15.1. the rate of a reaction is the change in reactant or product concentrations with time1 an...

15.1. The rate of a reaction is the change in reactant or product concentrations with time 1

An automotive catalytic muffler.

Chemical KineticsChapter 13

13.1 Five factors affect reaction rates 2

Rate of reaction -


A B

13.1

rate = -[A]t

rate = [B]t

time


Factors Affecting Reaction Rate

1. Chemical nature• Bond strengths

• General reactivity

2. Ability to establish contact with one another

• Physical state

• Surface area for liquids, solids, and heterogeneous mixtures

• Amount of Mixing

• Particle shape/size


Factors (Cont.)

3. Concentration of reactants Molarity for solutions Pressure effects for gases Volume effects for gases

4. Temperature

5. Catalysts


Your Turn!

Which of the following would speed a reaction?

A. stirring it

B. dissolving the reactants in water, if ionic

C. adding a catalyst

D. grinding any solids

E. all of these

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13.2 Rates of reaction are measured by monitoring change in concentration over time 7

Measuring Rates

instantaneous rate (text uses this unless specified)

average rate initial rate


Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g)

time

393 nmlight

Detector

[Br2] Absorption3

93 n

m

Br2 (aq)

13.1


Fig. 13.5


Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g)

average rate = -[Br2]t

= -[Br2]final – [Br2]initial

tfinal - tinitial

slope oftangent

slope oftangent slope of

tangent

instantaneous rate = rate for specific instance in time13.1


Fig. 13.6


rate [Br2]

rate = k [Br2] = rate law

k = rate[Br2]

13.1

= rate constant

= 3.50 x 10-3 s-1


Your Turn!

What is the average rate of B between 10 and 40 s?

A. -0.006 M/s

B. +0.006 M/s

C. -0.002 M/s

D. +0.002 M/s

E. can’t tell form the information 10 20 30 40

Time Elapsed in Reaction Progress (s)

Concentration of B (M)

0.0

0.1

0.2

0.3

0.4



Rates And Stoichiometry

• Rates based on each substance are related to one another by the stoichiometric coefficients of the reaction

• Examine the reaction: aA + bB →dD the stoichiometric relationship between substances A and

B is given as a mole A: b mole B RateA×(b/a)=RateB

sL

Bmol

A mola

Bmol b

sL

A mol


• Compared to the rate with respect to propane: Rate with respect to oxygen is five times faster Rate with respect to carbon dioxide is three times faster Rate with respect to water is four times faster

• Since the rates are all related any may be monitored to determine the reaction rate

)(4)(3)(5)( 22283 gOHgCOgOgHC

Consider the combustion of propane:


Learning Check

• In the reaction: 2A + 3B →5D We measured the rate of disappearance of substance A to be 3.5×10-5M/s. What is the rate of appearance of D?

• In the reaction 3A + 2B →C, we measured the rate of B. How does the rate of C relate?

8.75×10-5 M/s

RC=1/2 RB


3A + 2B + C Products

Rate = k [A]2[B][C]3

The exponents in the rate law are generally unrelated to the chemical equation’s coefficients Never simply assume the exponents and coefficients are the same The exponents must be determined from the results of experiments

The exponent in a rate law is called the order of reaction with respect to the corresponding reactant


Your Turn!

In the reaction 2CO(g) + O2(g) →2CO2(g), the rate of the reaction of CO is measured to be 2.0 M/s. What would be the rate of the reaction of O2?

A. the same

B. twice as great

C. half as large

D. you cannot tell from the given information


13.3 Rate laws give reaction rate as a function of reactant concentrations 20

Learning Check

The rate law for the reaction 2A +B→3C is

rate= 0.045M-1s-1 [A][B]

if the concentration of A is 0.2M and that of B is 0.3M, what will be the reaction rate?

rate=0.0027 M/s

rate=0.045 M-1 s-1 [0.2][0.3]


Table 13.2 from Page 529

5.40 0.30 0.30 5

2.40 0.20 0.30 4

0.60 0.10 0.30 3

0.40 0.10 0.20 2

0.20 0.10 0.10 1

)s L (mol )L (mol )L (molExpt

Rate Initial ][ ][

Conc. Inital

1-1-1-1-

BA

nm BAk

productsBA

][][rate

Determine the rate law


The initial rate for the reaction of nitrogen monoxide and oxygen was measured at 25 ºC for various concentrations shown in the table below. Determine the rate equation for the reaction, the value of the rate constant with proper units, and the initial rate if [NO]=[O2]=0.010 M

Exp# [NO] [O2] initial ratemol/L mol/L mol/Ls

1 0.020 0.010 0.028

2 0.020 0.020 0.057

3 0.020 0.040 0.114

4 0.040 0.020 0.227

5 0.010 0.020 0.014


Concentration rate data for reaction A + B + C ProductsInitial Conc.mol/L Initial Rate mol/Ls[A] [B] [C] Rate0.10 0.10 0.10 0.200.20 0.10 0.10 0.400.30 0.10 0.30 0.600.30 0.20 0.30 2.400.30 0.30 0.60 5.40

Determine the rate law for this reactionDetermine the rate constant for the reactionDetermine the overall reaction order for the reactionDetermine the rate of reaction when [A]=[B]=0.50 mol/L


A certain reaction follows the equation 2A + B 3C + D.

Experimental results yielded the following data. Determine the rate law, reaction order for A and B, the overall reaction order, the value for the rate constant k, and the rate of reaction when [A] = [B] = 1.0 mol/L

Concentration rate data for reaction A + B C + D

Initial Concentration mol/L

[A] [B] Rate

0.40 0.30 1.0e-4

0.80 0.30 4.0e-4

0.80 0.60 1.6e-3


Your Turn!For the following data, determine the order of NO2 in the

reaction at 25° 2 NO2(g) + F2(g)→ 2 NO2F(g):

Exp. [NO2] [F2] Rate NO2 disappearance (M/s)

1 0.001 0.005 2 (10-4)

2 0.002 0.005 4 (10-4)

3 0.006 0.002 4.8 (10-4)

A. 0 B. 1 C. 2 D. 3 E. not enough information given


Your Turn!

Chlorine Dioxide, ClO2, is a reddish-yellow gas that is soluble in water. In basic solution it gives ClO3

- and ClO2

- ions. 2ClO2(aq) + 2OH-(aq)→ 6ClO3

- (aq) +

ClO2- (aq) + H2O(l)

The rate law is Rate=k[ClO2]2[OH-], what is the value of the rate constant given that when [ClO2]=0.060M, [OH-] = 0.030, the reaction rate is 0.0248 M/s

A. 0.02 M-1 /sB. 0.02 M/sC. 0.02 s-

D. None of these 2.3(102) M-2 s-1


13.4 Integrated rate laws give concentration as a function of time 27

Zero-Order Reactions

• Rate=k [A]0 = k• Plot of [reactant ] vs. time will be linear• The equation of the line will be

[A]=[A0]-kt

A= amount remaining after elapsed time, t. Ao=original amount

• Diffusion controlled - usually are fast reactions in viscous media • Rate is independent of concentrations of reactants, but the reaction still

requires reactants


Learning Check

The rate law for the reaction of A→B is zero order in A and has a rate constant of 0.02 M/s. If the reaction starts with 1.50 M A, how much is present 15 seconds after the reaction begins?

•[A]=[A0]-kt

•[A]=1.2M


Learning Check

The rate law for the reaction of A→2B is zero order in A and has a rate constant of 0.12 M/s. If the reaction starts with 1.50 M A, after what time will the concentration of A be 0.90M?

•[A]=[A0]-kt

•t=5 s


Your Turn!

Which of the following is the correct set of units for the rate constant for a zero order reaction?

A. M/s

B. M-1/s

C. M-2/s

D. Can’t tell from the given data



First Order Reactions:

• Rate=k[A]1

• Typically these reactions are decomposition type, or radioactive decay

• If the rate law is specified as d[A]/dt=k[A] or Integrating the equation gives us:

ktA

A)ln(

0


Learning Check

The radioactive decay of a new atom occurs so that after 21 days, the original amount is reduced to 33%. What is the rate constant for the reaction in s-?

k = 6.11×10-7 s-1


Consider the first order decomposition reaction

N2O5 N2O4 + O2

For which rate = k[N2O5]. At 45C the rate constant is 6.22e-4 s-1.

If the initial concentration of dinitrogen pentoxide is 0.100 M, how long will it take for the concentration to drop to 0.0100 M?


i-Clicker Classroom Participation



Consider the first order decomposition reaction

N2O5 N2O4 + O2 for which rate = k[N2O5]. At 45C the rate constant is 6.22e-4 s-1.

If at 100C the concentration falls from 0.800 to 0.100 M in 45.0 minutes, what is the rate constant at 100C?


Fig. 13.12


Derive the equation for half-life

o

o

AAwhentimeist

ktA

A

2

1

)ln(

2

1

2/1t

693.0

k


Learning Check

ktAAo )ln(

21t)2ln(

k

The half-life of I-132 is 2.295h. What percentage remains after 24 hours?

0.302 h-1 = k

A = .0711 %


Your Turn!

What is the half-life of a new element, Barclium-146, if, after 2.2 h, 1.3% remains?

A. 2.0 h

B. 0.35 h

C. 0.51 h

D. None of these



Hydrogen peroxide decomposes in dilute sodium hydroxide at 20 ºC in a first-order reaction where the rate constant is 1.06e-3 min-1

2 H2O2 (aq) 2 H2O (l ) + O2 (g) If the initial concentration of H2O2 is 0.202 mol/L what is

the concentration after exactly 100 minutes?

What fraction of the original hydrogen peroxide is remaining after 100 minutes?

What is the rate of reaction after 100 minutes?

What is the half-life of this reaction at 20 ºC


Second Order Reaction

• Are of several types: Rate=k[A]2,

Rate=k[A]1[B]1 and Rate=k[A]2[B]0, etc…

t][A

1[A]1

0

k


Learning Check

The rate constant for the second order reaction 2A→B is 5.3×10-5 M-

1s-1. What is the original amount present if, after 2 hours, there is 0.35M available?

A0=0.40 M


Second Order Half-Life

• Depends on the amount present at the start of the time period

• What is the relationship between k and t1/2 for this reaction type?

1/20

t][A

1 k


Learning Check

1/20

t][A

1 kThe rate constant for

a second order reaction is 4.5×10-4 M-1s-1. What is the half-life if we start with a reactant concentration of 5.0 M?

t1/2 =440 s =7.4 min


The gas-phase decomposition of hydrogen iodide is second order with a rate constant of 30. L/mol min at 443 ºC. How much time does it take for the concentration to fall from 0.010 mol/L to 0.0050 mol/L at this temperature?

What will be the HI concentration after just 12 minutes?

HI (g) 1/2 H2 (g) + 1/2 I2 (g)


a) If k=0.020 L/mol s for the second order reaction NOCl NO + Cl2 what will the concentration be after 30 minutes if the initial concentration is 0.0500 M

b) How long will it take for the concentration of NOCl to fall from 0.0500 to 0.001 M at the same temperature?


Your Turn!

Which order has a half-life that is independent of the original amount?

A. Zero

B. First

C. Second

D. None depend on the original quantity


Your Turn!

A 0.10M solution of moxium, a new antidepressant is bottled. The drug decays to fortium, a toxic chemical as a second order process. The rate constant is 2.3×10-3 M-1h-1. What quantity of moxium is present after 90. days?

A. 0.098M

B. 5.5(10-5)M

C. 0.067M

D. None of the above


Graphical methods can be used to determine the first-order rate constant, note

bmxy

AktA

ktAA

ktAA

ktA

A

t

t

t

t

]ln[]ln[

]ln[]ln[

]ln[]ln[

][

][ln

0

0

0

0


A plot of ln[A]t versus t gives a straight line with a slope of -k

The decomposition of N2O5. (a) A graph of concentration versus time for the decomposition at 45oC. (b) A straight line is obtained from a logarithm versus time plot. The slope is negative the rate constant.


2N2O5(g) 4 NO2(g) + O2(g)

Time (s) [N2O5] [NO2] [O2]0 0.02 0 0

100 0.0169 0.0063 0.0016200 0.0142 0.0115 0.0029300 0.012 0.016 0.004400 0.0101 0.0197 0.0049500 0.0086 0.0229 0.0057600 0.0072 0.0256 0.0064

Learning Check

Determine the order of the reactant graphically

0 order plot

1st order plot

2nd order plot


Graphical methods can also be applied to second-order reactions

A plot of 1/[B]t versus t gives a straight line with a slope of k

Second-order kinetics. A plot of 1/[HI] versus time (using the data in Table 15.1).

13.5 Reaction rate theories explain experimental rate laws in terms of molecular collisions

56

Collision Theory Of ReactionsFor a reaction to occur, three conditions must be met:

1. Reactant particles must collide

2. Collision energy must be enough to break bonds/initiate

3. Particles must be oriented so that the new bonds can form


57

Potential Energy Diagrams

• Demonstrate the energy needs and products as a reaction proceeds

• Tell us whether a reaction is exothermic or endothermic

• Tell us if a reaction occurs in one step or several steps

• Show us which step is the slowest


58

Potential Energy Diagrams

What about the reverse reaction?



Where does Ea come from?


61

Features of PE Diagrams

Connect to the graph: Activation Energies

P.E.

Reaction Coordinate(progress of reaction)

Activated Complexes

Product Energy

Enthalpy of reaction

Reactant Energy


63

Your Turn!

Examine the Potential energy diagram. Which is the Slowest (Rate Determining) Step?

A. Step 1

B. Step 2

C. Can’t tell from the given information

Reaction Progress

Potential Energy


Fig. 13.13


Fig. 13.16

13.6 Activation energies are measured by fitting experimental data to the Arrhenius equation

66

Temperature Effects

Changes in temperature affect the rate constant, k, according to the Arrhenius equation: p is the steric factor Z is the frequency of collisions. Ea is the activation energy

R is the Ideal Gas Constant (8.314 J/mol K) T is the temperature (K) A is the frequency factor

/RTaEpZe k /RTaEAe k


67

Working With The Arrhenius Equation

Linear Form: To determine the Ea and A value

RTaE

Ak lnln

Ratio form: Can be used when A isn’t known.

121

2 11)ln(

TTR

E

k

k a


68

Learning Check

Given that k at 25°C is 4.61×10-1 M/s and that at 50°C it is 4.64×10-1 M/s, what is the activation energy for the reaction?

121

2 11)ln(

TTRE

kk a

208 J/mol=Ea


69

Working With The Arrhenius Equation

Given the following data, predict k at 75°C using the graphical approach

k (M/s) T °C

0.000886 25

0.000894 50

0.000918 150

0.000908 100graph

ln (k) = -0.0278/T-0.1917

k=8.25×10-1

lnAT1

RaE

ln k


The reaction CH3I + HI CH4 + I2 was observed to have rate constants

k= 3.2 L/(mol s) at 350C and

k=23 L/(mol s) at 400C.

What is the value of Eafor this reaction expressed in kJ/mol?

What would the rate constant be at 300C?

121

2 11ln

TTR

E

k

kAek ART

EA


71

Your Turn!

In the reaction 2N2O5(g) 4 NO2(g) + O2(g) the following temperature and rate constant information is obtained. What is the activation energy of the reaction?

A. 99.7 kJ

B. -99.7 kJ

C. 1004 kJ

D. -1004 kJ

E. none of these

T (K) k (s-1)

338

328

318

4.87(10-3)

1.50(10-3)

4.98(10-4)


The first order reaction 2NO2 2 NO + O2 has an activation energy of 111 kJ/mol. At 400C, k = 7.8 L/mol s

1. What is the value of k at 430C?

2. If the [NO2] is 1.5e-2M, what is the rate of reaction at 430 C?

121

2 11ln

TTR

E

k

kAek ART

EA

13.7 Experimental rate laws can be used to support or reject proposed mechanisms for a reaction

74

Reaction Mechanisms

• The rate determining step is the slowest step of the reaction that accounts for most of the reaction time

• Elementary steps sum to the overall reaction• Catalysts interact with the reactant, they will

appear in the mechanism• Intermediates are temporary products, formed in

an early step and consumed in a later step


75

Learning Check

The reaction mechanism that has been proposed for the decomposition of H2O2 is

1. H2O2 + I- → H2O + IO- (slow)

2. H2O2 + IO- → H2O + O2 + I- (fast)

• Which is the rate determining step?• Are there any intermediates?


76

Learning Check

The reaction mechanism that has been proposed for the decomposition of H2O2 is

1. H2O2 + I- → H2O + IO- (slow)

2. H2O2 + IO- → H2O + O2 + I- (fast)

What is the expected rate law?


77

Learning Check

The reaction: A + 3 B → D + F was studied and the following mechanism was finally determined

1. A + B → C (fast)

2. C + B → D + E (slow)

3. E + B → F (very fast)

What is the expected rate law?

13.8 Catalysts change reaction rates by providing alternative paths between reactants and products

78

Catalysts

• Speed a reaction, but are not consumed by the reaction

• May appear in the rate law

• Lower the Ea for the reaction.

• May be heterogeneous or homogeneous


CATALYSISCATALYSIS

Catalysis and activation energyCatalysis and activation energy

Catalysis and activation energyCatalysis and activation energy

Uncatalyzed reactionUncatalyzed reaction

Catalyzed reactionCatalyzed reaction

MnOMnO22 catalyzes catalyzes

decomposition of Hdecomposition of H22OO22

2 H2 H22OO22 ---> 2 H ---> 2 H22O + OO + O22


81

Catalytic Actions

• May serve to weaken bonds through induction• May serve to change polarity through

amphipathic/surfactant effects• May reduce geometric orientation effects

• Heterogeneous catalyst: reactant and product exist in different states.

• Homogeneous catalyst: reactants and catalyst exist in the same physical state


82

Heterogeneous catalysts


For the reaction

C2H6(g) 2CH3(g) rate = k[C2H6]

If k = 5.50 E–4 s–1 and [C2H6]initial = 0.0200 M, calculate the rate of reaction after 30 min.

15.1. the rate of a reaction is the change in reactant or product concentrations with time1 an...

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