Physical Chemistry 2 CH4003 Dr. Erzeng Xue

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Physical Chemistry 2 CH4003Dr. Erzeng Xue
CH4003 Lecture Notes 1 (Erzeng Xue)
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Course General Information
CH4003 Lecture Notes 1 (Erzeng Xue)

• Lectures Monday 9am Room No. BM015
• Friday 9am Room No. SG16
• Lecture Notes Available at the class and on the
  ULs web
• Tutorial Wednesday 2pm, Room C2062 (to be
  arranged)
• Labs Group 2A Monday 4-6pm, Room No. A3-009,
• Group 2B Thursday 1-3pm, Room No. A3-009
• Weeks 3,4,5,7,8,9,10 (both groups)
• Attendance is MANDATORY
• MUST have white lab coat and safety specs
• Assessment 75 End term Exam
• 25 Lab. Attendance/Reports

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CH4003 Course Syllabus
CH4003 Lecture Notes 1 (Erzeng Xue)
Course General Information

• Rate laws, integrated and differential forms
• Zero, first and second order rate laws
• Mechanism of reaction, steady state approximation
  
• Lindemann hypothesis, role of equilibria
• Arrhenius equation, collision theory, activated
  complex theory
• Ficks law, diffusion
• Photochemistry, fast reactions, polymerisation
• Langmuir adsorption isotherm
• Catalysis,
• Michaelis-Menten kinetics, Monod kinetics
• Applications to selected examples of industrially
  important reactions
• Basis of IR and UV spectroscopy, fluorescence and
  phosphorescence

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Recommended Texts
CH4003 Lecture Notes 1 (Erzeng Xue)
Course General Information

• Prime Texts
• Atkins P.W., 2002, Physical Chemistry, 7th ed.,
  Oxford University Press. Atkins P.W., 1998,
  Physical Chemistry, 6th ed., Oxford University
  Press.
  
  
  
•  
• Other Texts
• Atkins P.W, 2001, The Elements of Physical
  Chemistry, 3rd ed., Oxford University Press.
• Alberty, R.A. and Silbey, R.J., 2000, Physical
  Chemistry, 3rd ed., Wiley.
• Banwell, C.N. and McCash, E.M., 1994
  Fundamentals of Molecular Spectroscopy, 4th ed.
  McGraw Hill.

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Experiments
CH4003 Lecture Notes 1 (Erzeng Xue)
Course General Information

• There are 7 experiments
• 1. Kinetics of hydrolysis of ethyl acetate
  studied by conductance measurements.
•   2. The effect of temperature on reaction rate
  Application of the Arrhenius equation to the
  kinetics of oxidation of iodide by persulphate.
•   3. The catalytic decomposition of hydrogen
  peroxide.
•   4. Viscosity measurements in solution phase
  chemical kinetics.
•   5. Adsorption isotherms.
•   6. The kinetics of a reversible, first-order,
  consecutive reaction the reduction of Cr(VI) by
  glutathione.
•   7. Excited state properties of 2-naphthol
  excited state acidity constant.
•  
• Note A Laboratory Manual will be available
  for purchase in the UL Print Room before
  laboratory sessions commence in Week 3.

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What Does CH4003 Cover?
CH4003 Lecture Notes 1 (Erzeng Xue)
CH4002
System A
System B
Applications
Extent equilibrium of change
driving force and direction of change
Process of change
The rate of change
CH4003
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Methods of Study
CH4003 Lecture Notes 1 (Erzeng Xue)

• Fundamental laws
• The way various energies change
• Mathematics models
• Experiment validation

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Success !
CH4003 Lecture Notes 1 (Erzeng Xue)
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Thermodynamics - Review
CH4003 Lecture Notes 2 (Erzeng Xue)

• Thermodynamics is the science of ENERGY
• Properties of matter in terms of energy (micro-
  or macroscopic)
• The energy exchange in a process (quantity,
  direction and limit)
• Object of study in thermodynamics - SYSTEM
• System - a quantity of matter or a region in
  space chosen
• Closed system - no mass crosses system boundary
  but energy can be exchanged with surroundings.
• Open system - there is mass or energy exchange
  with its surroundings
• System contains MATTER, has a BOUNDARY and is
  always in some STATE

Surroundings
Process of change
state A
state B
Boundary
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Fundamental Laws of Thermodynamics
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• First Law of Thermodynamics - ENERGY CONSERVATION
• One of many expressions
• Energy cannot be created or destroyed. In a
  process energy changes from one form to another
  form and the total amount of energy remains
  constant.
• Second Law of Thermodynamics - DIRECTION of
  change in a process
• One of the several expressions states
• Processes occur in a direction of decreasing
  quality of energy.
• Third Zeroth Laws of Thermodynamics
  -Temperature definition measurement
• Third Law - Entropy definition
• The entropy of a pure crystalline substance at
  absolute zero temperature is zero.
• Zeroth Law - Temperature measurement
• If two bodies are in thermal equilibrium with a
  third body, they are also in thermal equilibrium
  with each other.

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State of System
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• State
• A state represents a snapshot of a system at a
  given time
• All the system properties have fixed values at a
  certain state
• (but you dont have to write down all system
  properties to specify a state, only a few
  independent properties are sufficient, the number
  depending on the system)
• Change of state
• For a change of state, one needs to specify
• the initial state and the final state
• the path of process of change
• if it is a reversible or irreversible process
• Equilibrium
• A special state at which no more change is
  possible

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Properties of System
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• Properties of system - characteristics of system
• Intensive properties - independent of the system
  size
• e.g. Temperature, pressure, density etc. (value
  does not change by the division)
• Extensive properties - dependent on the system
  size
• e.g. mass, volume, internal energy etc. (value
  changes by the division)

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Basic System Properties
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• Temperature, T
• T is the measurement of the hotness of a
  substance/system
• Several scales are in use C, F, K and R (less
  common).
• Pressure, P
• P is the force exerts by a fluid to a system per
  unit area
• absolute pressure and gage pressure
• Several units are commonly used (Pa, bar, mmHg,
  psi, atm.)
• Volume, V
• The volume of a system
• Entropy, S
• S is a measure of molecular disorder, or
  molecular randomness
• S has an energy unit but is NOT a form of energy
  
• important S is not conserved in a process.

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Other System Properties
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• Other properties used to define a system state
  and to describe a process
• enthalpy, h,
• internal energy, u,
• Helmholtz function, a
• Gibbs function, g
• Most important basic property functions
• 1st Gibbs equation du T ds - P dv (derived
  from entropy definition)
• 2nd Gibbs equation dh T ds v dP (derived
  from enthalpy definition)
• Helmholtz function da -s dT - P
  dv (Helmholtz definition)
• Gibbs function dg -s dT v dP (Gibbs
  definition)
• Maxwell relations

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Substance in a System
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• Substance
• Pure substance - has a fixed and uniform chemical
  composition.
• Mixture of pure substances
• properties of a mixture depend on the properties
  of each individual component / constituent and
  the amount of each in the mixture
• Phases of substances
• solid molecules are arranged in 3-D pattern that
  is repeated throughout. The attractive forces
  between molecules are large and keep the
  molecules in fixed positions
• liquid The molecular spacing is in the same
  order as in a solid and molecules remain ordered
  structure but the molecules position is not
  fixed in 3-D structure
• gas Molecules are far apart they move freely
  and collide each other
• The energies contain in the various phase
  following the order gas gt liquid gt solid.
• Property-relation diagrams
• Type of diagrams commonly used to describe
  property-relations of a substance
• T-V, P-V, P-T, P-V-T, T-S and H-S diagrams.

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Thermodynamics of Chemical Reaction Systems
CH4003 Lecture Notes 2 (Erzeng Xue)
Thermodynamics Review

• Energies transferred during a process
• Sensible energy - P, T
• Latent internal energy - energy associated with
  phase change
• Chemical internal energy - energy associated with
  destruction and formation of a chemical bond of
  molecules
• Thermodynamics of chemical reaction systems
• Study the energy transfer process in chemical
  reactions
• Predict the direction of a chemical reaction and
  the energy transfer associated with the reaction
• Predict the final state (equilibrium) of a
  chemical reaction system, and
• Study factors that affect the characteristics of
  the final state (not the process!) of a reaction
  system
• Chemical reactions
• For most gas-phase reactions occurring at elevate
  T. - the gases can be treated as ideal gases
• Many reactions proceed continuously at a constant
  P - can be treated as steady-flow process
• Many reactions are carried out at a constant T
  (very common) - these are isothermal process
• Many batch reactions are carried out at constant
  volume (T and P may vary)
• The reactions take place in a well-insulated
  chamber is usually treated as an adiabatic
  process.

non-chemical energy
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Chemical Reaction - The Process
CH4003 Lecture Notes 3 (Erzeng Xue)

• Consider a chemical reaction A B C D
• meaning molecules A react with molecules B,
  producing molecules C D

Step 3 A reacts with B giving CD
Step 4 C D move apart
Step 1 Add A B
Step 2 A meets B
activation reaction
product molecules travel to apart
reactant molecules travel to meet
Reaction Process
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Diffusion
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process

• The process for a molecule to travel through the
  pool of molecules is called diffusion.
• The reactant A can be molecules in a gas phase or
  a liquid phase or a solid phase so can reactant
  B, the products C and D
• The media (pool of molecules) for either reactant
  molecules or product molecules to diffuse through
  can also either be a gas, a liquid or a solid
• The rate of diffusion (diffusivity) has an order
  of gasgtliquidgtsolid. Most industrial reactions
  take place either in gas phase or in a liquid
  phase, or multi-phases

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Rate of Diffusion vs. Rate of Reaction
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process

• It is important to remember that the practical
  rate of a reaction cannot be larger than the
  rates of diffusion, which means that
• when the theoretical rate of a reaction is lower
  than the rate of diffusion, the maximum rate of
  reaction is then determined by the rate of the
  chemical reaction
• - we say reaction is kinetic control
• when the theoretical rate of a reaction is higher
  than the rate of diffusion, the maximum rate of
  reaction which can be achieved is the rate of
  diffusion
• - we say the reaction rate is diffusion control
  
• both the rate of reaction and the rate of
  diffusion can vary with the reactor design
  reaction conditions applied (e.g. T, P, pH etc.)
  however, the dependence of the reaction rate
  differs from that of diffusion rate on those
  reaction parameters.

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Molecular Diffusion
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process

• Molecules travel randomly in all directions
• Change direction upon collisions
• Net effect is molecule A diffusing from high
  density (concentration) region (1) to low density
  (concentration) region (2)
• Molecular diffusion involved at least 2
  components
• The model is valid for both gas and liquid systems

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Diffusion Equation - Ficks Law
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process

• Ficks Law of diffusion

(2) CA2 CB2
(1)CA1 CB1
x
L
0
t0 CA1 gt CA2 and CB2 gt CB1. A will start to
diffuse from (1) to (2) and B from (2) to
(1). tt For a close system when reaching
equilibrium CA2tt CA1tt and CB1 tt CB2
tt At steady-state, A and B are supplied at a
steady rate to the system A to point (1) B to
point (2) so that the diffusion of A (and B in
rev. direction) is constant
JA - flux of A mol s-1 m-2 CA - concentration
of A mol m-3 CB - concentration of B mol m-3 x
- direction of molecular diffusion m DAB - diffus
ion coefficient (of A in B) m2 s-1
Note - Mass is transferred in the direction of x
from high C to low C, thus minus sign in the
equation - For equimolar counter-diffusion DABDBA
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Application - Ficks Law of Diffusion
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process

• Ficks Law of diffusion (1-D)
• Integrating for steady-state situation using
  boundary conditions of
• CACA1 at x0 and CACA2 at xL
• When the distance L and the concentrations at
  the two points under concern, mass diffusion flux
  can easily be calculated, provided that the value
  of DAB (the diffusion coefficient) can be found
  or predetermined.
• Finding diffusion coefficient
• From literature
• Experimental determination
• Estimation/Prediction of diffusion coefficient
  from known theory

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Diffusion Coefficients of Gases at 1 atm.
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process
System Temp C Diffusivity cm2/s
System Temp C Diffusivity cm2/s

• Air-NH3 0 0.198
• Air-H2O 0 0.220
• 25 0.260
• 42 0.288
• Air-CO2 3 0.142
• 44 0.177
• Air-H2 0 0.611
• Air-C2H5OH 25 0.135
• 42 0.145
• Air-CH3COOH 0 0.106
• Air-n-hexane 21 0.080
• Air-benzene 25 0.0962
• Air-toluene 26 0.086
• Air-n-butanol 0 0.0703
• 26 0.087
• H2-CH4 25 0.726
• H2-N2 25 0.784
• 85 1.052

H2-benzene 38.1 0.404 H2-Ar 22.4 0.83 H2-NH3 25 0.
783 H2-SO2 50 0.61 H2-C2H5OH 67 0.586 He-Ar 25 0.7
29 He-n-butanol 150 0.587 He-air 44 0.765 He-CH4 2
5 0.675 He-N2 25 0.687 He-O2 25 0.729 CO2-N2 25 0.
167 CO2-O2 20 0.153 N2-n-butane 25 0.0960 H2O-CO2
34.3 0.202 CH3Cl-SO2 30 0.0693 (C2H5)
2O-NH3 26.5 0.1078
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Application - Ficks Law
CH4003 Lecture Notes 3 (Erzeng Xue)
Chemical Reaction Process

• For a gas system
• From Kinetic theory
• Chapman-Enskog equation (semi-theoritical)
• For a liquid system
• for solute molar weight gt 1000
• for solute molar weight lt 1000

u - average speed of molecule l - mean free path
length kB - Boltzmann constant P,T - pressure,
temperature m - mass of molecule or sphere d -
molecule diameter
P - pressure T - temperature MA, MB - molar
weight of A and B sAB - average collision
diameter WD,AB - collision integral
m, mB - viscosity of solution and solvent VA -
solute molar volume at its normal boiling
point f - associate parameter, value varies with
solvent used
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Chemical Reaction - The Equation
CH4003 Lecture Notes 4 (Erzeng Xue)

• Reaction equation for A reacting with B forming C
  and D
• A B C D (1) - general
  expression of a reaction
• vAA vBB vCC vDD (2) - quantitative
  representation of a reaction
• vAA vBB D vCC vDD (3) - representing an
  equilibrium controlled reaction
• Reaction stoichiometry
• vA, vB, vC and vD are numbers, called
  stoichiometry coefficients
• The concept of mole (the number of molecules) in
  a chemical reaction
• Determination of stoichiometry coefficients -
  balancing equation (equal number of each atom on
  both sides of the equation)
• e.g. 2NO O2 2NO2 we have 2 N, 4 O on both
  sides
• Q. For the same reaction can we write the
  equation as
• 4 NO 2 O2 4NO2 or
• NO ½O2NO2 ?

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Direction of a Reaction
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction

• Q. A reaction A B C D. Will it proceed in
  the direction indicated?
• Is there a general way to know reaction
  direction?
• A. We can tell from the change of Gibbs free
  energy in a reaction, DG
• The 2nd Law of Thermodyn. - Processes occur in a
  direction of decreasing quality of energy.
• We need to study reaction system in terms of
  energies and their changes
• The energies associated with a reaction system
• Many energy terms, a, U, H, G, - all depend on 4
  basic parameters P, T, V, S
• Usually P, T, V are specified by given reaction
  conditions. S is related to the substances in
  the reaction (reactants/products) and reaction
  conditions (P, T, V)
• Knowing P, T, V and S, all other energy terms can
  be determined. The most important ones in
  relation to chemical reactions are H and G.

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Entropy of Reaction System
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction

• Entropy definition meaning at T, change of S
  is proportional to change of heat
• Entropy calculation
• Basis of S calculation 3rd Law of
  thermodynamics S0 at absolute temperature0
• Assign standard entropy of a substance (1 mole,
  at 1 atm. 25C) as
• (S298 value of common substances are available
  in most chemistry / chem. engg handbooks.)
• The entropy change in a reaction at T, P
• reaction vAA vBB D vCC vDD
• If a reaction is adiabatic, it can only proceed
  when DSgt0 (rxn reaches equilibrium when DS0).
• Usually S analysis of a reaction system is
  complicated and less convenient to use.

This term becomes zero if there is no phase
change during the reaction
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Enthalpy of Reaction System
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction
gas phase (ideal gas) at const. T P g-l, g-s or
g-s,l mixture at const. T P liquid or solid
(dv0)

• Enthalpy definition
• HUPV Þ dHdUPdV VdP
• Enthalpy calculation
• Standard enthalpy of formation, Hf
• Assign Hf of all stable substances (O2, N2, CO2
  H2O etc.) at 298K 1atm as 0 (not at 0K as for
  S) (H298 values of common substances are
  available in most chemistry / chem. engg
  handbooks.)
• Enthalpy of combustion, Hc -Often used for
  combustn process, similar to enthalpy of
  formation
• Enthalpy change when 1 mole of substance
  combusted completely (reacted completely with
  O2).
• The enthalpy change in a reaction at T, P
• reaction vAA vBB D vCC vDD
• DH is a direct measure of the reaction heat
  associated with a reaction (if only chemical
  energy change exists). When DH lt 0 - the
  reaction is exothermic and when DH gt 0 is the
  reaction is endothermic.
• Reaction heat is of critical importance in
  reaction engineering (reactor process design).

The DH of phase transformations including g-l-s
or crystalline phase change
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Gibbs Free Energy of Reaction System (1)
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction

• Gibbs free energy (also called Gibbs function)
  definition
• G U PV -TS H - TS Þ DG DH - TDS
  at constant T,P
• Gibbs free energy calculation
• Standard Gibbs free energy, G298
• Similar to S and H, the standard Gibbs free
  energy of formation of a substance, G, is
  defined at reference state of T298 K and P1 atm
  
• (G298 values of common substances are available
  in most chemistry / chem. engg handbooks.)
• Gibbs free energy change in a reaction at T, P
• reaction vAA vBB D vCC vDD
• or, DGT can be determined directly from

value of each individual substance
value from overall reaction
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Gibbs Free Energy of Reaction System (2)
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction

• DG is one of the most important thermodyn.
  properties for a chemical reaction system.
• It determines the direction of reaction to
  proceed
• DGlt 0 is the pre-condition which MUST be met for
  any process (not limited to chemical reaction
  systems) to occur (spontaneous process).
• DGlt0 indicates a specified reaction has tendency
  to proceed however, it CANNOT tell how fast that
  reaction will occur - reaction kinetics tell the
  rxn rate.
• A process/reaction proceeds always in the
  direction of MINIMISING Gibbs free energy. This
  is a very important concept.
• A process/reaction will stop at DG0, this is
  called equilibrium state.

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Important Notes about DS, DH and DG
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction

• DS, DH and DG are widely used in analysing
  various systems. Our current discussion of these
  function is limited to the application to a
  reaction system.
• A clear definition of the reaction conditions is
  necessary before start calculation of these
  properties.
• There are many ways these thermodynamic
  properties can be determined. Only most commonly
  used ones in relation to a chemical reaction are
  given.
• It is very important to understand the study a
  chemical reaction by means of thermodynamics
  tells only state - a snapshot of system, and
  how a process proceeds from one state to another
  (reversible-irreversible, with or without work
  done / exchange heat with surrounding). There is
  no factor of time involved.

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Home Work
CH4003 Lecture Notes 4 (Erzeng Xue)
Chemical Reaction

• Calculate the DH and DG values at 25 C, 200
  C, 400 C and 600 C and constant pressure of 1
  atm. of reaction
• 2NO(g) O2(g) 2 NO2(g)
• Determine from your results
• a) can the reaction proceed at all given
  temperatures?
• b) is the reaction endothermic or exothermic?

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Chemical Reaction - The Equilibrium (1)
CH4003 Lecture Notes 5 (Erzeng Xue)

• For a chemical reaction vAA vBB D vCC vDD
• when GT 0, we say the reaction is in chemical
  reaction equilibrium
• - What is a chemical reaction equilibrium?
• Example 1 NH3(aq)H2O(l) D NH4(l)OH-(aq)
• At constant T and P, when t
• Example 2 2NO(g) O2(g) D 2NO2(g)
• At constant T and P, when t
• The concentration of a gas is usually measured
  as partial pressure
• At an equilibrium the reaction quotient becomes
  constant

reaction quotient
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Chemical Reaction - The Equilibrium (2)
CH4003 Lecture Notes 5 (Erzeng Xue)

• Chemical reaction equilibrium
• vAA vBB D vCC vDD
• An equilibrium is a state at which no further
  change is possible under that specific set of
  reaction system parameters
• An equilibrium is a dynamic process, meaning that
  the rate of forward reaction is equal to that of
  reverse
• At equilibrium GT 0
• i.e.
• Any change of reaction parameters will redefine a
  system leading to a new equilibrium, which may
  not be the same as that before the change
• Kp indicates only the relation between the
  partial pressures of reactants and products at
  equilibrium, how fast a reaction proceed is
  controlled by reaction kinetics.

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Equilibrium Constant (1)
CH4003 Lecture Notes 5 (Erzeng Xue)
Chemical Reaction equilibrium

• Definition of equilibrium constant, K
• The equilibrium constant is the reaction
  quotient at GT 0.
• Expressions of equilibrium constant for various
  reactions
• gas phase 2NO(g) O2(g) D 2NO2(g)
• gas-solid phase CaCO3(s) D CaO (s)CO2(g)
• liquid phase NH3(aq)H2O(l) D NH4(l)OH-(aq)
• liquid-solid Cu(OH)2(s) D Cu2(aq)2OH- (aq)
• gas-liquid NH3(g)H2O(l) D NH4OH(aq)
• general vAA vBB D vCC vDD

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Equilibrium Constant (2)
CH4003 Lecture Notes 5 (Erzeng Xue)
Chemical Reaction equilibrium

• Equilibrium constant, Kp, and Gibbs free energy
  DG
• A gas phase reaction vAA vBB vCC vDD
• When at equilibrium, assuming all the gases
  follow the ideal gas law
• at P1 atm, DGS(viGi)prod-S(viGi)reac0
  and at any P(¹1) DGS(viGi)prod-S(viGi)reac0
• when reaction occurs at constant temperature
  (isothermal reaction)
• dGVdP-SdT dGVdP dGRTdP/P
  DGRTln(P/P0)
• G is defined at P01 atm, so that
  DGG-GRTln(P/1) GiGiRTlnPi
• S(vi(GiRTln(PCPD))prod-S(vi
  (GiRTln(PAPB))reac0
• S(viGi)prod-S(vi Gi)reac-S(viRTln(PCPD))prod
  -S(vi RTln(PAPB))reac
• By definition

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Equilibrium Constant (3)
CH4003 Lecture Notes 5 (Erzeng Xue)
Chemical Reaction equilibrium

• Equilibrium constant, Kc, and Gibbs free energy
  DG
• Ideal solution (liquid and solid)
• Raoults law PixiPi or xiPi / Pi
  where
• thus for a solution we can also write
  Gi(GiRTln xi) (compare to gas GiGiRTlnPi)
• which lead to, in a similar way, the relation
  between DG and Kc,
• Summary of G calculation for ideal gas and
  solution
• For a pure substance at const T
  P, GGRTlnP (1)
• For a mixture of ideal gas at const T and P G
  SGiS(GiRTln Pi) (2-1)
• For a mixture of ideal solution at const T and
  P G SGiS(GiRTln xi) (2-2)
• For a situation that a mixture (gas or solution)
  under concern is not ideal, the Pi or xi cannot
  be related to G by expressions (2-1) (2-2). How
  do you calculate G?

Pi - vapour pressure of component i xi - mole
fraction of component i in solution Pi - equil.
vapour pressure of pure component i
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Equilibrium Constant (4)
CH4003 Lecture Notes 5 (Erzeng Xue)
Chemical Reaction equilibrium

• Real mixture (Non ideal substances)
• For a real gas Pi,real ¹ Pi,ideal, we define
  the effective pressure, f,
• f is called fugacity
• For a real solution Pi,vap,real ¹ Pi,vap,ideal,
  we define the effective concentration, ai
• a is called activity
• Chemical potential, m
• Using the same relation of G with Pi and xi for
  ideal gas and solution, but G is replaced by a
• new term, m, called chemical potential ,
  representing the non-ideal situation
• ideal gas GiGiRTlnPi real gas mi
  miRTlnPi,real miRTlnfiPi,ideal
• ideal solution GiGiRTlnxi real solution
  mi miRTlnxi,real miRTlnaixi,ideal
• Values of f and a for real gases and solutions
  can be found from literature
• Chemical potential can also be used to describe
  an ideal gas or solution, i.e. Gm
• i.e. for ideal gas mimiRTlnPi and for ideal
  solution mimiRTlnxi

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The Equilibrium (5)
CH4003 Lecture Notes 5 (Erzeng Xue)
Chemical Reaction equilibrium

• A chemical reaction,if in equilibrium (Dm0)
• vAA vBB D vCC vDD
• ideal gas
• real gas
• ideal solution
• real solution
• When solids or liquids are present either as
  reactants or products, their vapour pressures, at
  constant T, are usually constant - thus can be
  included in the Kp without appearing in the
  expression.
• e.g. CaCO3(s) CaO(s) CO2 (g) Kp
  PCaOPCO2/PCaCO3 Þ KpPCO2

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Equilibrium Constant (6)
CH4003 Lecture Notes 5 (Erzeng Xue)
Chemical Reaction equilibrium

• The equilibrium constant, K, is a function of
  temperature
• The effect of inert on the equil. composition -
  depending on the reaction stoichiometry
• Dv vC vD - vA - vB
• When Dvgt0, a high P push the equilibrium to the
  direction of more completion,and visa verse
• The expression of equilibrium constant depends on
  the way reaction equation is written
• For a reverse reaction its equilibrium constant
• vAA vBB D vCC vDD
• vCC vDD D vAA vBB
• For reaction equation written with different
  stoichiometery coefficient
• 2NO(g) O2(g) D 2NO2(g) NO(g) ½ O2(g) D
  NO2(g)

41
Chemical Reaction - The Rate
CH4003 Lecture Notes 6 (Erzeng Xue)

• What is reaction rate?
• The rate of a chemical reaction refers to the
  reactant consumption or the product formation per
  unit time.
• It is a quantitative measure of how fast a
  reaction can proceed.
• some reactions proceed very fast, other reactions
  may proceed very slow
• In thermodynamics where only the starting and
  ending states are characterised
• Why study the reaction rate?
• in industry we need to know how long do we need
  to produce a certain product
• the size and type of a reactor
• we also need to know what is the best reaction
  conditions we should apply
• using proper conditions such as T, P,
  concentration etc. to speed up the desired
  reaction
• to suppress undesired side reactions
• when apply a catalyst how effective it is on the
  desired / undesired reaction
• A study of reaction rate often reveal information
  on the reaction mechanism
• A good understanding of reaction mechanism helps
  us to find a more effective way to carry out a
  reaction and sometimes leads to discovery of new
  means of reaction
• A study of reaction rate is often referred as a
  study of Reaction Kinetics

42
Definition of Reaction Rate
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• For a reaction vAA vBB vCC vDD
• The reactant consumption or the product formation
  per unit time can be written as
• similarly we can write (eqn.1)
• Are these the same rate?
• Depending on the stoichiometry coefficients. The
  equivalent rate is
• e.g. N2 3H2 2NH3
• The appearance of rate expression depends on the
  way reaction equation is written. We use the
  format (eqn.1) if there is no need to specify the
  equivalent rates.

43
Rate Equations (or Rate Laws) (1)
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• For a reaction vAA vBB vCC vDD (1)
• Consider molecules in a reaction system
• The more reactant molecules in the system, the
  more chance for reactant molecules to meet - the
  more effective collision between these molecules,
  which lead to reaction to occur, thus
• rate µ AB (2a)
• Reactant A molecules may differ from B molecules
  in leading to reaction, this may be written as
• rate µ AaBb (2b)
• If a reaction approaches equilibrium conversion,
  the more product molecules in the system, the
  more chance for product molecules to meet -
  causing the reverse reaction, thus
• reverse rate µ CD or rate µ 1/CD
  C-1D-1 (3)
• Considering the effectiveness of product C and D
  molecules in causing the reverse reaction, we
  have rate µ C lDd
• Reaction rate, ri, in relation to
  reactant/product i, in general form
• where k is reaction rate constant

44
Rate Equations (2)
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• Different appearances of rate equation
• For a reaction vAA vBB vCC vDD (1)
• If reaction is far away from equilibrium
  conversion, the reverse reaction is negligible,
• If reactant A in large excess, which means that
  the conc. of A can be considered as constant,
• Some reactions do not depend on the concentration
  of neither reactant nor product,
• There exist other more complicated forms of rate
  equations.
• How do we study different types of reaction? Or,
  how we characterise these rate equations?

45
Reaction Order
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• Definition
• Reaction order with respect to a specific
  component (either reactant or product) to which
  the conc. of that component is raised in the rate
  eqn
• For a reaction vAA vBB vCC vDD (1)
• If rate equation is
• the order w.r.t. A is a, the order w.r.t. B is
  b, the order w.r.t. C is l, etc.
• Overall Reaction order - is the sum of orders of
  all reactants products
• The overall order of the above reaction is
  N(ab ld)
• Note 1) A reaction order do not have to be an
  integral, it can be a fraction.
• e.g. C4H103.5O2C4H2O34H2O
• 2) Some rate eqns. are very complicated - we do
  not use the term reaction order.
• e.g. COH2OCO2H2

46
Reaction Rate Constant
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• For a reaction vAA vBB vCC vDD
• The general form of rate equation
• k is the reaction rate constant
• Independent of reactant / product concentration
• Dependent on the reaction temperature
• The unit of k depends on the unit of all other
  terms in the rate equation
• e.g. (mol g-1 h-1), and Pi is the partial
  pressure in bar
• the unit of k
• Initially k is found to be temperature dependent,
  further study shows that
• or often written as

47
Rate Constant Arrhenius Equation
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• The Arrhenius Equation (1)
• where A pre-exponential factor
• Ea is the reaction activation energy
• R is the gas constant
• T is the reaction temperature in Kelvin
• Eqn.1 was initially found from fitting
  experimental results. After molecular kinetic
  theory was established, the relation can be
  derived directly from the theory
• Usually A is related to the molecule collision
  frequency or thermodynamically to the entropy
• Ea is an energy term which related to the
• energy barrier for a reaction has to overcome

Arrhenius parameters
48
Exp. Determination of Arrhenius Parameters
CH4003 Lecture Notes 6 (Erzeng Xue)
Reaction kinetics

• From the Arrhenius Equation (1)
• To determine A and Ea
• Take log
• Compare with linear equation yabx, where
  ylnk, a lnA, b-Ea/R and x1/T
• If when can measure k at various temperature Ts
• Note As k is a function of temperature, the k
  value measured
• at each T as mentioned above should be
  different.
• Therefore, the above method, strictly speaking,
  gives
• average values of Ea and A within the Ts
  applied.