Download - Kinetic Colloids Lam1
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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
Exercise 1: Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g)
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rate α [Br2]
rate = k [Br2]
k = rate[Br2]
= rate constant
= 3.50 x 10-3 s-1
Exercise 1: Br2 (aq) + HCOOH (aq) 2Br- (aq) + 2H+ (aq) + CO2 (g)
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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.
C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
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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.
C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
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Reaction Rates
• The reaction slows down
with time because the
concentration of the
reactants decreases.
C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
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Reaction Rates and Stoichiometry
• 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.
C4H9Cl(aq) + H2O(l) → C4H9OH(aq) + HCl(aq)
Rate = -∆[C4H9Cl]∆t
= ∆[C4H9OH]∆t
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Reaction Rates and Stoichiometry
• 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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Reaction Rates and Stoichiometry
• 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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First-Order Reactions
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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First-Order Reactions
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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Reverse Reactions – Chemical Equilibrium
Complicated homogenous reaction
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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Reverse Reactions – Chemical Equilibrium
Complicated homogenous reaction
( )
( )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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Reverse Reactions – Chemical Equilibrium
Complicated homogenous reaction
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
Complicated homogenous reaction
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
Complicated homogenous reaction
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)
Complicated homogenous 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)
Complicated homogenous 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
Complicated homogenous reaction
with
the differential equations giving the rates are
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Successive Reactions and non-negligible reverse reactions
Complicated homogenous reaction
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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Chemical Reaction MechanismsThe Collision Theory of Bimolecular Elementary - Processes in Gases
Collisions leading to probable reaction:
A2(g) + B2(g) ���� 2AB
68
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Chemical Reaction MechanismsThe Collision Theory of Bimolecular Elementary - Processes in Gases
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 MechanismsThe Collision Theory of Bimolecular Elementary - Processes in Gases
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Chemical Reaction MechanismsThe Collision Theory of Bimolecular Elementary - Processes in Gases
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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=16.2Ųfor 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=16.2Ų 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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
4. Sedimentation:
( ) g
vr
o .2
..9
ρσ
η
−=
Figurowsly’s balance
(a) Poly-dispersion (b) Mono-dispersion
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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
5. Viscosity:
Specific viscosity ηsp (viscosity ratio increment):
φ is dependent on concentration
For dilute solutions: For concentrated solutions:
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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Kinetics properties
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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Properties of Disperse Systems (Colloids)Optical properties
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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Properties of Disperse Systems (Colloids)Optical properties
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
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Properties of Disperse Systems (Colloids)Optical properties
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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Properties of Disperse Systems (Colloids)Optical properties
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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Properties of Disperse Systems (Colloids)Optical properties
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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Properties of Disperse Systems (Colloids)Electrical properties
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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Properties of Disperse Systems (Colloids)Electrical properties
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Properties of Disperse Systems (Colloids)Electrical properties
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Properties of Disperse Systems (Colloids)Electrical properties
-
-
-
--
--
-
-
+
+
+
+
++
++++
+
+
+
+
++
-
- - ---
---
--- -
-- -AgI
+
+
+
+
++
+
+
+
+
-
Colloidal nucleus
Tightly bound layer
Diffuse Region with excess"counterions“ (cations)
Aqueous Dispersion Medium(Electrically Neutral)
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Properties of Disperse Systems (Colloids)Electrical properties
-
-
-
--
--
-
-
+
+
+
+
++
++++
+
+
+
+
++
-
- - ---
---
--- -
-- -AgI
+
+
+
+
++
+
+
+
+
-
Colloidal nucleus
Tightly bound layer
Diffuse Region with excess"counterions“ (cations)
Aqueous Dispersion Medium(Electrically Neutral)
-
-
-
--
--
-
-
+
+
+
+
++
++++
+
+
+
+
++
-
- - ---
---
--- -
-- -AgI
+
+
+
+
++
+
+
+
+
-
-
-
-
--
--
-
-
+
+
+
+
++
++++
+
+
+
+
++
-
- - ---
---
--- -
-- -AgI
-
- - ---
---
--- -
-- --
- - ---
---
--- -
-- -AgI
+
+
+
+
++
+
+
+
+
-
Colloidal nucleus
Tightly bound layer
Diffuse Region with excess"counterions“ (cations)
Aqueous Dispersion Medium(Electrically Neutral)
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Properties of Disperse Systems (Colloids)Electrical properties
� 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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Properties of Disperse Systems (Colloids)Electrokinetic phenomena
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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Properties of Disperse Systems (Colloids)Electrokinetic phenomena
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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Properties of Disperse Systems (Colloids)Electrokinetic phenomena
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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Stability of lyophobic systems
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
CCC decreases with higher valence counterionsbecause they are strongly adsorbed into the Stern
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Stability of lyophobic systems
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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Stability of lyophilic colloids
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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Stability of lyophilic colloids
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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Sensitization and protective colloid action
2. Protective Colloid action
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Sensitization and protective colloid action
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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Soap and Surfactants
Cationic Surfactants
Cetyl trimethyl ammonium bromide
Lauryl dimethyl benzyl ammoniumchloride
Distearyl dimethyl ammonium chloride
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Soap and Surfactants
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.