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Rates of Chemical Reactions

© Jim Birk

Questions for Consideration

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1. What conditions affect reaction rates?2. How do molecular collisions explain

chemical reactions?3. How do concentration, temperature, and

catalysts affect molecular collisions and reaction rates?

Outline

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1. Reaction Rates definition

2. Collision Theory

3. Conditions That Affect Reaction Rates

– concentration, temperature,

catalysis, surface area

Reaction Rates

Reaction Rates

Reaction rate is a measure of how fast a reaction

occurs. Some reactions are inherently fast

and some are slow:

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Reaction Rates

How do we measure rates in our

everyday lives?

How do we measure rates of

chemical reactions?

Expressing the Reaction Rate

reaction rate - changes in the concentrations of reactants or products per

unit time

reactant concentrations decrease while product concentrations

increase

rate of reaction = -

for

A B

change in concentration of A

change in time

= -conc A2-conc A1

t2-t1

(conc A)-

t

Reaction Rates

Concentration of O3 at Various Time in its Reaction with C2H4 at 303K

C2H4(g) + O3(g) C2H4O(g) + O2(g)

Time (s) Concentration of O3 (mol/L)

0.0

20.0

30.0

40.0

50.0

60.0

10.0

3.20x10-5

2.42x10-5

1.95x10-5

1.63x10-5

1.40x10-5

1.23x10-5

1.10x10-5

(conc A)-

t

Reaction Rates

The concentrations of O3 vs. time during its reaction with C2H4

C2H4(g) + O3(g) C2H4O(g) + O2(g)

- [C2H4]

t

rate =

- [O3]

t=

Reaction Rates

(conc A)-

t

Plots of [C2H4] and [O2] vs. time.

Tools of the

Laboratory

Reaction Rates

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C2H4(g) + O3(g) C2H4O(g) + O2(g)

Reaction Rates

- [C2H4]

t-

[O3]

t

(conc A)-

t

[O2]

t

[C2H4O]

t

(conc B)

t

A B

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H 2 + I 2 2HI

Reaction Rates

- [H2]

t-

[I2]

t

1 [HI]

2 t

In general, for the reaction

aA + bB cC + dD

rate = 1

a- = -

[A]

t

1

b

[B]

t

1

c

[C]

t= +

1

d

[D]

t= +

The numerical value of the rate depends upon the substance that

serves as the reference. The rest is relative to the balanced

chemical equation.

Reaction Rates

PLAN:

SOLUTION:

Because it has a nonpolluting product (water vapor), hydrogen gas is used for fuel aboard the space shuttle and may be used by Earth-bound engines in the near future.

2H2(g) + O2(g) 2H2O(g)

(a) Express the rate in terms of changes in [H2], [O2], and [H2O] with time.

(b) When [O2] is decreasing at 0.23 mol/L*s, at what rate is [H2O] increasing?

Choose [O2] as a point of reference since its coefficient is 1. For every molecule of O2 which disappears, 2 molecules of H2 disappear and 2 molecules of H2O appear, so [O2] is disappearing at half the rate of change of H2 and H2O.

-1

2

[H2]

t= -

[O2]

t= +

[H2O]

t

1

2

0.23mol/L*s = +[H2O]

t

1

2; = 0.46mol/L*s

[H2O]

t

rate =(a)

[O2]

t- = -(b)

Sample Problem

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Sample Problem

How is the rate of disappearance of ozone related to the rate of

appearance of oxygen in the following equation: 2O3 (g) → 3 O2 (g)? If

the rate of appearance of oxygen is 6.0 x 10 -5 M/s at a particular instant,

what is the value of the rate of disappearance of ozone at this same time?

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Worksheet # 10-1

1. Consider the reaction: 4PH3 (g)→ P4(g) + 6 H2 (g)

If, in a certain experiment, over a specific time period, 0.0048 mol PH3 is

consumed in a 2.0 L container each second of reaction, what are the rates

of production of P4 and H2 in this experiment?

2. The decomposition of N2O5 proceeds according to the equation:

2N2O5 → 4NO2 + O2

If the rate of decomposition of N2O5 at a particular instant in a reaction

vessel is 4.2 x 10 -7 M/s, what is the rate of appearance of

a) NO2

b) O2

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Worksheet # 10-1: Answers

1. Consider the reaction: 4PH3 (g)→ P4(g) + 6 H2 (g)

If, in a certain experiment, over a specific time period, 0.0048 mol PH3 is

consumed in a 2.0 L container each second of reaction, what are the rates

of production of P4 and H2 in this experiment? ∆P4/ ∆t = 0.0006 M/sec

∆H2/ ∆t = 0.0036 M/sec

2. The decomposition of N2O5 proceeds according to the equation:

2N2O5 → 4NO2 + O2

If the rate of decomposition of N2O5 at a particular instant in a reaction

vessel is 4.2 x 10 -7 M/s, what is the rate of appearance of

a) NO2 8.4 x 10 -7 M/s

b) O2 2.1 x 10 -7 M/s

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Collision Theory

How do you think reactants lead to products?

Collision Theory

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• In order for a reaction to occur, reactant molecules must collide

– with proper orientation

– with enough energy

• Only a small fraction of the collisions that do occur meet these requirements.

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Collision Theory

Ea

21Chemical Equations: Kinetics

Collision Theory

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• In order for reactants to convert to products, an energy barrier called the activation energy, Ea, must be overcome.

• Collisions that have the proper orientation and have at least the minimum Ea can convert to products.

Activation Energy

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Activation Energy

Reactants must overcome an energy barrier before they can change to products!

• Energy is required to break bonds in reactants before the reactants can be converted into products

– The minimum amount of energy needed to overcome

the energy barrier is called the activation energy, Ea

– Reactions with large activation energies tend to be slow because a relatively small fraction of reactants have sufficient energy for an effective collision

– Reactions with small activation energies tend to be fast because a large fraction of reactants have sufficient energy for an effective collision 12-24

Activation Energy

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Activation Energy, n. The useful quantity of energy available in one cup of coffee.

Activation Energy: Analogy

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Activation Energy

Each reaction has its own reaction diagram, which shows the amount of energy required to form the activated complex as the reaction progresses.

• Activated complex

– Short-lived, unstable, high-energy chemical species that must be achieved before products can form

– Formed from reactant molecules that collide with the proper orientation and sufficient energy

– Actual structure is unknown

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Activation Energy

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• The following reaction is an endothermic reaction:

2NO2(g) → 2NO(g) + O2(g)

Draw an energy diagram that shows the relative energies of the reactants, products, and the activated complex. Label the diagram with molecular representations of reactants, products, and a possible structure for the activated complex.

Sample Problem

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2NO2(g) → 2NO(g) + O2(g)

Sample Problem

• Consider the following reaction that occurs in smog:

NO(g) + O3(g) O2(g) + NO2(g)

• Which of the following collisions has a proper orientation?

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Proper Orientation

The importance of molecular orientation to an effective collision.

NO + NO3 2 NO2

Proper Orientation

Nature of the transition state in the reaction between CH3Br and OH-.

CH3Br + OH- CH3OH + Br -

transition state or activated complex

Proper Orientation

Reaction energy diagram for the reaction of CH3Br and OH-.

Proper Orientation

Reaction energy diagrams and possible transition states.

Proper Orientation

Reaction progress

Po

ten

tia

l E

ne

rgySOLUTION:

PROBLEM: A key reaction in the upper atmosphere is

O3(g) + O(g) 2O2(g)

The Ea(fwd) is 19 kJ, and the Hrxn for the reaction is -392 kJ. Draw a reaction energy diagram for this reaction, postulate a transition state, and calculate Ea(rev).

PLAN: Consider the relationships among the reactants, products and transition state. The reactants are at a higher energy level than the products and the transition state is slightly higher than the reactants.

O3+O

2O2

Ea= 19kJ

Hrxn = -392kJ

Ea(rev)= (392 + 19)kJ =

411kJ

OO

OO

breakingbond

formingbond

transition state

Sample Problem

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Worksheet # 10-2

1. Draw a rough sketch of the energy profile for each of the following cases:

a) ∆H = 10 kJ/mol, Ea = 25 kJ/mol

b) ∆H = - 10 kJ/mol, Ea = 50 kJ/mol

c) ∆H = - 50 kJ/mol, Ea = 25 kJ/mol

2. The activation energy for the reaction:H2 + I2 → 2HI

is 167 kJ/mol and the ∆H for the reaction is +28 kJ/mol. What is the activation energy for the decomposition of HI?

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Worksheet # 10-2: Answers

1. Draw a rough sketch of the energy profile for each of the following cases:

a) ∆H = 10 kJ/mol, Ea = 25 kJ/mol

b) ∆H = - 10 kJ/mol, Ea = 50 kJ/mol

c) ∆H = - 50 kJ/mol, Ea = 25 kJ/mol

2. The activation energy for the reaction:H2 + I2 → 2HI

Is 167 kJ/mol and the ∆H for the reaction is +28 kJ/mol. What is the activation energy for the decomposition of HI? Ea = 139 kJ/mol

a) b, c)

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Energy of activation

Video of energy of activation: (bauer book: chapter 12)

Reaction Rate

Conditions that affect reaction rate:

– Temperature• Higher temperatures generally cause reactions to occur

faster.

– Reactant concentration• Increasing the concentration of a reactant generally

increases the reaction rate.

– Surface area• Increasing the surface area increases the reaction rate if

the reactant is a solid.

– Presence of a catalyst• Adding a catalyst increases the rate of the reaction.

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• Increasing the concentration of reactants or the reaction temperature increases reaction rate by increasing the number of effective collisions.

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Effect of Concentration

• Increasing the concentration of one or more reactants increases the number of effective collisions by increasing the total number of collisions (fraction of collisions that are effective remains the same).

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• Changing the concentration of a reactant can change the reaction rate:

12-42Figure 12.3

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How do you express the effect of concentration of a reactant on reaction rate?

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zero order, first order, second order

In math a α x0

a α x1

a α x2

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In chemistryrate α x0

rate α x1

rate α x2

Thus, for A → Brate α [A]0

rate α [A]1

rate α [A]2

zero order, first order, second order

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rate = -[A]

t= k [A]0

zero order rate equation

[A]t - [A]0 = - kt

Integrated Rate Laws

rate = -[A]

t= k [A]

first order rate equation

ln[A]t

[A]o

= - kt ln [A]t = -kt + ln [A]o


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1

[A]t

1

[A]0

- = kt1

[A]t

1

[A]0

+= kt

rate = -[A]

t= k [A]2

second order rate equation


Units of the Rate Constant k for Several Overall Reaction Orders

Overall Reaction Order Units of k (t in seconds)

0 mol/L*s (or mol L-1 s-1)

1 1/s (or s-1)

2 L/mol*s (or L mol -1 s-1)

3 L2 / mol2 *s (or L2 mol-2 s-1)


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However, the order of a reaction with respect to a particular reactant cannot be determined from the balanced chemical reaction.

They can only be obtained from experiments.

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The reaction A + 2B products has the rate law,rate = k[A][B]3. If the concentration of B is doubled while that of A is unchanged, by what factor will the rate of reaction increase?

Answer: 8

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The reaction A + 2B products was found to have the rate law, rate = k[A] [B]2. Predict by what factor the rate of reaction will increase when the concentration of A is doubled and the concentration of B is also doubled.

Answer: 8


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At 25C the rate constant for the first-order decomposition of a pesticide solution is6.40 103 min1. If the starting concentration of pesticide is 0.0314 M, what concentration will remain after 62.0 min at 25C?

Answer: 2.11 102 M


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It takes 42.0 min for the concentration of a reactant in a first-order reaction to drop from 0.45 M to 0.32 M at 25C. How long will it take for the reaction to be 90% complete?

Answer: 284 min


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Sucrose, C12H22O11, reacts slowly with water in the presence of an acid to form two other sugars, glucose and fructose, both of which have the same molecular formulas, but different structures.

C12H22O11 + H2O C6H12O6 (glucose) + C6H12O6 (fructose)The reaction is first order and has a rate constant of 6.2 105/s at 35C when the H+ concentration is 0.10 M. Suppose that the initial concentration of sucrose in the solution is 0.40 M.

a. What will the sucrose concentration be after 2.0 hours?b. How many minutes will it take for the sucrose concentration to drop to 0.30 M?

Answer: a. 0.26 M b. 77 min


PLAN:

SOLUTION:

At 10000C, cyclobutane (C4H8) decomposes in a first-order reaction, with the very high rate constant of 87s-1, to two molecules of ethylene (C2H4).

(a) If the initial C4H8 concentration is 2.00M, what is the concentration after 0.010 s?

(b) What fraction of C4H8 has decomposed in this time?

Find the [C4H8] at time, t, using the integrated rate law for a 1st order reaction. Once that value is found, divide the amount decomposed by the initial concentration.

; ln2.00

[C4H8]= (87s-1)(0.010s)

[C4H8] = 0.83mol/L

ln[C4H8]0

[C4H8]t

= kt(a)

(b) [C4H8]0 - [C4H8]t

[C4H8]0

=2.00M - 0.87M

2.00M= 0.58

Sample Problem

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Worksheet # 10 - 3

1. At 700 K, the rate constant for the following reaction is 6.2 104 min1. How many minutes are required for 20% of a sample of cyclopropane to isomerize to propene?

C3H6 (cyclopropane) C3H6 (propene)

2. A certain first-order reaction A B is 25% complete in 42 min at 25C. What is its rate constant?

3. A second - order reaction has a rate constant of 3.00 103 s1.The time required for the reaction to be 75.0% complete is _____?

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Worksheet # 10 – 3: Answers

1. At 700 K, the rate constant for the following reaction is 6.2 104 min1. How many minutes are required for 20% of a sample of cyclopropane to isomerize to propene?

Answer: 360 minC

3H6 (cyclopropane) C3H6 (propene)

2. A certain first-order reaction A B is 25% complete in 42 min at 25C. What is its rate constant? Answer: 6.8 103 min1

3. A second-order reaction has a rate constant of 3.00 103 s1.The time required for the reaction to be 75.0% complete is _____?Answer: 1000 s

A plot of [N2O5] vs. time for three half-lives.

t1/2 =

for a first-order process

ln 2

k

0.693

k=


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Half- life – time required for the concentration of a substance to be reduced to one-half of its original value

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An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions

Zero Order First Order Second Order

Half-life

Rate law rate = k rate = k [A] rate = k [A]2

[A]0/2k ln 2/k 1/k [A]0


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A certain first-order reaction A B is 25% complete in 42 min at 25C. What is the half-life of the reaction?

Answer: 101 min

PLAN:

SOLUTION:

Cyclopropane is the smallest cyclic hydrocarbon. Because its 600 bond angles allow poor orbital overlap, its bonds are weak. As a result, it is thermally unstable and rearranges to propene at 10000C via the following first-order reaction:

CH2

H2C CH2(g)

H3C CH CH2 (g)

The rate constant is 9.2s-1, (a) What is the half-life of the reaction? (b) How long does it take for the concentration of cyclopropane to reach one-quarter of the initial value?

Use the half-life equation, t1/2 = 0.693

k, to find the half-life.

One-quarter of the initial value means two half-lives have passed.

t1/2 = 0.693/9.2s-1 = 0.075s(a) 2 t1/2 = 2(0.075s) = 0.150s(b)

Sample Problem

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Sample Problem

A certain first order reaction has a half life of 20.0 minutes.a. Calculate the rate constant for this reaction.b. How much time is required for this reaction to be 75%

complete?

Answers:a) k = 0.693/t ½ = 0.693/20 = 0.00347 /minb)

time = 40.0 minutes

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Sample Problem

The isomerization of cyclopropane to form propeneH2C — CH2

\ / CH3 CH = CH2

CH2

is a first-order reaction. At 760 K, 15% of a sample of cyclopropane changes to propene in 6.8 min. What is the half-life of cyclopropane at 760 K?

Answer: 29 min

An Overview of Zero-Order, First-Order, and Simple Second-Order Reactions

Zero Order First Order Second Order

Plot for straight line

Slope, y-intercept

Half-life

Rate law rate = k rate = k [A] rate = k [A]2

Units for k mol/L*s 1/s L/mol*s

Integrated rate law in straight-line form

[A]t =

k t + [A]0

ln[A]t =

-k t + ln[A]0

1/[A]t =

k t + 1/[A]0

[A]t vs. t ln[A]t vs. t 1/[A]t = t

k, [A]0 -k, ln[A]0k, 1/[A]0

[A]0/2k ln 2/k 1/k [A]0


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Worksheet # 10 - 4

1. The rate constant for the first order reaction A B + C is k =

3.3 x 10–2 min–1 at 57 K. What is the half-life for this reaction at

57 K?

2. The half-life of the zero order reactionA B is 0.56 minutes.

If the initial concentration of A is 3.4 M, what is the rate constant?

3. The rate constant for the second order reaction 2NO2

N2O4 is 2.79 L/mol min at 48 oC. If the initial concentration of

NO2 is 1.05 M , what is the half-life?

4. The decomposition of dimethylether at 504°C is first order with

a half-life of 1570. seconds. What fraction of an initial amount of

dimethylether remains after 4710. seconds?

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Worksheet # 10 - 4: Answers

1. The rate constant for the first order reaction A B + C is k = 3.3 x

10–2 min–1 at 57 K. What is the half-life for this reaction at 57 K?

Answer: 21 min

2. The half-life of the zero order reactionA B is 0.56 minutes. If the

initial concentration of A is 3.4 M, what is the rate constant?

Answer: 3.04 mol/L min

3. The rate constant for the second order reaction 2NO2 N2O4 is

2.79 L/mol min at 48 oC. If the initial concentration of NO2 is 1.05 M ,

what is the half-life?

Answer: 0.34 min

4. The decomposition of dimethylether at 504°C is first order with a half-

life of 1570. seconds. What fraction of an initial amount of dimethylether

remains after 4710. seconds?

Answer: 1/8

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