Kinetic Colloids Lam1

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Dinh Lam – DUT - UD

1

ĐỘNG HÓA HỌC VÀHÓA LÝ HỆ PHÂN TÁN

- 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

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Phần 1: Động hóa học

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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

một quá trình.

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Một số khái niệm cơ bản-Tốc độ phản ứng (Reaction rates)

- Định luật tác dụng khối lượng (Rate Law).

- Bậc phản ứng (Reaction Order).

- Phản ứng nguyên tố (Elementary step).

- Phân tử số (Molecularity).

- 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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Part 1: Chemical Kinetics

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Kinetics

• Studies the rate at which a chemical process

occurs.

• Besides information about the speed at

which reactions occur, kinetics also sheds

light on the reaction mechanism (exactly

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?

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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.

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Chemical Kinetics(Simple Homogenous reaction)

Reaction rate is the change in the concentration of a reactant or a product with time (M/s).

A B

rate = -∆[A]∆t

rate = ∆[B]∆t

∆[A] = change in concentration of A overtime period ∆t

∆[B] = change in concentration of B overtime period ∆t

Because [A] decreases with time, ∆[A] is negative.

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A B

rate = -∆[A]∆t

rate = ∆[B]∆t

time

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

time

393 nmlight

Detector

∆[Br2] α ∆Absorption

393

nm

Br2 (aq)

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average rate = -∆[Br2]∆t

= -[Br2]final – [Br2]initial

tfinal - tinitial

slope oftangent

slope oftangent slope of

tangent

instantaneous rate = rate for specific instance in time


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rate α [Br2]

rate = k [Br2]

k = rate[Br2]

= rate constant

= 3.50 x 10-3 s-1


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

PV = nRT

P = RT = [O2]RTnV

[O2] = PRT

1

rate = ∆[O2]∆t RT

1 ∆P∆t

=

measure ∆P over time

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

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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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Reaction Rates and Stoichiometry

Factors That Affect Reaction Rates

• Concentration of Reactants

– As the concentration of reactants increases, so does the probability that reactant molecules will collide.

• Temperature

– At higher temperatures, reactant molecules have more kinetic energy, move faster, and collide more often and with greater energy.

• Catalysts

– Speed reaction by changing mechanism.

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Reaction Rates

The average rate of the

reaction over each

interval is the change in

concentration divided

by the change in time:

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

Average Rate, M/s

[ ]

[ ]s

M

t

ClHCrateaverage

t

ClHCrateaverage

0.00.50

0905.01000.094

94

−

−=

∆

∆−=

∆

∆−=

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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

molecules.


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Reaction Rates

• A plot of concentration vs.

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

that time.


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Reaction Rates

• The reaction slows down

with time because the

concentration of the

reactants decreases.


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• In this reaction, the ratio

of C4H9Cl to C4H9OH is

1:1.

• Thus, the rate of

disappearance of C4H9Cl

is the same as the rate of

appearance of C4H9OH.


Rate = -∆[C4H9Cl]∆t

= ∆[C4H9OH]∆t

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• What if the ratio is not 1:1?

H2(g) + I2(g) → 2 HI(g)

• 2 mol of HI are made for each mol of H2 used.

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• To generalize, for the reaction

aA + bB cC + dD

Reactants (decrease) Products (increase)

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Write the rate expression for the following reaction:

CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (g)

rate = -∆[CH4]

∆t= -

∆[O2]∆t

12

=∆[H2O]

∆t

12

=∆[CO2]

∆t

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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

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F2 (g) + 2ClO2 (g) 2FClO2 (g)

rate = k [F2]x[ClO2]y

Double [F2] with [ClO2] constant

Rate doubles

x = 1

Quadruple [ClO2] with [F2] constant

Rate quadruples

y = 1

rate = k [F2][ClO2]

Example:

This equation is called the rate law, and k is the rate constant.

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Rate Laws

• A rate law shows the relationship between the reaction rate and the concentrations of reactants.– For gas-phase, reactants use PA instead 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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F2 (g) + 2ClO2 (g) 2FClO2 (g)

rate = k [F2][ClO2]

Rate Laws

• 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:S2O8

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

Experiment [S2O82-] [I-]

Initial Rate (M/s)

1 0.08 0.034 2.2 x 10-4

2 0.08 0.017 1.1 x 10-4

3 0.16 0.017 2.2 x 10-4

rate = k [S2O82-]x[I-]y

Double [I-], rate doubles (experiment 1 & 2)

y = 1

Double [S2O82-], rate doubles (experiment 2 & 3)

x = 1

k = rate

[S2O82-][I-]

=2.2 x 10-4 M/s

(0.08 M)(0.034 M)= 0.08/M•s

rate = k [S2O82-][I-]

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Experiment [S2O82-] [I-]

Initial Rate (M/s)

1 0.08 0.034 2.2 x 10-4

2 0.08 0.017 1.1 x 10-4

3 0.16 0.017 2.2 x 10-4

rate = k [S2O82-]x[I-]y

y = 1

x = 1

rate = k [S2O82-][I-]

• Exponents tell the order of the reaction with respect to each reactant.

• This reaction is

First-order in [S2O82-]

First-order in [I-]

• 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:S2O8

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

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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]0 is 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…

…which is in the form y = mx + b

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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.

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Exercise 4: The reaction 2A B is first order in A with a rate constant of 2.8 x 10-2 s-1 at 800C. How long will it take for A to decrease from 0.88 M to 0.14 M ?

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

kt = ln[A]0 – ln[A]

t =ln[A]0 – ln[A]

k= 66 s

[A]0 = 0.88 M

[A] = 0.14 M

ln[A]0[A]

k=

ln0.88 M

0.14 M

2.8 x 10-2 s-1=

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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.

t½ = t when [A] = [A]0/2

ln[A]0[A]0/2

k=t½

ln2k

=0.693

k=

What is the half-life of N2O5 if it decomposes with a rate constant of 5.7 x 10-4 s-1?

t½ln2k

=0.693

5.7 x 10-4 s-1= = 1200 s = 20 minutes

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Second-Order Reactions

A product rate = -d[A]dt

rate = k [A]2

k = rate[A]2

= 1/M•sM/sM2=

d[A]dt

= k [A]2-

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

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

1[A]

=1

[A]0+ kt

t½ = t when [A] = [A]0/2

t½ = 1k[A]0

also in the form

y = mx + b

The half-life, t½

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Zero-Order Reactions

A product rate = k [A]0 = k

k = rate[A]0

= M/s

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

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

t½ = t when [A] = [A]0/2

t½ = [A]02k

[A] = [A]0 - kt

rate = -d[A]dt

d[A]dt

= k-

The half-life, t½also in the form

y = mx + b

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Summary of the Kinetics of Zero-Order, First-Orderand Second-Order Reactions

Order Rate LawConcentration-Time

Equation Half-Life

0

1

2

rate = k

rate = k [A]

rate = k [A]2

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

1[A]

=1

[A]0+ kt

[A] = [A]0 - kt

t½ln2k

=

t½ = [A]02k

t½ = 1k[A]0

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Nth Order Reactions

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Forward Reactions with More Than One ReactantSecond-Order Reactions

A + B product

H2 + I2 2HI

2NO2 2NO + O2

CH3COOC2H5 + NaOH CH3COONa + C2H5OH

t=0 a bt a-x b-x

( )( )( )( )

( )

−

−

−=

=−−

⇒−−== ∫∫

a

b

xb

xa

batk

dtkxbxa

dxxbxak

dt

dxrate

.ln.

1

..

..

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Reverse Reactions – Chemical Equilibrium

Complicated homogenous reaction

The observable rate of the reaction is a net rate

At equilibrium,

K: equilibrium constant

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t=0 a 0t a-x xAt Equilibrium t∞ a-x∞ x∞

[ ] [ ] ( )

( )( )

( ) ( )

( )

( )( )

rff

f

rf

rf

rf

rf

f

rf

rfrf

kkxak

ak

tkk

xA

A

tkk

AconsttAtconsttkkxA

kk

akAwithxAkk

dt

dx

xkxakBkAkdt

dxrate

+−=+

−=+

−==++=−−

+=−+=

−−=−==

ln.1

ln.1

ln,0.ln

..

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( )

( )xx

x

tkk

Akk

akxorxkxak

k

kK

rf

rf

f

rf

r

f

−=+

=+

==−

=

∞

∞

∞∞∞

ln.1

...

If we know K, then we can calculate kf and kr

Signification of A

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

CH2OH-(CH2)2-COOHCH2-(CH2)2-CO

O+ H2O

Time (min) 21 50 100 120 160 220 ∞∞∞∞

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, kf and kr .

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Parallel (Competing) Reactions


Simplest case: that two competing reactions are first order with negligible reverse reaction.

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

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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 k1 = 0.100 s−1 and k2 = 0.500 s−1 Case of k1 = 0.50 s−1 and that k2 = 0.10 s−1.

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Successive Reactions and non-negligible reverse reactions


with

the differential equations giving the rates are

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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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Determination of Reaction Order� Using Integrated Rate Laws

� Using the Half-Life

Order Rate Law Concentration-Time Equation

Half-Life

0

1

2

rate = k

rate = k [A]

rate = k [A]2

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

1[A]

=1

[A]0+ kt

[A] = [A]0 - kt

t½ln2k

=

t½ = [A]02k

t½ = 1k[A]0

n rate = k [A]n

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Determination of Reaction Order

�Method of Initial Rates

See the anterior exercises and examples

� Method of Isolation

For calculating the reaction order of each reactant

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Temperature Dependence of the Rate Constant

The Arrhenius Relation (1889)(The Simplest and Empirical Equation)

Reaction rates depend strongly on temperature ( )310 ≈= + γγT

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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Temperature Dependence of the Rate ConstantThe 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 Ea = NAvεa is the molar activation energy

R = kB.NAv 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.

lnk = -Ea

R

1T

+ lnA

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Exothermic Reaction Endothermic Reaction

The activation energy (Ea) is the minimum amount of energy required to initiate a chemical reaction.

Temperature Dependence of the Rate ConstantActivation Energy

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lnk = -Ea

R

1T

+ lnA

Temperature Dependence of the Rate Constant

Activation Energy Determination(Arrhenius plot)

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Temperature Dependence of the Rate ConstantExercise 6:

Exercise 7:

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Temperature Dependence of the Rate ConstantExercise 5:

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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 stepsor 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: N2O2 + O2 2NO2

Overall reaction: 2NO + O2 2NO2

+

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Elementary step: NO + NO N2O2

Elementary step: N2O2 + O2 2NO2

Overall reaction: 2NO + O2 2NO2

+

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

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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 NO2and 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]2 is 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.

Example:

In an elementary process, the order of any substance is equal to the molecularity of that substance.

Unimolecular Bimolecular Termolecular

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Chemical Reaction MechanismsThe Collision Theory of Bimolecular Elementary - Processes in Gases

( )BA

BB

BA

BAAvB

dddmm

mmwith

nnNTk

dZ

+=+

=

=

2

1;

.

...

..8.

1212

21

12

2

12

µ

µππ

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Collisions leading to probable reaction:

A2(g) + B2(g) �� 2AB

68

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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 Eact, the activation energy of the reaction.

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Chemical Reaction MechanismsLiquid-State Reactions

The temperature dependence of rate constants for both gaseous and liquid-state reactions is usually well described by the Arrhenius formula

Activation-limited reactions

Activation energies equal to those for gas-phase reactions

Diffusion-limited reactions

Rate constant governed by the diffusion coefficients

Diffusion coefficients in liquids given by Eq. which is also of the same form as the Arrhenius formula:

The activation energies of the diffusion-limited reactions (~10kJ.mol-1) are smaller than for activation-limited reactions

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Chemical Reaction MechanismsChange of mechanism with temperature (T in K)

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Chemical Reaction MechanismsLiquid-State Reactions

Example: For the reaction 2I → I2 in carbon tetrachloride, the value of the rate constant at 23°C is 7.0 × 106 m3mol−1s−1. At 30°C, the value is 7.7×106 m3mol−1s−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.

k = A • exp( -Ea/RT ) Ea k

uncatalyzed catalyzed

ratecatalyzed > rateuncatalyzed

Ea < Ea‘

Catalysis - Catalyst

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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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N2 (g) + 3H2 (g) 2NH3 (g)Fe/Al2O3/K2O

catalyst

Haber Process

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Ostwald Process

Hot Pt wire over NH3 solutionPt-Rh catalysts used

in Ostwald process

4NH3 (g) + 5O2 (g) 4NO (g) + 6H2O (g)Pt catalyst

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

2NO2 (g) + H2O (l) HNO2 (aq) + HNO3 (aq)

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Catalytic Converters

CO + Unburned Hydrocarbons + O2 CO2 + H2Ocatalytic

converter

2NO + 2NO2 2N2 + 3O2catalytic

converter

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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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Enzyme Catalysis

KM: the Michaelis-Menten constant

[E]o: the total enzyme concentration

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Enzyme Catalysis

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uncatalyzedenzyme

catalyzed

Enzyme Catalysis

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Part 2: Disperse Systems - Colloids

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Definition

A system in which one substance (particulate matter),

the disperse phase, is dispersed as particles

throughout another, the dispersion medium or the

continuous phase.

Disperse Systems - Colloids

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Disperse Systems - Colloids

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Class Size Examples Properties

Molecular dispersion

< 1.0 nmOxygen gas,

ordinary ions, glucose

- Invisible in electron microscope

-Pass through ultra filter and semi-

permeable membrane

- Rapid diffusion

Colloidal dispersion

1.0 nm to 0.5 µµµµm

Silver sols, natural and synthetic

polymer lattices

- Detected by electron microscope but

not by ordinary

- Pass through ultra filter but not semi-

permeable membrane

-- Very slow diffusion

Coarse dispersion

> 0.5 µµµµm

Sand, pharmaceutical

emulsions & dispersions, red

blood cells

- Visible under ordinary microscope

- Do not pass through ultra filter and

semi-permeable membrane

-- Very slow diffusion

Types of Disperse Systems - On the basis of particle size

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Types of Disperse SystemsOn the basis of physical states

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Types of Disperse SystemsOn the basis of the interaction of the dispersed

particles with the dispersion medium.

surfactant micelles and phospholipidvesicles, also known as association colloids.

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Preparation of Disperse Systems (Colloids)

Lyophilic colloids

Spontaneous, e.g.: gelatin soaked in water

Lyophobic colloids

A- Dispersion methods: breakdown of coarse particle

- Colloid mill

- Electric dispersion

- Ultrasonic irradiation

- Peptisation: addition of preferentially adsorbed ions.

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Preparation of Disperse Systems (Colloids)

Lyophobic colloids

B- Condensation method: aggregation off subcolloidalparticles

1- Chemical reaction

- Reduction: e.g.: colloidal Ag- Oxidation: e.g.: H2S � S- Hydrolysis: e.g.: Fe(OH)3

- Double decomposition: colloidal AgI

2- Change of solvent:

- Precipitation of colloidal S from alcoholic solution by addition of water

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Purification of Disperse Systems (Colloids)

1. Dialysis

Applications:

- Membrane filters

- Membrane diffusion

- Study of drug/protein binding

- Heamodyalysis

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Purification of Disperse Systems (Colloids)

2. Electrodialysis:

Application of an electric potential across the semi-permeable membrane

3. Electrodecantation:

Concentration of charged colloidal particles at one side and at the base of the membrane

4. Ultrafiltration:

Application of a pressure or suction across a filter

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Structure of a Colloids Micelle

The x value depends on the concentration

At dilute concentration, the x value is large, the colloid particles having the same charges; the stability of the system is good.

At higher concentration, the x value decreases, the charge of colloid micelles decreases and the system is less stable.

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• Solid surfaces show strong affinity towardsgas molecules that it comes in contact withand some of them are trapped on the surface

• Process of trapping or binding ofmolecules to the surface is called adsorption

• Desorption is removal of these gasmolecules from the surface

Two types of adsorption

– Physical adsorption :* Van der Waals forces * bond energy is less than 50 kJ/mole

– Chemical adsorption :* bond energy is more than 50 kJ /mole* direct chemical bond

Definition of adsorption

Solid

Gas

Nature of Adsorption

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Physical adsorption - PhysisorptionGeneral

- Physisorption is not adsorbent or adsorptive specific. This is a process similar to condensation of gas on a surface

- Quantity of physisorbed molecules depends on the accessible surface area and not on its chemical nature

- Physisorbed molecules progressively form successive layers when the gas pressure P increases. When P reaches the vapor pressure P0, there is condensation on the surface.

- Capillary condensation in the pores for P < P0 depending on the pore size.

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For molecules in contact with a solid surface at a fixed temperature, the Langmuir Isotherm, developed by Irving Langmuir in 1916, describes the partitioning between gas phase and adsorbed species as a function of applied pressure.

The adsorption process between gas phase molecules, A, vacant surface sites, S, and occupied surface sites, SA, can be represented by the equation,

assuming that there are a fixed number of surface sites present on the surface.

An equilibrium constant, K, can be written:

Theoretical approach

Langmuir theory (monolayer adsorption)a. Thermodynamic Derivation

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Langmuir theory based on three assumptions:

1. Adsorption cannot proceed beyond monolayer coverage.

2. All surface sites are equivalent and can accommodate, at most,

one adsorbed molecule.

3. The ability of a molecule to adsorb at a given site is independent

of the occupation of neighboring sites.

Langmuir theory (monolayer adsorption)Thermodynamic Derivation

θ = Fraction of surface sites occupied (0 < θ < 1)

θ = V/Vm

Where: V = adsorbed volume of gas ;

Vm = adsorbed volume at saturation (θ = 1)

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Thus it is possible to define the equilibrium constant, b:

Rearranging gives the expression for surface coverage:

Langmuir theory (monolayer adsorption)Thermodynamic Derivation

[SA] is proportional to the surface coverage of adsorbed molecules, or proportional to θ

[S] is proportional to the number of vacant sites, (1 - θ)

[A] is proportional to the pressure of gas, P

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The rate of adsorption will be proportional to the pressure of the gas and the number of vacant sites for adsorption. If the total number of sites on the surface is N, then the rate of change of the surface coverage due to adsorption is:

The rate of change of the coverage due to the adsorbed species leaving the surface (desorption) is proportional to the number of adsorbed species:

In these equations, ka and kd are the rate constants for adsorption and desorptionrespectively, and p is the pressure of the adsorbed gas.

Langmuir theory (monolayer adsorption)Kinetic Derivation

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At equilibrium, the coverage is independent of time and thus the adorption and desorption rates are equal.

The solution to this condition gives us a relation for θ:

ka P (1 – θ) = kd θThis leads to :

where b = ka/kd

Langmuir theory (monolayer adsorption)Kinetic Derivation

= -

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b = ka/kd is an equilibrium constant of adsorption

Value of b at various temperatures determined from the Langmuirisotherm allows for the evaluation of the enthalpy of adsorption, ∆Hads, through the van't Hoff equation:

b

Langmuir theory (monolayer adsorption)Heat of adsorption

where b = ka/kd

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where b3 > b2 > b1

Isotherm is an equation which relates the amt of substance attached to the surface (or surface coverage θ) to its concentration in the gas phase (or gas pressure P) at a fixed temperature.

For small P values : θθθθ ≈≈≈≈ bP

For high P values : θθθθ ≈≈≈≈ 1

Langmuir theory (monolayer adsorption)Graphical form of the Langmuir Isotherm

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can be linearized as

1/bVM

)(VfV

P=)(PfV =

V=V mbP

Graphical determination of b and Vm

mV

P

bPV

P+=

1

bP

bP

V

V

m +==

1θ

Langmuir theory (monolayer adsorption)Linearization of Langmuir isotherm

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First theory : Langmuir for monolayer adsorption

Second theory : BET for multilayer adsorption

The specific surface area SL of the adsorbent evaluated from Langmuir theory can be calculated from Vm by :

Where :

σ: the area of the surface occupied by a single physisorbed gas molecule (σ=16.2Å²for N2)

NA : Avogadro constant = 6.02 1023 mol-1

m: Mass of the adsorbent solid sample

V0 : Molar volume of the gas (22414 cm3)

0mV

NVS Am

L

σ=

Langmuir theory (monolayer adsorption)Specific surface area - Determination by using Langmuir theory

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When the pressure system is increased, the adsorbed

species adsorb in multilayer on the surface.

BET theory (multilayer adsorption)Derivation of the BET Isotherm

BET : Brunauer, Emmet, Teller

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Brunauer, Emmet, Teller (BET) theory :

Generalization of the Langmuir theory to multilayer adsorption, with the following hypotheses :

• The evaporation (desorption) rate of adsorbed molecules in a layer is equal to the condensation (adsorption) rate on the layer under it.

• The adsorption heat in the layers (except the first one) is equal to the liquefaction heat of the gas.

• At saturation the number of layers is considered as infinite.

BET theory (multilayer adsorption)Assumptions

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Graphical form of the BET isotherm V = f(P)

−+−

=

0

0

0

)1(1)1(P

PcP

P

PcV

V

m

BET theory (multilayer adsorption)Isotherm adsorption Equation of BET and Graphical form

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x = P/P0

BET theory (multilayer adsorption)Isotherm adsorption Equation of BET and Graphical form

−+−

=

0

0

0

)1(1)1(P

PcP

P

PcV

V

m

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Intercept = 1/cVmSlope = (c-1)/cVm

InterceptSlopeVM

+=

1

Slope

InterceptSlopec

+=

linearized as

00

)1(1

)( P

P

cV

c

cVPPV

P

mm

−+=

−

BET theory (multilayer adsorption)Linearization of BET isotherm

−+−

=

0

0

0

)1(1)1(P

PcP

P

PcV

V

m

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From Vm value obtained using BET linearized isotherm, the specific surface area called SBET is calculated using the same formula as in Langmuir theory :

Where :σ: Area of the surface occupied by a single physisorbed gas molecule (σ=16.2Å² for N2)NA Avogadro constant = 6.02 1023 mol-1

m the mass of the adsorbent solid sampleV0 the molar volume of the gas (22414 cm3)

0mV

NVS Am

BET

σ=

Ex : 2 linearised isotherms

BET theory is valuable in the range

0.05 < P/P0 < 0.35

At low P : heterogeneous surfaceAt high P : capillary condensation

BET theory (multilayer adsorption)Specific surface area determination

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Depending on the hypotheses made (mono or multilayer adsorption,interactions between the adsorbed molecules or not, several theories have been developed.

Langmuir and the BET theories are the mostly used.

Other theories proposed

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Typical Adsorbed Species

Adsorbed speciesAdsorption

Temperature, K

Area of surface occupied

σσσσ (n.m2)

N2 77 0,162

O2 90 0,141

Ar77 0,138

90 0,144

Kr

77 0,202

90 0,15

195 0,217

CO 90 0,168

CO2 195 0,207

C6H6 273 0,430

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Six types of adsorption isotherms following IUPAC classification :Type I : non porous or micro-porous samples (∅ < 2 nm)Types II and III : macroporous samples (∅ > 50 nm) Types IV and V : mesoporous samples (2 nm < ∅ < 50 nm) Type VI : step isotherm (rare)

Types III and V correspond to a low enthalpy of adsorption

IUPAC: The International Union of Pure and Applied Chemistry

Types of the adsorption - desorption isotherms

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Apparatus used for adsorption

Scheme

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Once clean, the sample is brought to a constant temperature by means of an external bath. Then adsorptive pressure is slowly increased and adsorption takes place.

Apparatus used for adsorption

Picture

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Properties of Disperse Systems (Colloids)I. Kinetics properties

Motion of the particles with respect to the dispersion medium

• Thermal motion

- Brownian movement

- Diffusion

- Osmosis

• Gravity or centrifugal field

- Sedimentation

• Viscous flow

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Properties of Disperse Systems (Colloids)Kinetics properties

1. Brownian movement (1827)

Bombardment of the particles by the molecules of the dispersion medium

n

n

22

2

2

1 ∆++∆+∆=∆

K

r

tTk

r

t

N

TRx

...3

..

...6

2.

.

µπηπ==∆

Einstein and Smoluchowski Equation (1906)

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Consequences of Brownian movement

– Stable system: the force of gravity is counteracted by Brownian movement

– Diffusion: the colloidal sols will from a region of high concentration to a region of low concentration

– Colligative properties: colloidal sols show colligative properties

r

tTk

r

t

N

TRx

...3

..

...6

2.

.

µπηπ==∆

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2. Diffusion

Diffusion of particles according to a concentration gradient

First Fick’s Law (1855)

dtSdx

dCDdm ..−=

dx

dCD

Sdt

dmik −==

Stdx

dCDm −=

1,1,1 === tSdx

dC

12

2

3

...

...

.

−==−= smmolsm

mmmol

dC

dx

tS

mD

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The radius ( r ) of the colloidal particle is obtained from the Diffusion coefficient (D)

r

kTD

..6 ηπ=

The molecular weight (M) of colloidal particle is obtained from

NrM ..3

4 3πρ=

D: diffusion coefficient (m2.s-1)

η: viscosity of the dispersion medium (kg.s-1.m-1)

N: Avogadro’s number

r: radius (m)

M: molecular weight

ρ: specific gravity of dispersed phase (kg.m3)

10 P = 1 kg·m−1·s−1= 1 Pa·s 1 cP = 0.001 Pa·s = 1 mPa·s

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2. Diffusion

Second Fick’s Law - Instable Diffusion

++=

2

2

2

2

2

2

dz

Cd

dy

Cd

dx

CdD

dt

dC

CDdt

dC.. 2∇=

++=∇

2

2

2

2

2

22

dz

d

dy

d

dx

d

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3. Osmosis: Flow of solvent across a semipermeable membrane to equalize concentrations

Van’t Hoff equation:

TRC ..=π

TkorTRN

B

A

... γπγ

π ==

Dilute Colloids: AN

Cγ

=

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4. Sedimentation:

Stokes’ law for a spherical particle

Where :x: distance to be travelled (m)dx/dt: rate of sedimentation (m.s-1)r: radius of the particle (m)σ: density of the particle (kg.m-3)ρ: density of the medium (kg.m-3)η: viscosity of the medium (kg.m-1.s-1)g: acceleration due to gravity (m.s-2)

( ) g

vr

o .2

..9

ρσ

η

−=

t

Hv =

Mono-dispersion

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4. Sedimentation:

( ) g

vr

o .2

..9

ρσ

η

−=

Figurowsly’s balance

(a) Poly-dispersion (b) Mono-dispersion

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4. Sedimentation:

For particles less than 0.5 µm, centrifugal force is required

Where :

w : angular velocity (s-1)

x : distance of the particle from the center of rotation (m)

η: viscosity of the medium (kg.m-1.s-1)

Where :

s : sedimentation coeffecient (s)

Molecular weight M is given by

υ: specific volume

( )η

ρσ

9

2 2

orswith

−=

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5. Viscosity:

The Einstein equation for dilute colloidal dispersions:

Whereηο = viscosity of the dispersion mediumη = viscosity of the disperse systemϕ = the volume fraction of colloidal particle (volume of the particles relative to the volume of the dispersion)

Relative viscosity ηrel (viscosity ratio):

)

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5. Viscosity:

Specific viscosity ηsp (viscosity ratio increment):

φ is dependent on concentration

For dilute solutions: For concentrated solutions:

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5. Viscosity:

Reduced viscosity

Linear relationship between ηsp/c and c

Intrinsic viscosity [ η ] :

For a polymer solution

K and a are constants characteristic of the particular polymer solution

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5. Viscosity:

Effect of shape of the particles on the viscosityof the colloidal dispersions.

� Spherocolloids dispersions are of relatively low viscosity.

� Linear particles systems are more viscous due to solvation.

1. Prolate (a>b)2. oblate (a<b)3. Rod4. Plate, 5. Coil

Morphology (shape, inner structure)

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Properties of Disperse Systems (Colloids)Optical properties

1. The Faraday-Tyndall Effect:

Light may be absorbed, scattered, polarized or reflected by the dispersed phase of a colloid

Light scattering and cone formation with turbid appearance of the

colloid

Tyndall Effect

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1. The Faraday-Tyndall Effect:The Tyndall effect is an effect of light scattering by colloidal particles or

particles in suspension.

A 5 mW green laser pointer is visible at night due to Rayleighscattering and airborne dust.

Colorado sky

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1. The Faraday-Tyndall Effect:

The Tyndall effect is an effect of light scattering by colloidalparticles or particles in suspension.

- Intensity of the scattered light depends on the fourth power of the frequency (or wave length), so blue light is scattered more strongly than red light.

o

o

o

pt Iv

nn

nnI

4

22

22

1

22

13 .

2.24

λ

γπ

+

−=

Ipt : Intensity of light scattered

n1, no : Refractive Index of the particle and the dispersion medium

γ : Concentration of particles

v : Volume of the particle.

λ : Wave length

Io : Intensity of incident light

Rayleigh scattering Equation

Dependence of Ipt on refractive index, on the particle concentration, on the γv

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2. Absorption of light - Lambert-Beer Law (1760)

( )[ ]{ }particletheofradiusrwhere

lCrfII o

:

..exp. +−= ε

Disperse Systems (Colloids): Scattering the short wave length radiation (light) - “Pseudo-absorption”

Diagram of Beer–Lambert absorption of a beam of light

as it travels through a cuvette of width l.

Transmission (or transmissibility) TAbsorption coefficient of the substance (α)Distance the light travels through the material (l)

tyabsorptiviMolarC :. εεα =

lCl

I

IT

εα −− === 10100

1

Empirical relationship that relates the absorption of light to the properties of the material through which the light is travelling.

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3. Other optical methods for studying the Disperse systems

Microscope: 200 nm-150 µµµµm

Ultra microscope 10 nm -1 µµµµm

Electron microscope: 1 nm- 1 µµµµm

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3. Other optical methods for studying the Disperse systems

Optical Opacity

2211 ........ hICvkhICvk oo =

ooopt ICvkIvvkIvkI .......... 2 === γγ

C=γ.v

1

221

h

hvv =

1

221

h

hCC =

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Properties of Disperse Systems (Colloids)Electrical properties

Why particles in liquid are charged?

1. Selective adsorption of a particular ionic species present in solution

2. Ionization of surface groups as COOH. Charge is a function of pH.

E.g.: Addition of dilute solution of KI to an equimolar solution of AgNO3� positively charged colloidal AgI

Iso-eclectric point

A pH at which the protein exist as a zweitterion, which is electrically neutral, although both groups are ionized. At the isoelectric point the solubility of the protein is at a minimum and precipitation is facilitated.

3. Difference in the dielectric constant between the particle and its dispersion medium

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Electric double layer

AgI particle (AgNO3 + NaI) in an aqueous solution of 150 moles of NaI: 150 anions and 150 cations

� 100 anions are adsorbed on the colloidal particle

� 50 anions and 150 cations remain in the solution

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-

-

-

--

--

-

-

+

+

+

+

++

++++

+

+

+

+

++

-

- - ---

---

--- -

-- -AgI

+

+

+

+

++

+

+

+

+

-

Colloidal nucleus

Tightly bound layer

Diffuse Region with excess"counterions“ (cations)

Aqueous Dispersion Medium(Electrically Neutral)

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-

-

-

--

--

-

-

+

+

+

+

++

++++

+

+

+

+

++

-

- - ---

---

--- -

-- -AgI

+

+

+

+

++

+

+

+

+

-

Colloidal nucleus

Tightly bound layer



-

-

-

--

--

-

-

+

+

+

+

++

++++

+

+

+

+

++

-

- - ---

---

--- -

-- -AgI

+

+

+

+

++

+

+

+

+

-

-

-

-

--

--

-

-

+

+

+

+

++

++++

+

+

+

+

++

-

- - ---

---

--- -

-- -AgI

-

- - ---

---

--- -

-- --

- - ---

---

--- -

-- -AgI

+

+

+

+

++

+

+

+

+

-

Colloidal nucleus

Tightly bound layer



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� Stability of the Colloids

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Properties of Disperse Systems (Colloids)Electrokinetic phenomena

1. Electrophoresis:

The movement of a charged particle through a liquid under the

influence of an applied potential difference (electric current)

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2. Electro-osmosis (F.F. Reuss in 1809):The movement of a liquid relative to an immobile charged surface of a

capillary tube under the influence of an electric field.

The motion of polar liquid through a membrane or other porous structure (generally, along charged surfaces of any shape and also through non-macroporous materials which have ionic sites and allow for water uptake, the latter sometimes referred to as "chemical porosity") under the influence of an applied electric field.

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3. Sedimentation potential: (Dorn in 1879):

The creation of a potential when particles undergo sedimentation

under influence of either gravity or centrifugation.

4. Streaming potential: (1859 Quincke)

The potential created by forcing a liquid to flow through a bed of

charged particles

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5. Zeta Potential Zeta potential is an abbreviation for electrokinetic potential in colloidal systems

l

Eu o

.

...

η

ζεε=

E

lu

o ..

..

εε

ηζ =

Henry equation

Ef

lu

o ...

...

εε

ηπζ =

Where:

u: Velocity of the colloid particle

ε, εo: Dielectric constant of the dispersion

milieu and the vacuum (εo=8,85.10-12F/m)

E: Potential difference

η: Viscosity of the dispersion milieu

l: distance between two electrodes

f: Coefficient of the particle size and the

electric double layer thickness: 1/4 - 1/6

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Physical stability of colloidal systems

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Physical stability of colloidal systems

What will be the situation ?This will depend on the type of interaction forces resulting from collision

1. Electric forces of repulsion :

Arise due to the overlap of the diffuse parts of the electric double layer

2. Electric forces of attraction :

Arise due from van der Waals forces of attraction

3. Solvation

Arise from binding of solvent molecules to the colloidal particles solvent sheath

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Stability of lyophobic systems

DLVO theory : Derjaguin, Landan, Verwey, and Overbeek

The involved interactions :

1. Electrical repulsion, VR , (electric double layer) and

2. Van der Waals attraction, VA

The total potential energy, VT is given by :

VT= VR +VA

Thermodynamically unstable

SEbm ×= σ

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1. Effect of electrolytes :

� Small amounts

Stabilize the systemImparts charges to the particles

(Peptization)

� Large amounts

Reduce the zeta potential Salting out

The Critical Coagulation (or Flocculation) Concentration (CCC):

The CCC is the lowest concentration of the electrolyte at which a rapid

flocculation occurs

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1. Effect of electrolytes :

Schulze-Hardy rule

• CCC value is mainly determined by the valence rather than the

type of the ions with opposite charge to the particles.

• Ions with the same charge as the particles are of secondary

importance.

• The higher valence of the ion, the lower CCC.

2. Mutual precipitation (coagulation):

Mixing of oppositely charged lyophobic colloids

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Stability of lyophilic colloids

Stabilization factors :

1. Electric double layer interactions

2. Solvation

Thermodynamically stable systems

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Hofmeister or lyotropic series :

2- Effect of solvents

The colloid becomes susceptible to small amounts of electrolytes

SO42- > CH3COO- > NCS- > I- > NO3

- > Br- > Cl-

Mg2+ > Ca2+ > Ba2+ > K+ > Na+ > Li+

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3- Coacervation :

The separation from a lyophilic sol of a colloid - rich layer upon

addition of another substance

E.g.: Mixing of oppositely charged lyophilic colloid

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Sensitization and protective colloid action

1. Sensitization

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2. Protective Colloid action

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2. Protective Colloid action

The protective property of a lyophilic colloid is expressed in terms of the gold number

The Gold number :

The minimum weight in mg of the protective colloid (dry weight of dispersed phase) required to prevent a color change from red to violet in 10 ml of a gold sol on the addition of 1 ml of a 10% sodium chloride

The lower the gold number, the higher is the protective property

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Soap and Surfactants

Anionic Surfactants

Soap

Alkyl aryl sulphonate

Alkyl ether sulphate

Fatty alcohol sulphate

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Cationic Surfactants

Cetyl trimethyl ammonium bromide

Lauryl dimethyl benzyl ammoniumchloride

Distearyl dimethyl ammonium chloride

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Nonionic Surfactants

Glycol and glycerol esters - Glyceryl monostearate

Polyoxyethylene esters - Polyoxyethylene 8 stearate

Polyoxyethylene ethers -

Polyoxyethylene-polyoxypropylene copolymers

Sorbitan derivatives

Sucrose esters

Esters of sucrose with fatty acids

such as stearic or palmitic acid

END.

Kinetic Colloids Lam1

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