Động hoá học và hoá lý hệ phân tán

1 Prepared by NGUYEN Dinh Lam – DUT - UD 30 Exercise 3: Determine the rate law and calculate the rate constant for the following reaction from the following data: S2O82-aq+ 3I-aq 2SO42-a

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-Tài liệu tham khảo chính:

1 Hóa lý và Hóa Keo, Nguyễn Hữu Phú, Nhà Xuất bản Khoa học

và Kỹ thuật, 2003

2 Bài tập Hóa lý cơ sở, Lâm Ngọc Thiềm, Trần Hiệp Hải, Nguyễn

Thị Thu, Nhà Xuất bản Khoa học và Kỹ thuật, 2003

3 Physical Chemistry, Third Edition, Robert G Mortimer, Elsevier

Inc., 2008

4 Physical Chemistry – Understanding our Chemical Word, Paul

Monk, John Wiley & Sons, Ltd, 2004

Prepared by NGUYEN Dinh Lam – DUT - UD

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Phần 1: Động hóa học

Một số khái niệm cơ bản

- Động hóa học là môn học nghiên cứu về tốc độ và cơ

chế của quá trình hóa học.

- Nghiên cứu động học: Năng suất và Công nghệ của

- Cơ chế phản ứng (Reaction Mechanism)

- Lý thuyết va chạm (The Collision Theory)

- Năng lượng hoạt hóa (Activation Energy)

-Xúc tác (Catalyst)

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how the reaction occurs).

At 298K, reaction: H2(g) + 1/2O2(g) = H2O(l) ∆Go298(r)= -254,8 kJ.mol -1

Thermodynamics – does a reaction take place?

Kinetics – how fast does a reaction proceed?

Outline: Kinetics

Reaction Rates How we measure rates.

Rate Laws How the rate depends on amounts of reactants.

Integrated Rate Laws How to calc amount left or time to reach a given amount.

Half-life How long it takes to react 50% of reactants.

Arrhenius Equation How rate constant changes with T.

Mechanisms Link between rate and molecular scale processes.

Chemical Kinetics (Simple Homogenous reaction)

Reaction rate is the change in the concentration of a

reactant or a product with time (M/s).

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Exercise 1: Br2(aq) + HCOOH (aq) 2Br-(aq) + 2H+(aq) + CO2(g)

time

393 nm light Detector

slope of tangent slope of

tangent

instantaneous rate = rate for specific instance in time

rate α [Br2]

rate = k [Br2]

k = rate[Br2]= rate constant

= 3.50 x 10-3s-1

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Exercise 2: 2H2O2(aq) 2H2O (l) + O2(g)

1 The absorbance of radiation at some wavelength at which a given

product or reactant absorbs.

2 The intensity of the emission spectrum of the system at a

wavelength at which a given product or reactant emits.

3 The volume of a solution required to titrate an aliquot removed from

the system.

4 The pressure of the system (for a reaction at constant volume).

5 The volume of the system (for a reaction at constant pressure).

6 The electrical conductance of the system.

7 The mass spectrum of the system.

8 The ESR or NMR spectrum of the system.

9 The dielectric constant or index of refraction of the system.

10 The mass loss if a gas is evolved.

The “classical” methods for determining the reaction rate

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by the change in time:

C4H9Cl(aq)+ H2O(l)→ C4H9OH(aq)+ HCl(aq)

Cl H C rate average

t Cl H C rate average

0 0 0 50 0905 0 1000 0

9 4

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Reaction Rates

• Note that the average rate decreases as the reaction proceeds

• This is because as the reaction goes forward, there are fewer collisions between reactant

time for this reaction

yields a curve like this

• The slope of a line tangent

to the curve at any point is

the instantaneous rate at

C4H9Cl(aq)+ H2O(l)→ C4H9OH(aq)+ HCl(aq)

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Dinh Lam – DUT - UD

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Reaction Rates and Stoichiometry

• In this reaction, the ratio

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• What if the ratio is not 1:1?

• To generalize, for the reaction

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The Rate Law

The rate law expresses the relationship of the rate of a reaction

to the rate constant and the concentrations of the reactants

raised to some powers

aA + bB cC + dD

Rate = k [A] x[B]y

reaction is xth order in A reaction is yth order in B

reaction is (x +y)th order overall

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Concentration and Rate

Each reaction has its own equation that gives its rate as

a function of reactant concentrations.

⇒ this is called its Rate Law

To determine the rate law we measure the rate at different starting concentrations.

The Rate Law

This equation is called

Rate Laws

• A rate law shows the relationship between the reaction rate and the concentrations of reactants

– For gas-phase, reactants use PAinstead of [A]

• k is a constant that has a specific value for each reaction

• The value of k is determined experimentally

“Constant” is relative here - k is unique for each reaction,

k changes with T

rate = k [F2][ClO2]

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• Rate laws are always determined experimentally.

• Reaction order is always defined in terms of reactant

(not product) concentrations

• The order of a reactant is not related to the

stoichiometric coefficient of the reactant in the

balanced chemical equation

1

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Exercise 3: Determine the rate law and calculate the rate constant for the following reaction from the following data:

S2O82-(aq)+ 3I-(aq) 2SO42-(aq)+ I3-(aq)

Experiment [S2O82- ] [I - ] Initial Rate (M/s)

• The overall reaction order can be found by adding the exponents on the

reactants in the rate law.

• This reaction is second-order overall.

Exercise 3: Determine the rate law and calculate the rate

constant for the following reaction from the following data:

S2O82-(aq)+ 3I-(aq) 2SO42-(aq)+ I3-(aq)

Integrated Rate Laws First order reaction

Consider a simple first order reaction: A → B

How much A is left after time t? Integrate:

Differential form:

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The integrated form of first order rate law:

Can be rearranged to give:

[A]0is the initial concentration of A (t=0).

[A]t is the concentration of A at some time, t, during the course of

the reaction.

Integrated Rate Laws First order reaction

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First-Order Reactions

Manipulating this equation produces…

If a reaction is first-order, a plot of ln [A]t vs t will yield a

straight line with a slope of -k

So, use graphs to determine reaction order.

ln [A]0[A]

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The half-life, t½ , is the time required for the concentration of a

reactant to decrease to half of its initial concentration

t ½ = t when [A] = [A]0/2

ln [A]0[A]0/2

M 2

dt = k [A]2

-[A] is the concentration of A at any time t

[A]0is the concentration of A at time t=0

1[A] =

1[A]0 + kt

t ½ = t when [A] = [A]0/2

[A] is the concentration of A at any time t

[A]0is the concentration of A at time t=0

t ½ = t when [A] = [A]0/2

Summary of the Kinetics of Zero-Order, First-Order

and Second-Order Reactions

Concentration-Time

012

rate = k rate = k [A]

rate = k [A]2

ln[A] = ln[A]0- kt

1[A] =

1[A]0 + kt

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x a b a t k

dt k x b x a

dx x

b x a k dt

dx rate

ln

1

.

Reverse Reactions – Chemical Equilibrium

Complicated homogenous reaction

The observable rate of the reaction is a net rate

At equilibrium,

K: equilibrium constant

f r

f

r f

f r

f

r f

k k x a k

a k t

k k

x A

A t k k

A const t

At const t k k x A

k k

a k A with x

A k k dt dx

x k x a k B k A k dt

dx rate

+

−

= +

−

= +

−

=

= +

ln 1

ln ,

0

ln

.

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x x

x t

k k

A k k

a k x

or x k x a k

k

k K

r f

f r

f

r f

−

= +

.

If we know K, then we can calculate kfand kr

Signification of A

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Exercise 5: Transformation of γ-hydroxybutiric acid on γ-lacton

CH2OH-(CH2)2-COOH CH2-(CH2)2-CO

O + H2O

Reacted concentration 2,41 4,96 8,11 8,9 10,35 11,15 13,28

Initial concentrations of the acid and the lacton are 18,23M and 0M

Determine the values of K, kfand kr

Parallel (Competing) Reactions

Simplest case: that two competing reactions are first

order with negligible reverse reaction.

If [Fo] and [Go] = 0, we have

Parallel (Competing) Reactions

Simplest case: that two competing reactions are first order and the reverse reactions cannot be neglected.

If [Fo] and [Go] = 0, we have:

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Successive Reactions (series or consecutive reaction)

Almost every chemical reaction takes place through a set of steps,

called the reaction mechanism.

The substance B is called

a reactive intermediate.

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Successive Reactions (series or consecutive reaction)

Case of k 1 = 0.100 s −1 and k 2 = 0.500 s −1 Case of k 1 = 0.50 s −1 and that k 2 = 0.10 s −1

Successive Reactions

and non-negligible reverse reactions

with

the differential equations giving the rates are

Successive Reactions

and non-negligible reverse reactions

with

Both steps are at equilibrium when the entire reaction is at equilibrium:

The equilibrium constant K

for the overall reaction is equal to

and

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Determination of Reaction Order

Using Integrated Rate Laws

Using the Half-Life

Method of Initial Rates

Method of Isolation

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Using Integrated Rate Laws

Using the Half-Life

012

rate = k rate = k [A]

rate = k [A]2

ln[A] = ln[A]0- kt

1[A] =

1[A]0 + kt

Method of Initial Rates

See the anterior exercises and examples

Method of Isolation

For calculating the reaction order of each reactant

Temperature Dependence of the Rate Constant

The Arrhenius Relation (1889)

(The Simplest and Empirical Equation)

≈

= + γ γ

T

k k

Only “activated” molecules can react

Numbers of activated molecules would be governed by the Boltzmann probability distribution

Arrhenius postulates:

Svante Arrhenius, 1859–1927, was a Swedish chemist who won the 1905 Nobel Prize in chemistry for his theory of dissociation and ionization of electrolytes in solution.

This assumption leads to the Arrhenius relation:

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The Arrhenius Relation

Arrhenius relation:

εa is the energy that the molecules must have in order to react and is

called the activation energy

A is called the pre-exponential factor

We can express Arrhenius relation in the form

where E a = N Avεa is the molar activation energy

R = k B .N Av is the ideal gas constant

Experimental molar activation energy values are usually in the range from 50 to

200kJ.mol −1 , somewhat smaller than energies required to break chemical bonds.

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The activation energy (E a ) is the minimum amount of

energy required to initiate a chemical reaction

Activation Energy Determination

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Reaction Mechanisms

The overall progress of a chemical reaction can be represented

at the molecular level by a series of simple elementary steps

or elementary reactions.

The sequence of elementary steps that leads to product

formation is the reaction mechanism.

2NO (g) + O2(g) 2NO2(g)

N2O2 is detected during the reaction!

Elementary step: NO + NO N2O2

+

Elementary step: NO + NO N2O2

+

Intermediates are species that appear in a reaction

mechanism but not in the overall balanced equation

An intermediate is always formed in an early elementary step

and consumed in a later elementary step

The molecularity of a reaction is the number of molecules reacting in an

elementary step.

• Unimolecular reaction – elementary step with 1 molecule

• Bimolecular reaction – elementary step with 2 molecules

• Termolecular reaction – elementary step with 3 molecules

Reaction Mechanisms

Unimolecular reaction A products rate = k [A]

Bimolecular reaction A + B products rate = k [A][B]

Bimolecular reaction A + A products rate = k [A]2

Rate Laws and Elementary Steps

Writing reasonable (plausible) reaction mechanisms:

• The sum of the elementary steps must give the overall balanced

equation for the reaction.

• The rate-determining step should predict the same rate law that is determined experimentally.

The rate-determining step is the slowest step in the sequence of

steps leading to product formation.

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The experimental rate law for the reaction between NO2

and CO to produce NO and CO2 is rate = k[NO2]2 The

reaction is believed to occur via two steps:

Step 1: NO2 + NO2 NO + NO3

Step 2: NO3 + CO NO2+ CO2

What is the equation for the overall reaction?

NO2+ CO NO + CO2

What is the intermediate? NO3

What can you say about the relative rates of steps 1 and 2?

rate = k[NO2]2is the rate law for step 1 so

step 1 must be slower than step 2

Rate Laws and Elementary Steps

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Chemical Reaction Mechanisms

- Most chemical reactions occur through mechanisms that involve at least two steps

- Sequential mechanism, with one step being completed before the next step occurs.

The Collision Theory of Bimolecular Elementary - Processes in Gases

B B

B A

B A Av B

d d d

m m

m m with

n n N T

k d

Z

+

= +

.

8

12 12

2 1

12

2 12

µ

µ π π

Collisions leading to probable reaction:

A 2(g) + B 2(g)2AB

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The steric factor, p, is the fraction of collisions in which the

molecules have a favorable relative orientation for the

reaction to occur

p is sometimes called the probability factor, the orientation,

factor or the fudge factor.

In any group of reactant molecules, only a fraction of

molecules have energies at least equal to E act , the activation

energy of the reaction

This fraction is given by the expression:

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Activation-limited reactions

Activation energies equal

to those for gas-phase reactions

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Change of mechanism with temperature (T in K)

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Liquid-State Reactions

Example: For the reaction 2I → I2 in carbon tetrachloride, the value

of the rate constant at 23°C is 7.0 × 10 6 m 3 mol −1 s −1 At 30°C, the

value is 7.7×10 6 m 3 mol −1 s −1 Find the activation energy and compare

it with the activation energy for the viscosity of carbon tetrachloride

10400J.mol −1

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A catalyst is a substance that increases the rate of a chemical

reaction without itself being consumed.

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In heterogeneous catalysis, the reactants and the catalysts

are in different phases

In homogeneous catalysis, the reactants and the catalysts

are dispersed in a single phase, usually liquid

• Haber synthesis of ammonia

• Ostwald process for the production of nitric acid

• Catalytic converters

• Acid catalysis

• Base catalysis

Catalysis - Catalyst

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Ostwald Process

Hot Pt wire over NH3solution

CO + Unburned Hydrocarbons + O2 convertercatalytic CO2+ H2O

2NO + 2NO2 convertercatalytic 2N2 + 3O2

Enzyme Catalysis

Enzymes (which are large protein molecules) are nature's catalysts Michaelis-Menten mechanism for the catalysis of biological chemical reactions

E is the enzyme, S is the "substrate" and ES is an enzyme-substrate complex

Solve for [ES],

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