for aA bB 0 products
Trial Initial [A] Initial [B] Initial Rate(M) (M) (mol(Lmiddots))
1 0100 0100 200 103
2 0200 0100 400 103
3 0200 0200 160 103
Table 17-3
The time it takes for bonds toform and break during a chem-
ical reaction is measured in fem-toseconds A femtosecond is onethousandth of a trillionth of asecond Until recently scientistscould only calculate and imaginethe actual atomic activity ofchemical bonding In 1999 DrAhmed Zewail of the CaliforniaInstitute of Technology won aNobel Prize for his achievementsin the field of femtochemistryZewail has developed an ultrafastlaser device that can monitor andrecord chemical reactions in realtime Zewailrsquos laser flashesevery ten femtoseconds allowingchemists to record changes in thewavelengths (colors) that vibrat-ing molecules emitted during thecourse of a reaction The changescorrespond to bond formationand breakage and are mapped tothe various intermediates andproducts that are formed duringa reaction and that were previ-ously impossible to witness
PhysicsCONNECTION
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173 Reaction Rate Laws 545
PRACTICE PROBLEMS
Section 173 Assessment
19 What does the rate law for a chemical reaction tellyou about the reaction
20 Use the rate law equations to show the differencebetween a first-order reaction having a single reac-tant and a second-order reaction having a singlereactant
21 What relationship is expressed by the specific rateconstant for a chemical reaction
22 Thinking Critically When giving the rate of achemical reaction explain why it is significant toknow that the reaction rate is an average reactionrate
23 Designing an Experiment Explain how youwould design an experiment to determine the ratelaw for the general reaction aA bB 0 productsusing the method of initial rates
16 Write the rate law for the reaction aA 0 bB if the reaction is thirdorder in A [B] is not part of the rate law
17 Given the following experimental data use the method of initialrates to determine the rate law for the reaction aA bB 0 productsHint Any number to the zero power equals one For example(022)0 1 and (556)0 1
18 Given the following experimental data use the method of initialrates to determine the rate law for the reaction CH3CHO(g) 0CH4(g) CO(g)
Practice Problem 17 Experimental Data
Trial Initial [A] Initial [B] Initial Rate(M) (M) (mol(Lmiddots))
1 0100 0100 200 103
2 0200 0100 200 103
3 0200 0200 400 103
Practice Problem 18 Experimental Data
Trial Initial [CH3CHO] Initial rate(M) (mol(Lmiddots))
1 200 103 270 1011
2 400 103 108 1011
3 800 103 432 1011
In summary the rate law for a reaction relates reaction rate the rate con-stant k and the concentration of the reactants Although the equation for areaction conveys a great deal of information it is important to remember thatthe actual rate law and order of a complex reaction can be determined onlyby experiment
For more practicedetermining reactionorders go toSupplemental Practice
Problems in Appendix A
Practice
chemistrymccomself_check_quiz
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22517511
Section 174
Instantaneous Reaction Ratesand Reaction Mechanisms
Objectivesbull Calculate instantaneous
rates of chemical reactions
bull Understand that manychemical reactions occur insteps
bull Relate the instantaneousrate of a complex reactionto its reaction mechanism
Vocabularyinstantaneous ratecomplex reactionreaction mechanismintermediaterate-determining step
The average reaction rate you learned to calculate in Section 173 givesimportant information about the reaction over a period of time Howeverchemists also may need to know at what rate the reaction is proceeding at aspecific time A pharmacist developing a new drug treatment might need toknow the progress of a reaction at an exact instant This information makesit possible to adjust the product for maximum performance Can you think ofother situations where it might be critical to know the specific reaction rateat a given time
Instantaneous Reaction RatesThe decomposition of hydrogen peroxide (H2O2) is represented as follows
2H2O2(aq) 0 2H2O(l) O2(g)
For this reaction the decrease in H2O2 concentration over time is shown inFigure 17-15 The curved line shows how the reaction rate decreases as thereaction proceeds The instantaneous rate or the rate of decomposition ata specific time can be determined by finding the slope of the straight linetangent to the curve at that instant This is because the slope of the tangentto the curve at a particular point is [H2O2]t which is one way to expressthe reaction rate In other words the rate of change in H2O2 concentrationrelates to one specific point (or instant) on the graph
Another way to determine the instantaneous rate for a chemical reactionis to use the experimentally determined rate law given the reactant concen-trations and the specific rate constant for the temperature at which the reactionoccurs For example the decomposition of dinitrogen pentoxide (N2O5) intonitrogen dioxide (NO2) and oxygen (O2) is given by the following equation
2N2O5(g) 0 4NO2(g) O2(g)
[H2O
2]
(mol
L)
020
040
060
080
100
Relative time
Change in [H2O2] with Time
00 1 2 3 4 5 6 7 8 9 10
t
[H2O2]Instantaneous rate = t
[
H2
O2]
Figure 17-15
The instantaneous rate for aspecific point in the reactionprogress can be determinedfrom the tangent to the curvethat passes through that pointThe equation for the slope ofthe line (∆y∆x) is the equationfor instantaneous rate in termsof ∆[H2O2] and ∆t
instantaneous rate
546 Chapter 17 Reaction Rates
∆[H
∆2
tO2]
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174 Instantaneous Reaction Rates and Reaction Mechanisms 547
EXAMPLE PROBLEM 17-2
Calculating Instantaneous Reaction RatesThe following equation is first order in H2 and second order in NO with arate constant of 290 102 (L2(mol2middots))
2NO(g) H2(g) 0 N2O(g) H2O(g)
Calculate the instantaneous rate when the reactant concentrations are[NO] = 000200M and [H2] = 000400M
1 Analyze the ProblemThe rate law can be expressed by Rate k[NO]2[H2] Therefore the instantaneous reaction rate can be determined by insertingreactant concentrations and the specific rate constant into therate law equation
Known Unknown
[NO] 000200M Rate mol(Lmiddots)[H2] 000400Mk 290 102 (L2(mol2middots))
2 Solve for the UnknownInsert the known quantities into the rate law equation
Rate k[NO]2[H2]
Rate 290 102 (L2(mol2middots)(000200 molL)2(000400 molL))
Rate 464 106 mol(Lmiddots)
3 Evaluate the AnswerAre the units correct Units in the calculation cancel to give mol(Lmiddots)which is the common unit for the expression of reaction rates Is themagnitude reasonable A magnitude of approximately 106 mol(Lmiddots)fits with the quantities given and the rate law equation
PRACTICE PROBLEMSUse the rate law in Example Problem 17-2 and the concentrations given ineach practice problem to calculate the instantaneous rate for the reactionbetween NO and H2
24 [NO] 000500M and [H2] 000200M
25 [NO] 00100M and [H2] 000125M
26 [NO] 000446M and [H2] 000282M
The experimentally determined rate law for this reaction is
Rate k[N2O5]
where k 10 105 s1 If [N2O5] 0350M the instantaneous reactionrate would be calculated as
Rate (10 105 s1)(0350 molL)
35 106 mol(Lmiddots)
For more practice calcu-lating instantaneousreaction rates go toSupplemental PracticeSupplemental Practice
Problems in Appendix A
Practice
MathHandbookMath
Handbook
Review solving algebraic equa-tions in the Math Handbook onpage 897 of this text
Chem MC-547
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Figure 17-16
In an automobile assemblyplant the process that is mosttime consuming limits the pro-duction rate For examplebecause it takes longer to installthe onboard computer systemthan it takes to attach the hoodassembly the computer installa-tion is a rate-determining step
Reaction MechanismsMost chemical reactions consist of a sequence of two or more simpler reac-tions For example recent evidence indicates that the reaction 2O3 0 3O2occurs in three steps after intense ultraviolet radiation from the sun liberateschlorine atoms from certain compounds in Earthrsquos stratosphere Steps 1 and2 in this reaction may occur simultaneously or in reverse order
1 Chlorine atoms decompose ozone according to the equation Cl O3 0 O2 ClO
2 Ultraviolet radiation causes the decomposition reaction O3 0 O2 O
3 ClO produced in the reaction in step 1 reacts with O produced in step 2according to the equation ClO O 0 Cl O2
Each of the reactions described in steps 1 through 3 is called an elementarystep These three elementary steps comprise the complex reaction 2O3 0 3O2A complex reaction is one that consists of two or more elementary steps Thecomplete sequence of elementary steps that make up a complex reaction iscalled a reaction mechanism Adding the elementary steps in steps 1 through3 and canceling formulas that occur in equal amounts on both sides of the reac-tion arrow produce the net equation for the complex reaction as shown below
Elementary step Cl O3 0 O2 ClO
Elementary step O3 0 O2 O
Elementary step ClO O 0 Cl O2
Complex reaction 2O3 0 3O2
Because chlorine atoms react in step 1 of the reaction mechanism and arere-formed in step 3 chlorine is said to catalyze the decomposition of ozoneDo you know why Because ClO and O are formed in the reactions in steps1 and 2 respectively and are consumed in the reaction in step 3 they arecalled intermediates In a complex reaction an intermediate is a substanceproduced in one elementary step and consumed in a subsequent elementarystep Catalysts and intermediates do not appear in the net chemical equation
Rate-determining step You have probably heard the expression ldquoAchain is no stronger than its weakest linkrdquo Chemical reactions too have aldquoweakest linkrdquo in that a complex reaction can proceed no faster than theslowest of its elementary steps In other words the slowest elementary stepin a reaction mechanism limits the instantaneous rate of the overall reaction
Food TechnologistEveryone needs to eat and intodayrsquos fast-paced world wersquovebecome accustomed to havingsafe convenient and nutri-tious food at our fingertipsready to toss in the microwaveFood technologists help makenutrition in our fast-pacedlifestyle more convenient bydeveloping new ways toprocess preserve package andstore food
Food technologists are alsocalled food chemists food sci-entists and food engineersThey find ways to make foodproducts more healthful moreconvenient and better tastingPart of their job is searchingfor ways to stop or slow chemi-cal reactions and lengthen theshelf life of food Food tech-nologists might find careers inthe food industry universitiesor the federal government
548 Chapter 17 Reaction Rates
Chem MC-548
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For that reason the slowest of the elementary steps in a complex reaction iscalled the rate-determining step Figure 17-16 illustrates this concept in amanufacturing plant
To see how the rate-determining step affects reaction rate again considerthe gas-phase reaction between hydrogen and nitrogen monoxide discussedearlier in the chapter
2NO(g) 2H2(g) 0 N2(g) 2H2O(g)
A proposed mechanism for this reaction consists of the following elementarysteps
2NO 0 N2O2 (fast)
N2O2 H2 0 N2O H2O (slow)
N2O H2 0 N2 H2O (fast)
Although the first and third elementary steps occur relatively fast the mid-dle step is the slowest and it limits the overall reaction rate It is the rate-determining step The relative energy levels of reactants intermediatesproducts and activated complex are illustrated in Figure 17-17
Chemists can make use of instantaneous reaction rates reaction ordersand rate-determining steps to develop efficient ways to manufacture prod-ucts such as pharmaceuticals By knowing which step of the reaction is slow-est a chemist can work to speed up that rate-determining step and therebyincrease the rate of the overall reaction
174 Instantaneous Reaction Rates and Reaction Mechanisms 549
Section 174 Assessment
27 How can the rate law for a chemical reaction beused to determine an instantaneous reaction rate
28 Compare and contrast an elementary chemicalreaction with a complex chemical reaction
29 What is a reaction mechanism An intermediate
30 Thinking Critically How can you determinewhether a product of one of the elementary stepsin a complex reaction is an intermediate
31 Communicating How would you explain thesignificance of the rate-determining step in achemical reaction
Reaction progress
Ener
gy
Activatedcomplex
Activatedcomplex
Activatedcomplex
Reactants2NO 2H2 Intermediate
N2O2 2H2
IntermediateN2O H2O H2
N2 2H2O
Products
Figure 17-17
The three peaks in this energydiagram correspond to activa-tion energies for the intermedi-ate steps of the reaction Themiddle hump represents thehighest energy barrier to over-come therefore the reactioninvolving N2O2 2H2 is the rate-determining step
chemistrymccomself_check_quiz
Chem MC-549
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550 Chapter 17 Reaction Rates
Pre-Lab
1 Read the entire CHEMLAB Prepare all writtenmaterials that you will take into the laboratory Besure to include safety precautions procedure notesand a data table
2 Use emery paper or sand paper to polish the mag-nesium ribbon until it is shiny Use scissors to cutthe magnesium into four 1-cm pieces
3 Place the four test tubes in the test-tube rack Labelthe test tubes 1 (60M HCl) 2 (3M HCl)3 (15M HCl) and 4 (075M HCl)
4 Form a hypothesis about how the chemical reactionrate is related to reactant concentration
5 What reactant quantity is held constant What arethe independent and dependent variables
6 What gas is produced in the reaction between mag-nesium and hydrochloric acid Write the balancedformula equation for the reaction
7 Why is it important to clean the magnesium rib-bon If one of the four pieces is not thoroughlypolished how will the rate of the reaction involv-ing that piece be affected
Procedure
1 Use a safety pipette to draw 10 mL of 60Mhydrochloric acid (HCl) into a 10-mL graduatedpipette
2 Dispense the 10 mL of 60M HCl into test tube 1
3 Draw 50 mL of the 60M HCl from test tube 1with the empty pipette Dispense this acid into testtube 2 and use the pipette to add an additional
Safety Precautions
bull Always wear safety goggles and an apron in the labbull Never pipette any chemical by mouthbull No open flame
ProblemHow does the concentrationof a reactant affect the reac-tion rate
Objectivesbull Sequence the acid concen-
trations from the most tothe least concentrated
bull Observe which concentra-tion results in the fastestreaction rate
Materialsgraduated pipette
10-mLsafety pipette filler6M hydrochloric
aciddistilled water25 mm 150 mm
test tubes (4)test-tube rack
magnesium ribbonemery cloth or fine
sandpaperscissorsplastic rulertongswatch with second
handstirring rod
Concentration and ReactionRateThe collision theory describes how the change in concentration of
one reactant affects the rate of chemical reactions In this labora-tory experiment you will observe how concentration affects the reac-tion rate
CHEMLAB 17
Reaction Time Data
Test tube [HCl] (M) Time (s)
1
2
3
4
CHEMLAB 551
50 mL of distilled water to the acid Use the stirringrod to mix thoroughly This solution is 30M HCl
4 Draw 50 mL of the 30M HCl from test tube 2with the empty pipette Dispense this acid into testtube 3 and use the pipette to add an additional 50 mL of distilled water to the acid Use the stirringrod to mix thoroughly This solution is 15M HCl
5 Draw 50 mL of the 15M HCl from test tube 3with the empty pipette Dispense this acid into testtube 4 and use the pipette to add an additional 50 mL of distilled water to the acid Use the stir-ring rod to mix thoroughly This solution is 075MHCl
6 Draw 50 mL of the 075M HCl from test tube 4with the empty pipette Neutralize and discard it inthe sink
7 Using the tongs place a 1-cm length of magnesiumribbon into test tube 1 Record the time in sec-onds that it takes for the bubbling to stop
8 Repeat step 7 using the remaining three test tubesof HCl and the three remaining pieces of magne-sium ribbon Record in your data table the time (inseconds) it takes for the bubbling to stop
Cleanup and Disposal
1 Place acid solutions in an acid discard containerYour teacher will neutralize the acid for proper disposal
2 Wash thoroughly all test tubes and lab equipment
3 Discard other materials as directed by your teacher
4 Return all lab equipment to its proper place
Analyze and Conclude
1 Analyzing In step 6 why is 50 mL HCl discarded
2 Making and Using Graphs Plot the concentra-tion of the acid on the x-axis and time it takesfor the bubbling to stop on the y-axis Draw asmooth curve through the data points
3 Interpreting Graphs Is the curve in question 2linear or nonlinear What does the slope tell you
4 Drawing a Conclusion Based on your graphwhat do you conclude about the relationshipbetween the acid concentration and the reactionrate
5 Hypothesizing Write a hypothesis using thecollision theory reaction rate and reactant concen-tration to explain your results
6 Designing an Experiment Write a brief state-ment of how you would set up an experiment totest your hypothesis
7 Compare your experimentalresults with those of several other students in thelaboratory Explain the differences
Real-World Chemistry
1 Describe a situation that may occur in your dailylife that exemplifies the effect of concentration onthe rate of a reaction
2 Some hair-care products such as hot-oil treat-ments must be heated before application Explainin terms of factors affecting reaction rates why heatis required
Error Analysis
CHAPTER 17 CHEMLAB
1 Inferring Why is it necessary to have additional air in exhaust before it enters thecatalytic converter
2 Hypothesizing A catalytic converter is noteffective when cold Use the concept of acti-vation energy to explain why
How It Works
552 Chapter 17 Reaction Rates
Nitricoxide
Nitricoxide
Nitrogengas
Hot (500C) rhodium particle2 NO 0 N2 O2
Oxygengas
Oxygen
CarbondioxideCarbon
monoxide
Hydro-carbon
Water
Hot (500C) platinum particle2 CO O2 0 2 CO2
CxHy O2 0 CO2 H2O
Rhodium
Platinum
In many models of catalytic converters this inner structure resembles tubes in a honeycomb arrangement which provides significant surface area to accommodate the catalysts
At high temperatures (300ndash500C) on the platinum catalyst surface the dangerous carbon monoxide and hydrocarbons react with oxygen to form the compounds carbon dioxide and water
Inside the catalytic converter is a porous ceramic structure with a surface coating of platinum and rhodium particles
1
2
3
4
5 At the rhodium catalyst surface nitric oxide is converted to nitrogen and oxygen
Gasesfrom the engine and the air pass through the exhaust system to the catalytic converter Oxygen intake into the engine at this point is critical for the reactions of the catalysts
Catalytic ConverterConcerns for our environment have made a hugeimpact in the products and processes we use every dayThe catalytic converter is one of those impacts
When a combustion engine converts fuel into ener-gy the reactions of the combustion process are incom-plete Incomplete combustion results in the productionof poisonous carbon monoxide and undesirable nitro-gen oxides Since 1975 catalytic converters havereduced the exhaust emissions that contribute to airpollution by approximately 90
Study Guide 553
CHAPTER STUDY GUIDE17
Vocabulary
Key Equations and Relationships
Summary171 A Model for Reaction Ratesbull The rate of a chemical reaction is expressed as the
rate at which a reactant is consumed or the rate atwhich a product is formed
bull Reaction rates are generally calculated and expressedin moles per liter per second (mol(Lmiddots))
bull In order to react the particles in a chemical reactionmust collide in a correct orientation and with suffi-cient energy to form the activated complex
bull The rate of a chemical reaction is unrelated to thespontaneity of the reaction
172 Factors Affecting Reaction Ratesbull Key factors that influence the rate of chemical reac-
tions include reactivity concentration surface areatemperature and catalysts
bull Catalysts increase the rates of chemical reactions bylowering activation energies
bull Raising the temperature of a reaction increases therate of the reaction by increasing the collision fre-quency and the number of collisions forming theactivated complex
173 Reaction Rate Lawsbull The mathematical relationship between the rate of a
chemical reaction at a given temperature and theconcentrations of reactants is called the rate law
bull The rate law for a chemical reaction is determinedexperimentally using the method of initial rates
174 Instantaneous Reaction Rates andReaction Mechanisms
bull The instantaneous rate for a chemical reaction iscalculated from the rate law the specific rate con-stant and the concentrations of all reactants
bull Most chemical reactions are complex reactions con-sisting of two or more elementary steps
bull A reaction mechanism is the complete sequence ofelementary steps that make up a complex reaction
bull For a complex reaction the rate-determining steplimits the instantaneous rate of the overall reaction
bull Average rate qu
ant
tity
(p 529)
bull Rate k[A](p 542)
bull Rate k[A]m[B]n
(p 543)
bull activated complex (p 532)bull activation energy (p 533)bull catalyst (p 539)bull collision theory (p 532)bull complex reaction (p 548)bull heterogeneous catalyst (p 541)
bull homogeneous catalyst (p 541)bull inhibitor (p 540)bull instantaneous rate (p 546)bull intermediate (p 548)bull method of initial rates (p 544)bull rate-determining step (p 549)
bull rate law (p 542)bull reaction mechanism (p 548)bull reaction order (p 543)bull reaction rate (p 530)bull specific rate constant (p 542)bull transition state (p 532)
chemistrymccomvocabulary_puzzlemaker
554 Chapter 17 Reaction Rates
Go to the Chemistry Web site atchemistrymccom for additionalChapter 17 Assessment
Concept Mapping32 Complete the following concept map using the follow-
ing terms surface area collision theory temperaturereaction rates concentration reactivity catalyst
Mastering Concepts33 For a specific chemical reaction assume that the change
in free energy (G) is negative What does this infor-mation tell you about the rate of the reaction (171)
34 How would you express the rate of the chemical reac-tion A 0 B based on the concentration of reactant AHow would that rate compare with the reaction ratebased on the product B (171)
35 What does the activation energy for a chemical reac-tion represent (171)
36 What is the role of the activated complex in a chemi-cal reaction (171)
37 Suppose two molecules that can react collide Underwhat circumstances do the colliding molecules notreact (171)
38 How is the activation energy for a chemical reactionrelated to whether or not a collision between mole-cules initiates a reaction (171)
39 In the activated complex for a chemical reaction whatbonds are broken and what bonds are formed (171)
40 If A 0 B is exothermic how does the activationenergy for the forward reaction compare with the acti-vation energy for the reverse reaction (A 9 B) (171)
41 What role does the reactivity of the reactants play indetermining the rate of a chemical reaction (172)
42 Explain why a crushed solid reacts with a gas morequickly than a large chunk of the same solid (172)
43 What do you call a substance that increases the rate ofa chemical reaction without being consumed in thereaction (172)
44 In general what is the relationship between reactionrate and reactant concentration (172)
45 In general what is the relationship between reactionrate and temperature (172)
46 Distinguish between a homogeneous catalyst and aheterogeneous catalyst (172)
47 Explain how a catalyst affects the activation energyfor a chemical reaction (172)
48 Use the collision theory to explain why increasing theconcentration of a reactant usually increases the reac-tion rate (172)
49 Use the collision theory to explain why increasing thetemperature usually increases the reaction rate (172)
50 In a chemical reaction what relationship does the ratelaw describe (173)
51 What is the name of the proportionality constant in themathematical expression that relates reaction rate andreactant concentration (173)
52 What does the order of a reactant tell you about theway the concentration of that reactant appears in therate law (173)
53 Why does the specific rate constant for a chemicalreaction often double for each increase of 10 K (173)
54 Explain why the rates of most chemical reactionsdecrease over time (173)
55 In the method of initial rates used to determine the ratelaw for a chemical reaction what is the significance ofthe word initial (173)
56 If a reaction has three reactants and is first order inone second order in another and third order in thethird what is the overall order of the reaction (173)
57 What do you call the slowest of the elementary stepsthat make up a complex reaction (174)
58 What is an intermediate in a complex reaction (174)
59 Distinguish between an elementary step a complexreaction and a reaction mechanism (174)
60 Under what circumstances is the rate law for the reac-tion 2A 3B 0 products correctly written as Rate k[A]2[B]3 (173)
CHAPTER ASSESSMENTCHAPTER ASSESSMENT17
3
4
1
influenced byexplained by
6
7
5
2
chemistrymccomchapter_test
Assessment 555
CHAPTER 17 ASSESSMENT
61 How does the activation energy of the rate-determin-ing step in a complex reaction compare with the acti-vation energies of the other elementary steps (174)
Mastering ProblemsA Model for Reaction Rates (171)62 In the gas-phase reaction I2 Cl2 0 2ICl the [I2]
changes from 0400M at time 0 to 0300M at time 400 min Calculate the average reaction rate inmoles I2 consumed per liter per minute
63 If a chemical reaction occurs at a rate of 225 102
moles per liter per second at 322 K what is the rateexpressed in moles per liter per minute
64 On the accompanying energy level diagram match theappropriate number with the quantity it represents
a reactants c productsb activated complex d activation energy
65 Given the following data for the decomposition ofhydrogen peroxide calculate the average reaction ratein moles H2O2 consumed per liter per minute for eachtime interval
66 At a given temperature and for a specific time intervalthe average rate of the following reaction is 188 104 moles N2 consumed per liter per second
N2 3H2 0 2NH3
Express the reaction rate in moles H2 consumed perliter per second and in moles NH3 produced per literper second
Factors Affecting Reaction Rates (172)67 Estimate the rate of the reaction described in problem 63
at 332 K Express the rate in moles per liter per second
68 Estimate the rate of the reaction described in problem 63at 352 K and with [I2] doubled (assume the reaction isfirst order in I2)
Reaction Rate Laws (173)69 Nitrogen monoxide gas and chlorine gas react accord-
ing to the equation 2NO Cl2 0 2NOCl Use thefollowing data to determine the rate law for the reac-tion by the method of initial rates Also calculate thevalue of the specific rate constant
70 Use the following data to determine the rate law andspecific rate constant for the reaction 2ClO2(aq) 2OH(aq) 0 ClO3
(aq) ClO2(aq) H2O(l)
Instantaneous Reaction Rates andReaction Mechanisms (174)71 The gas-phase reaction 2HBr NO2 0 H2O NO
Br2 is thought to occur by the following mechanism
HBr NO2 0 HOBr NO H 42 kJ (slow)
HBr HOBr 0 H2O Br2 H 862 kJ (fast)
Draw the energy diagram that depicts this reactionmechanism On the diagram show the energy of thereactants energy of the products and relative activa-tion energies of the two elementary steps
Decomposition of H2O2
Time (min) [H2O2] (M)
0 250
2 212
5 182
10 148
20 100
2NO Cl2 Reaction Data
Initial [NO] Initial [Cl2] Initial rate (M) (M) (mol(Lmiddotmin))
050 050 190 102
100 050 760 102
100 100 1520 102
2ClO2(aq) 2OH(aq) Reaction Data
Initial [ClO2] Initial [OH] Initial rate(M) (M) (mol(Lmiddotmin))
00500 0200 690
0100 0200 276
0100 0100 138
2
3
4
Reaction progress
Ener
gy 1
556 Chapter 17 Reaction Rates
72 Are there any intermediates in the complex reactiondescribed in problem 71 Explain why or why not Ifany intermediates exist what are their formulas
73 Given the rate law Rate k[A][B]2 for the genericreaction A B 0 products the value for the specificrate constant (475 107 L2(mol2s)) the concentra-tion of A (0355M) and the concentration of B(00122M) calculate the instantaneous reaction rate
Mixed ReviewSharpen your problem-solving skills by answering thefollowing
74 Use the method of initial rates and the following datato determine and express the rate law for the reactionA B 0 2C
75 The concentration of reactant A decreases from 0400molL at time 0 to 0384 molL at time 400 minCalculate the average reaction rate during this timeperiod Express the rate in mol(Lmiddotmin)
76 It is believed that the following two elementary stepsmake up the mechanism for the reaction betweennitrogen monoxide and chlorine
NO(g) Cl2(g) 0 NOCl2(g)
NOCl2(g) NO(g) 0 2NOCl(g)
Write the equation for the overall reaction and identifyany intermediates in the reaction mechanism
77 One reaction that takes place in an automobilersquosengine and exhaust system is described by the equa-tion NO2(g) CO(g) 0 NO(g) CO2(g) This reac-tionrsquos rate law at a particular temperature is given bythe relationship rate 050 L(molmiddots)[NO2]
2 What isthe reactionrsquos initial instantaneous rate at [NO2] 00048 molL
78 At 232 K the rate of a certain chemical reaction is320 102 mol(Lmiddotmin) Predict the reactionrsquosapproximate rate at 252 K
Thinking Critically79 Using Numbers Draw a diagram that shows all of
the possible collision combinations between two mole-cules of reactant A and two molecules of reactant BNow increase the number of molecules of A from twoto four and sketch each possible AndashB collision combi-nation By what factor did the number of collisioncombinations increase What does this imply aboutthe reaction rate
80 Applying Concepts Use the collision theory toexplain two reasons why increasing the temperature ofa reaction by 10 K often doubles the reaction rate
81 Formulating Models Create a table of concentra-tions starting with 0100M concentrations of all reac-tants that you would propose in order to establish therate law for the reaction aA bB cD 0 productsusing the method of initial rates
Writing in Chemistry82 Research the way manufacturers in the United States
produce nitric acid from ammonia Write the reactionmechanism for the complex reaction If catalysts areused in the process explain how they are used andhow they affect any of the elementary steps
83 Write an advertisement that explains why CompanyArsquos lawn care product (fertilizer or weed killer) worksbetter than the competitionrsquos because of the smallersized granules Include applicable diagrams
Cumulative ReviewRefresh your understanding of previous chapters byanswering the following
84 Classify each of the following elements as a metalnonmetal or metalloid (Chapter 6)a molybdenumb brominec arsenicd neone cerium
85 Balance the following equations (Chapter 10)a Sn(s) NaOH(aq) Na2SnO2 H2b C8H18(l) O2(g) CO2(g) H2O(l)c Al(s) H2SO4(aq) Al2(SO4)3(aq) H2(g)
86 What mass of iron(III) chloride is needed to prepare100 L of a 0255M solution (Chapter 15)
87 H for a reaction is negative Compare the energy ofthe products and the reactants Is the reactionendothermic or exothermic (Chapter 16)
CHAPTER ASSESSMENT17
A B 0 2C Reaction Data
Initial [A] Initial [B] Initial rate (M) (M) (mol C(Lmiddots))
0010 0010 00060
0020 0010 00240
0020 0020 00960
Use these questions and the test-taking tip to preparefor your standardized test
1 The rate of a chemical reaction is all of the followingEXCEPT
a the speed at which a reaction takes placeb the change in concentration of a reactant per unit
timec the change in concentration of a product per unit
timed the amount of product formed in a certain period of
time
2 The complete dissociation of acid H3A takes place inthree steps
H3A(aq) rarr H2A(aq) H(aq)
Rate k1[H3A] k1 32 102 s1
H2A(aq) rarr HA2(aq) H(aq)
Rate k2[H2A] k2 15 102 s1
HA2(aq) rarr A3(aq) H(aq)Rate k3[HA2] k3 08 102 s1
overall reaction H3A(aq) rarr A3(aq) 3H(aq)
When the reactant concentrations are [H3A] 0100M [H2A
] 0500M and [HA2] 0200Mwhich reaction is the rate-determining step
a H3A(aq) rarr H2A(aq) H(aq)
b H2A(aq) rarr HA2(aq) H(aq)
c HA2(aq) rarr A3(aq) H(aq)d H3A(aq) rarr A3(aq) 3H(aq)
3 Which of the following is NOT an acceptable unit forexpressing a reaction rate
a Mmin c mol(mLmiddoth)b Ls d mol(Lmiddotmin)
Interpreting Tables Use the table to answer questions46
Reaction SO2Cl2(g) rarr SO2(g) Cl2(g)
4 What is the average reaction rate for this reactionexpressed in moles SO2Cl2 consumed per liter perminute
a 130 103 mol(Lmiddotmin)b 260 101 mol(Lmiddotmin)c 740 103 mol(Lmiddotmin)d 870 103 mol(Lmiddotmin)
5 On the basis of the average reaction rate what will theconcentrations of SO2 and Cl2 be at 2000 min
a 0130M c 039Mb 0260M d 052M
6 How long will it take for half of the original amountof SO2Cl2 to decompose at the average reaction rate
a 285 min c 385 minb 335 min d 500 min
7 Which of the following does NOT affect reaction rate
a catalystsb surface area of reactantsc concentration of reactantsd reactivity of products
8 The reaction between persulfate (S2O82) and iodide
(I) ions is often studied in student laboratoriesbecause it occurs slowly enough for its rate to bemeasured
S2O82(aq) 2I(aq) rarr 2SO4
2(aq) I2(aq)
This reaction has been experimentally determinedto be first order in S2O8
2 and first order in ITherefore what is the overall rate law for thisreaction
a Rate k[S2O82]2[I]
b Rate k[S2O82][I]
c Rate k[S2O82][I]2
d Rate k[S2O82]2[I]2
9 The rate law for the reaction A B C rarr productsis Rate k[A]2[C]
If k 692 105 L2(mol2middots) [A] 0175M[B] 0230M and [C] 0315M what is theinstantaneous reaction rate
a 668 107 mol(Lmiddots)b 877 107 mol(Lmiddots)c 120 106 mol(Lmiddots)d 381 106 mol(Lmiddots)
Standardized Test Practice 557
STANDARDIZED TEST PRACTICECHAPTER 17
Watch the Little Words Underline words likeleast not and except when you see them in testquestions They change the meaning of the question
Experimental Data Collected for Reaction
Time (min) [SO2Cl2] (M) [SO2] (M) [Cl2] (M)
00 100 000 000
1000 087 013 013
2000 074
chemistrymccomstandardized_test
- Chemistry Matter and Change
-
- Contents in Brief
-
- Table of Contents
-
- Chapter 1 Introduction to Chemistry
-
- Discovery Lab Where is it
- Section 11 The Stories of Two Chemicals
-
- Chemistry Online
-
- Section 12 Chemistry and Matter
-
- Problem-Solving Lab Chemical Models
- Careers Using Chemistry Chemistry Teacher
-
- Section 13 Scientific Methods
- Section 14 Scientific Research
-
- Biology Connection
- ChemLab The Rubber Band Stretch
- MiniLab Developing Observation Skills
-
- Chemistry and Society The Human Genome Project
- Chapter 1 Study Guide
- Chapter 1 Assessment
-
- Chapter 2 Data Analysis
-
- Discovery Lab Layers of Liquids
- Section 21 Units of Measurement
-
- Astronomy Connection
- Chemistry Online
- MiniLab Density of an Irregular Solid
-
- Section 22 Scientific Notation and Dimensional Analysis
- Section 23 How reliable are measurements
-
- Careers Using Chemistry Scientific Illustrator
-
- Section 24 Representing Data
-
- Problem-Solving Lab How does speed affect stopping distance
- ChemLab Using Density to Find the Thickness of a Wire
-
- How It Works Ultrasound Devices
- Chapter 2 Study Guide
- Chapter 2 Assessment
-
- Chapter 3 Matter-Properties and Changes
-
- Discovery Lab Observing Chemical Change
- Section 31 Properties of Matter
-
- Careers Using Chemistry Science Writer
- Problem-Solving Lab How is compressed gas released
-
- Section 32 Changes in Matter
-
- ChemLab Matter and Chemical Reactions
-
- Section 33 Mixtures of Matter
-
- MiniLab Separating Ink Dyes
- Chemistry Online
-
- Section 34 Elements and Compounds
-
- History Connection
-
- Chemistry and Society Green Buildings
- Chapter 3 Study Guide
- Chapter 3 Assessment
-
- Chapter 4 The Structure of the Atom
-
- Discovery Lab Observing Electrical Charge
- Section 41 Early Theories of Matter
-
- History Connection
- ChemLab Very Small Particles
-
- Section 42 Subatomic Particles and the Nuclear Atom
-
- Chemistry Online
- Problem-Solving Lab Interpreting STM Images
-
- Section 43 How Atoms Differ
-
- MiniLab Modeling Isotopes
-
- Section 44 Unstable Nuclei and Radioactive Decay
-
- Careers Using Chemistry Radiation Protection Technician
-
- Chemistry and Society Nanotechnology
- Chapter 4 Study Guide
- Chapter 4 Assessment
-
- Chapter 5 Electrons in Atoms
-
- Discovery Lab Whats Inside
- Section 51 Light and Quantized Energy
-
- Chemistry Online
- MiniLab Flame Tests
- ChemLab Line Spectra
-
- Section 52 Quantum Theory and the Atom
-
- Problem-Solving Lab How was Bohrs atomic model able to explain the line spectrum of hydrogen
- Physics Connection
-
- Section 53 Electron Configurations
-
- Careers Using Chemistry Spectroscopist
-
- How It Works Lasers
- Chapter 5 Study Guide
- Chapter 5 Assessment
-
- Chapter 6 The Periodic Table and Periodic Law
-
- Discovery Lab Versatile Metals
- Section 61 Development of the Modern Periodic Table
-
- Astronomy Connection
- Problem-Solving Lab Francium-solid liquid or gas
- ChemLab Descriptive Chemistry of the Elements
-
- Section 62 Classification of the Elements
-
- Chemistry Online
- Careers Using Chemistry Medical Lab Technician
-
- Section 63 Periodic Trends
-
- MiniLab Periodicity of Molar Heats of Fusion and Vaporization
-
- How It Works Television Screen
- Chapter 6 Study Guide
- Chapter 6 Assessment
-
- Chapter 7 The Elements
-
- Discovery Lab Magnetic Materials
- Section 71 Properties of s-Block Elements
-
- Careers Using Chemistry Dietician
- MiniLab Properties of Magnesium
- ChemLab Hard Water
-
- Section 72 Properties of p-Block Elements
-
- History Connection
- Problem-Solving Lab Cost of Fertilizer
-
- Section 73 Properties of d-Block and f-Block Elements
-
- Chemistry Online
-
- How It Works Semiconductor Chips
- Chapter 7 Study Guide
- Chapter 7 Assessment
-
- Chapter 8 Ionic Compounds
-
- Discovery Lab An Unusual Alloy
- Section 81 Forming Chemical Bonds
- Section 82 The Formation and Nature of Ionic Bonds
-
- Chemistry Online
- ChemLab Making Ionic Compounds
- Problem-Solving Lab How is color related to a transferred electron
-
- Section 83 Names and Formulas for Ionic Compounds
-
- Careers Using Chemistry Wastewater Treatment Operator
- Earth Science Connection
-
- Section 84 Metallic Bonds and Properties of Metals
-
- MiniLab Heat Treatment of Steel
-
- Everyday Chemistry Color of Gems
- Chapter 8 Study Guide
- Chapter 8 Assessment
-
- Chapter 9 Covalent Bonding
-
- Discovery Lab Oil and Vinegar Dressing
- Section 91 The Covalent Bond
- Section 92 Naming Molecules
-
- Careers Using Chemistry Organic Chemist
-
- Section 93 Molecular Structures
- Section 94 Molecular Shape
-
- MiniLab Building VSEPR Models
-
- Section 95 Electronegativity and Polarity
-
- History Connection
- ChemLab Chromatography
- Chemistry Online
- Problem-Solving Lab How do dispersion forces determine the boiling point of a substance
-
- How It Works Microwave Oven
- Chapter 9 Study Guide
- Chapter 9 Assessment
-
- Chapter 10 Chemical Reactions
-
- Discovery Lab Observing a Change
- Section 101 Reactions and Equations
-
- Earth Science Connection
-
- Section 102 Classifying Chemical Reactions
-
- Problem-Solving Lab Can you predict the reactivities of halogens
- ChemLab Small Scale Activities of Metals
- Chemistry Online
-
- Section 103 Reactions in Aqueous Solutions
-
- MiniLab Observing a Precipitate-Forming Reaction
- Careers Using Chemistry Pastry Chef
-
- How It Works Hot and Cold Packs
- Chapter 10 Study Guide
- Chapter 10 Assessment
-
- Chapter 11 The Mole
-
- Discovery Lab How much is a mole
- Section 111 Measuring Matter
-
- History Connection
-
- Section 112 Mass and the Mole
-
- Problem-Solving Lab Molar Mass Avogadros Number and the Atomic Nucleus
-
- Section 113 Moles of Compounds
- Section 114 Empirical and Molecular Formulas
-
- Careers Using Chemistry Analytical Chemist
- MiniLab Percent Composition and Gum
- Chemistry Online
-
- Section 115 The Formula for a Hydrate
-
- ChemLab Hydrated Crystals
-
- Chemistry and Technology Making Medicines
- Chapter 11 Study Guide
- Chapter 11 Assessment
-