1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = ...
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Transcript of 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = ...
![Page 1: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/1.jpg)
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KineticsKinetics
Chapter 15Chapter 15
![Page 2: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/2.jpg)
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The study of rxn ratesThe study of rxn rates
• Rxn rate = Rxn rate = concentration/concentration/timetime
• Example: Example: 2N2N22OO55 4NO 4NO22 + O + O22
• As reactant As reactant concentration concentration decreases decreases products’ products’ concentrations concentrations increaseincrease
2 5
2
2
- [N O ]rate of rxn =
t[NO ]
rate of rxn = t
[O ]rate of rxn =
t
![Page 3: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/3.jpg)
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Let’s do some calculationsLet’s do some calculations
• From 300s to 400s, From 300s to 400s,
--[N[N22OO55]/]/t = t =
-.0019M/100s-.0019M/100s
• What are What are [NO[NO22]/]/t & t & [O[O22]/]/t during the same t during the same time interval?time interval?
• Let’s work this out…Let’s work this out…
• Is rxn rate constant?Is rxn rate constant?
– Let’s look at Let’s look at [NO[NO22]/]/t t at different time at different time intervalsintervals
![Page 4: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/4.jpg)
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More…More…
• The previous rates The previous rates were were average ratesaverage rates
• Different from Different from instantaneous ratesinstantaneous rates (@ single pt)(@ single pt)
• Ex:Ex:[N[N22OO55]=-0.0019M ]=-0.0019M
((@ 200s)@ 200s)• Car speed is Car speed is
analogousanalogous
![Page 5: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/5.jpg)
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Continued Continued
• We can also We can also calculate changes calculate changes mathematically mathematically based on based on stoichiometric stoichiometric relationshipsrelationships
• Let’s seeLet’s see
• http://wps.prenhall.http://wps.prenhall.com/wps/media/objcom/wps/media/objects/167/172009/Dects/167/172009/DecompositionofN2OecompositionofN2O5.html5.html
![Page 6: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/6.jpg)
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Writing rate expressionWriting rate expression
2N2N22OO55 4NO 4NO22 + O + O22
• To equate rates of To equate rates of disappearance or disappearance or appearanceappearance– Divide the Divide the
stoichiometric stoichiometric coefficient in the coefficient in the balanced equationbalanced equation
2 5 2 2[N O ] [NO ] [O ]1 1 = + = +2 4t t t
![Page 7: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/7.jpg)
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Let’s work on thisLet’s work on this
• a) Give four related rate expressions for a) Give four related rate expressions for the rate of the following reaction:the rate of the following reaction:
2H2H22COCO(g)(g) + O + O2(g)2(g) 2CO 2CO(g)(g) + 2H + 2H22OO(g)(g)
• b) Give three related rate expressions b) Give three related rate expressions for the rate of the following reaction:for the rate of the following reaction:
NN2(g)2(g) + 3H + 3H2(g)2(g) 2NH 2NH3(g)3(g)
![Page 8: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/8.jpg)
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Let’s also work on this:Let’s also work on this:
• Consider the reaction:Consider the reaction: A + 2B A + 2B C C
• Give the three related Give the three related rate expressions for rate expressions for the rate of the the rate of the reaction.reaction.
• Using the following Using the following data, determine the data, determine the average rate of the average rate of the reaction, and the rate reaction, and the rate between 30 and 40 between 30 and 40 seconds.seconds.
• Time (s): 0.0, 10.0, Time (s): 0.0, 10.0, 20.0, 30.0, & 40.020.0, 30.0, & 40.0
• [A] (M): 1.000, 0.833, [A] (M): 1.000, 0.833, 0.714, 0.625, & 0.555, 0.714, 0.625, & 0.555, respectivelyrespectively
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Reaction conditions and Reaction conditions and ratesrates• Higher temp Higher temp faster rxn rate faster rxn rate
– Raise in temp by 10Raise in temp by 10°C °C double reaction rate double reaction rate
• Higher concentration Higher concentration faster rxn rate faster rxn rate
• CatalystsCatalysts speed up rxn rates speed up rxn rates– They don’t reactThey don’t react– They lower the activation energyThey lower the activation energy
• Enzymes (proteins) in organismsEnzymes (proteins) in organisms
• Metals, salts, etc. in chemical rxnsMetals, salts, etc. in chemical rxns
• Question: What does acid rain do to enzymes?Question: What does acid rain do to enzymes?
![Page 10: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/10.jpg)
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Concentration:Concentration:2N2N22OO55 4NO 4NO22 + O + O22
• If you double [NIf you double [N22OO55], you double the ], you double the rxn raterxn rate– Rate of rxn Rate of rxn [N [N22OO55]]
• Other rxns have different Other rxns have different relationships w/concentration-rxn relationships w/concentration-rxn ratesrates
![Page 11: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/11.jpg)
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Rate equationsRate equations
• Describe relationship between reactant Describe relationship between reactant concentration and rxn rateconcentration and rxn rate
• For 2NFor 2N22OO55 4NO 4NO22 + O + O22
– Rate of rxn = k[NRate of rxn = k[N22OO55]]• k = rate constantk = rate constant
– Is the rate of rxn constant too?Is the rate of rxn constant too?• Generic expression for rate eq: aA + bB Generic expression for rate eq: aA + bB xX xX• So rate = k[A]So rate = k[A]mm[B][B]nn
– Where m & n need not equal stoichiometric ratios!Where m & n need not equal stoichiometric ratios!– They can be zero, fractions, even negative #’sThey can be zero, fractions, even negative #’s– Empirically verified valuesEmpirically verified values
![Page 12: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/12.jpg)
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Order of rxn:Order of rxn:Exponent of its concentration Exponent of its concentration term for each itemterm for each item • 2NO2NO(g)(g) + Cl + Cl2(g)2(g) 2NOCl 2NOCl(g)(g) • Rxn rate for NO is Rxn rate for NO is second ordersecond order• Rxn rate for ClRxn rate for Cl22 is is first orderfirst order
– Thus, rxn rate = k[NO]Thus, rxn rate = k[NO]22[Cl[Cl22]]• Total order of rxn = Total order of rxn = summationsummation of of
exponents of all concentration itemsexponents of all concentration items– Therefore, overall rxn rate is Therefore, overall rxn rate is third orderthird order
• Remember, m & n need not equal Remember, m & n need not equal stoichiometric ratios!stoichiometric ratios!
![Page 13: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/13.jpg)
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Reaction mechanismsReaction mechanisms
• Step by step chemical equations that, when Step by step chemical equations that, when summed, give net rxnsummed, give net rxn
• For ex: For ex:
BrBr2(g)2(g) + 2NO + 2NO(g)(g) 2BrNO 2BrNO(g)(g)
1) Br1) Br2(g) 2(g) + NO+ NO(g)(g) Br Br22NONO(g)(g)
2) Br2) Br22NONO(g) (g) + NO+ NO(g)(g) 2BrNO 2BrNO(g)(g)
• Each step:Each step:– Elementary stepElementary step
![Page 14: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/14.jpg)
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MolecularityMolecularity
• Elementary steps Elementary steps classified according to # classified according to # of reactant molecules of reactant molecules – MolecularityMolecularity
• Unimolecular: Unimolecular: – A A products products – Rate expression: Rate expression: k[A]k[A]
• Bimolecular: Bimolecular: – A + B A + B products products– Rate expression: Rate expression: k[A]k[A]
[B][B]
• Termolecular:Termolecular:– A + B + C A + B + C products products
• (Or 3A or 2A + B, etc.)(Or 3A or 2A + B, etc.)
– Rate expression: Rate expression: k[A][B]k[A][B][C][C] (or (or k[A]k[A]33 or or k[A]k[A]22[B][B], , etc.)etc.)
• In elementary steps, In elementary steps, stoichiometry defines stoichiometry defines rate equation!rate equation!– K different for each stepK different for each step
![Page 15: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/15.jpg)
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Rate-determining stepRate-determining step
• The slowest elementary step is the The slowest elementary step is the rate-limiting steprate-limiting step– Overall rxn follows this rate-limiting stepOverall rxn follows this rate-limiting step
•However, intermediate not included in final However, intermediate not included in final rate lawrate law
![Page 16: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/16.jpg)
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An exampleAn example
2NO2NO(g)(g) + O + O2(g)2(g) → 2NO → 2NO2(g)2(g) • NONO(g)(g)
+ NO+ NO(g)(g) N N22OO2(g)2(g) (fast, eq.) (fast, eq.) • NN22OO2(g) 2(g) + O+ O2(g)2(g) → NO → NO2(g)2(g) (slow) (slow) • Using slow, rate-determining, step Using slow, rate-determining, step
– Rate = kRate = k22[N[N22OO22][O][O22]]• Since fast-step at eq. Since fast-step at eq.
– kk11[NO][NO]22 = k = k-1-1[N[N22OO22]]– Thus, K = kThus, K = k11/k/k-1 -1 = [N= [N22OO22]/[NO]]/[NO]22
• Intermediate ([NIntermediate ([N22OO22]) = K[NO]]) = K[NO]22
– Since rate = kSince rate = k22[N[N22OO22][O][O22]]•Rate = kRate = k2 2 K[NO]K[NO]22[O[O22]]
• Let’s say kLet’s say k2 2 K = k’K = k’ rate = k’[NO]rate = k’[NO]22[O[O22]]
![Page 17: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/17.jpg)
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Another problemAnother problem
2H2H2(g)2(g) + 2NO + 2NO(g)(g) 2H 2H22OO(g)(g) + N + N2(g)2(g)
• 2NO2NO(g)(g) N N22OO2(g)2(g); fast; fast
• HH2(g)2(g) + N + N22OO2(g)2(g) H H22OO(g)(g) + N + N22OO(g)(g); slow; slow
• NN22OO(g)(g) + H + H2(g)2(g) N N2(g)2(g) + H + H22OO(g)(g); fast; fast
![Page 18: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/18.jpg)
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Solution Solution (g) 2 2(g)
2(g) 2 2(g) 2 (g) 2 (g)
2 (g) 2(g) 2(g) 2 (g)
2fwd 1 rev -1 2 2
2fwd rev 1 -1 2 2
12 2
2NO N O ; fast
H + N O H O + N O ; slow
N O + H N + H O ; fast
fast: rate = k [NO] , rate = k [N O ]
Since rate rate , k [NO] k [N O ]
k [NO]Thus, [N O ]=
2
2
-1
22 2 2 2 2 2
22
K'[NO]k
slow: rate = k [H ][N O ]=k [H ] K'[NO]
rate = K"[H ][NO]
![Page 19: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/19.jpg)
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Rate = changeRate = change
• 2NH2NH33 N N22 + 3H + 3H22
• Rate = k[NHRate = k[NH33]]00 = k = k– Zero order Zero order rxn rxn
raterate
• Any tinkering of Any tinkering of concentration will concentration will not change rxn not change rxn rate of speciesrate of species
• k = mol/(L k = mol/(L time) time)
![Page 20: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/20.jpg)
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Rate = k[NO]Rate = k[NO]22[Cl[Cl22]]
• Rxn rate for ClRxn rate for Cl22 is is first orderfirst order
rate doubled rate doubled when [Clwhen [Cl22] doubled] doubled
• k = timek = time-1-1
![Page 21: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/21.jpg)
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Rate = k[NO]Rate = k[NO]22[Cl[Cl22]]
• Rxn rate for NO is Rxn rate for NO is second ordersecond order
• Doubling [NO] Doubling [NO] quadruples (x4) rxn quadruples (x4) rxn raterate
• k = L/(mol k = L/(mol time) time)
![Page 22: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/22.jpg)
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Let’s do this:Let’s do this:
• Nitrosyl bromide, NOBr, is formed from Nitrosyl bromide, NOBr, is formed from NO and BrNO and Br22..
2NO2NO(g) (g) + Br+ Br2(g)2(g) 2NOBr 2NOBr(g)(g)
• Experiment show that the reaction is first Experiment show that the reaction is first order in Brorder in Br22 and second order in NO. and second order in NO.
– Write the rate law for the reaction.Write the rate law for the reaction.• If the concentration of BrIf the concentration of Br22 is tripled, how is tripled, how
will the reaction rate change?will the reaction rate change?• What happens to the reaction rate when What happens to the reaction rate when
the concentration of NO is doubled?the concentration of NO is doubled?
![Page 23: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/23.jpg)
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Determining rate equationsDetermining rate equations
• Done in the labDone in the lab
• Generally, calculated after 1-2% of Generally, calculated after 1-2% of limiting reactant consumedlimiting reactant consumed– Lessens chance of side-rxns throwing Lessens chance of side-rxns throwing
things offthings off
![Page 24: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/24.jpg)
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Let’s work on this:Let’s work on this:
• The rate for the oxidation of iron (II) by cerium (IV) is The rate for the oxidation of iron (II) by cerium (IV) is measured at several different initial concentrations of the measured at several different initial concentrations of the two reactants:two reactants:
CeCe4+4+(aq)(aq) + Fe + Fe2+2+
(aq)(aq) Ce Ce3+3+(aq)(aq) + Fe + Fe3+3+
(aq)(aq)
• [Ce[Ce4+4+] (M): 1.1 x 10] (M): 1.1 x 10-5-5, 1.1 x 10, 1.1 x 10-5-5, 3.4 x 10, 3.4 x 10-5-5
• [Fe[Fe2+2+] (M): 1.8 x 10] (M): 1.8 x 10-5-5, 2.8 x 10, 2.8 x 10-5-5, 2.8 x 10, 2.8 x 10-5-5
• Rate (M/s): 2.0 x 10Rate (M/s): 2.0 x 10-7-7, 3.1 x 10, 3.1 x 10-7-7, 9.5 x 10, 9.5 x 10-7-7
– Write the rate law for this reaction, determining the Write the rate law for this reaction, determining the orders of the reaction with respect to Ce (IV) and Fe (II). orders of the reaction with respect to Ce (IV) and Fe (II). What is the overall order of the reaction? What is the overall order of the reaction?
– Calculate the rate constant, k, and give its units.Calculate the rate constant, k, and give its units.– Predict the reaction rate for a solution in which [CePredict the reaction rate for a solution in which [Ce4+4+] is ] is
2.6 x 102.6 x 10-5-5 M and [Fe M and [Fe2+2+] is 1.3 x 10] is 1.3 x 10-5-5 M. M.
![Page 25: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/25.jpg)
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Concentration-time Concentration-time relationships: Integrated rate relationships: Integrated rate lawslaws• Zero-order rxnsZero-order rxns• -(-([R]/[R]/t) = k[R]t) = k[R]00
• Using integral Using integral calculus, calculus, integrated rate integrated rate equationequation::
k = concentration/timek = concentration/time
i f[R] - [R] = kt
![Page 26: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/26.jpg)
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Concentration-time Concentration-time relationships: Integrated rate relationships: Integrated rate lawslaws• First-order rxnsFirst-order rxns• --[R]/[R]/t = k[R]t = k[R]
k = timek = time-1-1
f
i
[R]ln = -kt
[R]
![Page 27: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/27.jpg)
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Integrated rate lawsIntegrated rate laws
• Second-order rxnsSecond-order rxns• --[R]/[R]/t = k[R]t = k[R]22
k=1/k=1/(concentration(concentrationtime)time)
f i
1 1 - = kt
[R] [R]
![Page 28: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/28.jpg)
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Using graphs to solve rxn order Using graphs to solve rxn order and rate constantsand rate constants
• Zero-order: Zero-order:
• [R][R]ii – [R] – [R]ff = kt = kt
• Rearrange this in the form:Rearrange this in the form:y = mx + by = mx + b
![Page 29: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/29.jpg)
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Using graphs to solve rxn order Using graphs to solve rxn order and rate constantsand rate constants• First-order:First-order:
• Rearrange this in the form:Rearrange this in the form:y = mx + by = mx + b
• Solve the following: 2H2O2(aq) 2H2O(l) + O2(g)
• The reaction is first order in peroxide, and the rate constant, k, for this reaction is 1.06 x 10-3/min.
• If the initial peroxide concentration is 0.020 M, what is the concentration after 135 min?
f
i
[R]ln = -kt
[R]
![Page 30: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/30.jpg)
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Solution Solution
f
i
-3f
-3
f
4.06f
[R]ln = -kt
[R]
[R] -1.06 10ln = (135 mins)min[0.020 M]
-1.06 10ln[R] ln[0.020 M] (135 mins)min
[R] .017Me
![Page 31: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/31.jpg)
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Using graphs to solve rxn order Using graphs to solve rxn order and rate constantsand rate constants• Second-order:Second-order:
• Rearrange this in the form:Rearrange this in the form:y = mx + by = mx + b
• The gas phase decomposition of HI into hydrogen and iodine is second order in HI.
• The rate constant for the reaction is 30/Mmin. • How long must one wait for the concentration of
HI to decrease from 0.010 M to 0.0050 M?
f i
1 1 - = kt
[R] [R]
![Page 32: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/32.jpg)
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Solution Solution
f i
1 1 - = kt
[R] [R]
1 1 M - 30 tmin[0.0050M] [0.010M]
t=3.3 min
![Page 33: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/33.jpg)
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Half-lifeHalf-life
• Time required for Time required for reactant reactant concentration to concentration to decrease to ½ initial decrease to ½ initial valuevalue– Longer half-life Longer half-life
means slower rxnmeans slower rxn– Usually used for Usually used for
11stst-order rxns (like -order rxns (like radioactive decay)radioactive decay)
f i
f
i
f1
2i
12
12
1[R] = [R]2[R]1
2 [R]
[R]1ln( ) ln( ) kt2 [R]
1ln( ) 0.693 kt2
0.693t =
k
![Page 34: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/34.jpg)
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Half-lifeHalf-life
• For 1For 1stst-order rxns, -order rxns, tt1/21/2 is independent is independent of concof conc
![Page 35: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/35.jpg)
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Half-life: 2Half-life: 2ndnd order rxns order rxns
• Half-life increases Half-life increases with decreasing with decreasing concentrationconcentration
• Derive this!Derive this!
12
i
1t =
k[R]
![Page 36: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/36.jpg)
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Half-life: zero-order rxnsHalf-life: zero-order rxns
• Half-life decreases Half-life decreases with decreasing with decreasing concentrationconcentration
i1
2
[R]t
2k
![Page 37: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/37.jpg)
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Problem Problem
• Sucrose decomposes to fructose and Sucrose decomposes to fructose and glucose in acid solution with the rate glucose in acid solution with the rate law of:law of:
Rate = k[sucrose]; k=0.208 hrRate = k[sucrose]; k=0.208 hr-1-1 @ @ 2525°C°C
• What amount of time is required for What amount of time is required for 87.5% of the initial concentration of 87.5% of the initial concentration of sucrose to decompose?sucrose to decompose?
![Page 38: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/38.jpg)
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Solution Solution
[12.5M] -0.208ln = thr[100.0M]
t=1.00hr
![Page 39: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/39.jpg)
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Collision TheoryCollision Theory
1. Reacting molecules must collide 1. Reacting molecules must collide with one another.with one another.
2. Reacting molecules must collide 2. Reacting molecules must collide with sufficient energy to break with sufficient energy to break bonds.bonds.
3. Molecules must collide in correct 3. Molecules must collide in correct orientation to form new species.orientation to form new species.
![Page 40: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/40.jpg)
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Temperature Temperature
• Higher Higher temperatures lead temperatures lead to fast reactionsto fast reactions
• Molecules have Molecules have varying varying temperaturestemperatures– At higher At higher
temperatures, more temperatures, more molecules have molecules have higher energieshigher energies
![Page 41: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/41.jpg)
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Activation energy and Activation energy and catalystscatalysts• Activation energy:Activation energy:
– Energy required to form Energy required to form productsproducts
• Methane + oxygen gasMethane + oxygen gas– Low activation energyLow activation energy
• Xenon + oxygen gasXenon + oxygen gas– Humongous activation Humongous activation
energyenergy
• Catalysts dramatically Catalysts dramatically reduce activation reduce activation energy w/out being energy w/out being consumedconsumed
![Page 42: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/42.jpg)
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Arrhenius equationArrhenius equation• Includes tenets of collision Includes tenets of collision
theory; i.e., collision theory; i.e., collision frequency, temp (energy), frequency, temp (energy), and correct orientationand correct orientation
• k = Aek = Ae-E-Eaa/RT/RT
• A = frequency factor A = frequency factor (L/mol(L/mols)s)– Empirically derived Empirically derived
relationship between relationship between reaction rate and tempreaction rate and temp
• ee-E-Eaa/RT /RT = fraction of molecules = fraction of molecules w/min energy needed for rxn w/min energy needed for rxn (R = gas constant = 8.314 (R = gas constant = 8.314 J/molJ/molK)K)
• Can put equation in Can put equation in “y=mx+b” form“y=mx+b” form– How?How?
a-E 1ln k = + ln A
R T
![Page 43: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/43.jpg)
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The Arrhenius equationThe Arrhenius equation
![Page 44: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/44.jpg)
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Problem Problem
• Given:Given:y = -24371x + 28.204y = -24371x + 28.204
• Solve for ESolve for Eaa
![Page 45: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/45.jpg)
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Solution Solution
a a
5a
y = -24371x + 28.204
E E-24371K = -
JR 8.314 mol KJE 2.0262 10 mol
![Page 46: 1 Kinetics Chapter 15. 2 The study of rxn rates Rxn rate = concentration/ time Rxn rate = concentration/ time Example: Example: 2N 2 O 5 4NO.](https://reader035.fdocument.pub/reader035/viewer/2022062320/56649d625503460f94a44e61/html5/thumbnails/46.jpg)
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If given two points…If given two points…
a2
1 2 1
-Ek 1 1ln( ) = ( - )
k R T T