Physical Chemistry 2 CH4003 Dr. Erzeng Xue CH4003 Lecture Notes 1 (Erzeng Xue)

Physical Chemistry 2

CH4003

Dr. Erzeng Xue

CH4003 Lecture Notes 1 (Erzeng Xue)

2

Course General InformationLectures Monday 9am Room No.: BM015

Friday 9am Room No.: SG16Lecture Notes: Available at the class and on the UL’s 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.: A3-009Weeks 3,4,5,7,8,9,10 (both groups)

Attendance is MANDATORYMUST have white lab coat and safety specs

Assessment 75% End term Exam25% Lab. Attendance/Reports


3

CH4003 Course Syllabus 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 Fick’s 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

Course General Information


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Recommended Texts

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.



5

Experiments

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?

SystemA

SystemB

System: definitioncharacterisation

driving force and directionof change

Extent & equilibrium of change:

The rate of change:

Applications

CH4003

CH4002

Process of change


7

Methods of Study

Fundamental laws

The way various energies change

Mathematics models

Experiment validation


8

Success !


9

Thermodynamics - Review 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

state A state B

Process of changeSurroundings

Boundary


10

Fundamental Laws of Thermodynamics 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.

Thermodynamics Review


11

State of System 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 don’t 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



12

Properties of System 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)



13

Basic System Properties 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 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


PT

vT

PS

vS

T

v

P

s

T

P

v

s

s

v

P

T

s

P

v

T


15

Substance in a System 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 > liquid > 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 Energies transferred during a process

Sensible energy - P, TLatent 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 systemsStudy the energy transfer process in chemical reactionsPredict the direction of a chemical reaction and the energy transfer associated with the reactionPredict 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 reactionsFor most gas-phase reactions occurring at elevate T. - the gases can be treated as ideal gasesMany reactions proceed continuously at a constant P - can be treated as steady-flow processMany reactions are carried out at a constant T (very common) - these are isothermal processMany 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


17

Chemical Reaction - The Process

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

A

B

A B C DC

D

Step 1Add A & B

Step 2A meets B

Step 3 A reacts with B giving C&D

Step 4 C & D move apart

reactant molecules travel to meet

activation & reaction product molecules travel to apart

Reaction Process


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Diffusion 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 gas>liquid>solid. Most industrial reactions take place either in gas phase or in a liquid phase, or multi-phases

Chemical Reaction Process


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Rate of Diffusion vs. Rate of Reaction

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 DiffusionChemical 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

A

A

B

B

B

B

BB B

B

B

B

B

(2)

(1)


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Diffusion Equation - Fick’s LawChemical Reaction Process

x

CDJ

x

CDJ B

BAxBA

ABxA

Fick’s Law of diffusion

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 DAB=DBA

t=0: CA1 > CA2 and CB2 > CB1. A will start to diffuse from (1) to (2) and B from (2) to (1).

t=t: For a close system when reaching equilibrium CA2|t=t CA1|t=t and CB1 |t=t CB2 |t=t

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

(1)CA1

CB1

(2)CA2

CB2

x

0 L

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 mDAB - diffusion coefficient (of A in B) m2 s-1

dx

dCDJ A

ABxAor in 1-D


22

Application - Fick’s Law of Diffusion

Fick’s Law of diffusion (1-D)

Integrating for steady-state situation using boundary conditions of

CA=CA1 at x=0 and CA=CA2 at x=L

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


dx

dCDJ A

xA

L

)cc(DJ AAAB

A12


23

Diffusion Coefficients of Gases at 1 atm.Chemical Reaction Process

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

System Temp °C Diffusivity cm2/s

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 0.729

He-n-butanol 150 0.587

He-air 44 0.765

He-CH4 25 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 - Fick’s Law For a gas system

From Kinetic theory

Chapman-Enskog equation (semi-theoritical)

For a liquid system

for solute molar weight > 1000

for solute molar weight < 1000


DT

MABA

9 40 10 15

1 3

.

( ) /

DT

P M MABAB D AB A B

18583 10 1 17 3 2

2

1 2. /

,

/

P - pressure; T - temperature

MA, MB - molar weight of A and B

AB - average collision diameter

D,AB - collision integral

, B - viscosity of solution and solvent

VA - solute molar volume at its normal boiling point

- associate parameter, value varies with solvent used

D u where uk T

m

k T

d PABB B

1

3

8

2

1 2

1 2 2

/

/

u - average speed of molecule- mean free path lengthkB - Boltzmann constantP,T - pressure, temperaturem - mass of molecule or sphered - molecule diameter

6.02/116 )(10173.1

ABBBAB

V

TMD


25

Chemical Reaction - The Equation 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 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 + ½O2=NO2 ?


26

Direction of a ReactionQ. 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, G

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.

Chemical Reaction

reaction can proceed (however, we don’t know how fast it will be!)

reaction at equilibrium (no further change in system - ‘dead’ state)

reaction will NOT proceed (or can proceed backward!)

0

0

0

T

T

T

G

G

Gfor a reaction at constant T, P,

we have


27

Entropy of Reaction System Entropy definition meaning: at T, change of S is proportional to change of heat

Entropy calculation Basis of S calculation: 3rd Law of thermodynamics: S=0 at absolute temperature=0

Assign standard entropy of a substance (1 mole, at 1 atm. 25°C) as

(S°298 value of common substances are available in most chemistry / chem. engg handbooks.)

The entropy change in a reaction at T, P

reaction: vAA + vBB vCC + vDD

If a reaction is adiabatic, it can only proceed when S>0 (rxn reaches equilibrium when S=0).

Usually S analysis of a reaction system is complicated and less convenient to use.

Chemical Reaction

in which 298

0298

0000

j

phaseT

i,pT,ireacT,iiprodT,iiT T

Q

T

dTCSS)Sv()Sv(S

This term becomes zero if there is no phase change during the reaction

298

0

0298 dT

T

CS p

T

dQdS


28

Enthalpy of Reaction System Enthalpy definition

H=U+PV dH=dU+PdV + VdP

Enthalpy calculation Standard enthalpy of formation, H°f

Assign H°f of all stable substances (O2, N2, CO2 H2O etc.) at 298K & 1atm as 0 (not at 0K as for S) (H°298 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


H is a direct measure of the reaction heat associated with a reaction (if only chemical energy change exists). When H < 0 - the reaction is exothermic and when H > 0 is the reaction is endothermic.

Reaction heat is of critical importance in reaction engineering (reactor & process design).

Chemical Reaction

in which 298

0298

0000 i,changephase

T

i,p,iT,ireacT,iiprodT,iiT HdTCHH)Hv()Hv(H

UH

nRTUH gas phase (ideal gas) at const. T & P

g-l, g-s or g-s,l mixture at const. T & P

liquid or solid (dv=0)

The H of phase transformations including g-l-s or crystalline phase change


29

Gibbs Free Energy of Reaction System (1)

Gibbs free energy (also called Gibbs function) definition

G = U + PV -TS = H - TS G= H - TS at constant T,P

Gibbs free energy calculation Standard Gibbs free energy, G°298

Similar to S° and H°, the standard Gibbs free energy of formation of a substance, G°, is defined at reference state of T=298 K and P=1 atm

(G°298 values of common substances are available in most chemistry / chem. engg handbooks.)

Gibbs free energy change in a reaction at T, P


or, GT° can be determined directly from

Chemical Reaction

- 000TTT STHG

- in which 000000T,iT,iT,ireacT,iiprodT,iiT STHG)Gv()Gv(G

value of each individual substance

value from overall reaction


30

Gibbs Free Energy of Reaction System (2)

G° is one of the most important thermodyn. properties for a chemical reaction system. It determines the direction of reaction to proceed

G°< 0 is the pre-condition which MUST be met for any process (not limited to chemical reaction systems) to occur (spontaneous process).

G°<0 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 G°0, this is called equilibrium state.

Chemical Reaction

reaction can proceed in the direction specified

reaction at equilibrium (no further change occurs)

reaction will NOT proceed (it can proceed backward!)

0

0

0

T

T

T

G

G

Gfor a reaction at constant T, P,

we have


31

Important Notes about S, H and G

S, H and G 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.

Chemical Reaction


32

Home WorkChemical Reaction

Calculate the H° and G° 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?


33

For a chemical reaction vAA + vBB vCC + vDD when G°T =0, we say the reaction is in chemical reaction equilibrium

- What is a chemical reaction equilibrium?

Example 1: NH3(aq)+H2O(l) NH4+(l)+OH-(aq)

At constant T and P, when t

Example 2: 2NO(g) + O2(g) 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

Chemical Reaction - The Equilibrium (1)

t

NO2

NOO2

t

NH4

NH3

constant2

2

2

2

ONO

NO

PP

P

constantO]][H[NH

]][OH[NH

23

4

reaction quotient


34

Chemical Reaction - The Equilibrium (2)

Chemical reaction equilibrium

vAA + vBB 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 G°T =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.

reacT,iiprodT,iireacT,iiprodT,iiT )Gv()Gv()Gv()Gv(G 00000 0


35

Equilibrium Constant (1) Definition of equilibrium constant, K

The equilibrium constant is the reaction quotient at G°T =0.

Expressions of equilibrium constant for various reactions

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

gas-solid phase CaCO3(s) CaO (s)+CO2(g)

liquid phase NH3(aq)+H2O(l) NH4+(l)+OH-(aq)

liquid-solid Cu(OH)2(s) Cu2+(aq)+2OH- (aq)

gas-liquid NH3(g)+H2O(l) NH4OH(aq)

general vAA + vBB vCC + vDD

Chemical Reaction equilibrium

2

2

2

2

ONO

NOp PP

PK

O]][H[NH

]][OH[NH

23

4

cK

2COp PK

22 ]][OH[Cu cK

31 NHp P/K

BA

DC

BA

DC

vB

vA

vD

vC

vv

vv

c PP

PPDCK

[B][A]

][][


36

Equilibrium constant, Kp, and Gibbs free energy G

A gas phase reaction vAA + vBB vCC + vDD

When at equilibrium, assuming all the gases follow the ideal gas law

at P=1 atm, G°=(viG°i)prod-(viG°i)reac=0 and at any P(1) G=(viGi)prod-(viGi)reac=0

when reaction occurs at constant temperature (isothermal reaction)

dG=VdP-SdT dG=VdP dG=RTdP/P G=RTln(P/P0)

G° is defined at P0=1 atm, so that G=G-G°=RTln(P/1) Gi=Gi°+RTlnPi

(vi(G°i+RTln(PCPD))prod-(vi (G°i+RTln(PAPB))reac=0

(viG°i)prod-(vi G°i)reac=-[(viRTln(PCPD))prod-(vi RTln(PAPB))reac]

By definition:

Equilibrium Constant (2)Chemical Reaction equilibrium

BA

DC

BA

DC

vB

vA

vD

vC

vB

vA

vD

vC

PP

PPlnRT

)atm/P()atm/P(

)atm/P()atm/P(lnRTG

pKRTG ln

BA

DC

vB

vA

vD

vC

pPP

PPK

T=const PV=RT intergration


37

Equilibrium constant, Kc, and Gibbs free energy G Ideal solution (liquid and solid)

Raoult’s law Pi=xiPi* or xi=Pi / Pi* where

thus for a solution we can also write Gi=Gi°+RTln xi) (compare to gas Gi=Gi°+RTlnPi)

which lead to, in a similar way, the relation between G and Kc,

Summary of G calculation for ideal gas and solution For a pure substance at const T & P, G=G°+RTlnP (1) For a mixture of ideal gas at const T and P G =Gi=Gi°+RTln Pi) (2-1)

For a mixture of ideal solution at const T and P G =Gi=Gi°+RTln xi) (2-2)

For a situation that a mixture (gas or solution) under concern is not ideal, the P i or xi cannot be related to G by expressions (2-1) & (2-2). How do you calculate G?


Pi - vapour pressure of component ixi - mole fraction of component i in solutionPi* - equil. vapour pressure of pure component i

BA

DC

BA

DC

BA

DC

vv

vv

vv

vv

vB

vA

vD

vC KKRTRT

xx

xxRTG

[B][A]

[D][C] where)ln(

[B][A]

[D][C]ln ln cc


38

Real mixture (Non ideal substances) For a real gas: Pi,real Pi,ideal, we define the effective pressure, f,

f is called fugacity

For a real solution: Pi,vap,real Pi,vap,ideal, we define the effective concentration, ai

a is called activity

Chemical potential, Using the same relation of G with Pi and xi for ideal gas and solution, but G is replaced by a new term, , called chemical potential , representing the non-ideal situation

ideal gas Gi=Gi°+RTlnPi real gas: i= =i°+RTlnPi,real= i°+RTlnfiPi,ideal

ideal solution Gi=Gi°+RTlnxi real solution: i= i°+RTlnxi,real= i°+RTlnaixi,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. G=

i.e. for ideal gas i=i°+RTlnPi and for ideal solution i=i°+RTlnxi


ideal,iireal,iideal,i

real,ii PfP

P

Pf or

ideal,vap,iireal,vap,iideal,vap,i

real,vap,ii PaP

P

Pa or


39

The Equilibrium (5) A chemical reaction,if in equilibrium (=0)

vAA + vBB 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 Kp’=PCO2


BA

DC

vB

vA

vD

vC

pppPP

PPKKRTKRTG wherelnor ln

pvB

vA

vD

vC

vB

vA

vD

vC

vB

vA

vD

vC

ff Kff

ff

PP

PP

ff

ffKKRT

BA

DC

BA

DC

BA

DC

whereln

cvB

vA

vD

vC

vv

vv

vB

vA

vD

vC

aa Kaa

aa

aa

aaKKRT

BA

DC

BA

DC

BA

DC

[B][A]

[D][C] whereln

BA

DC

vv

vv

ccc KKRTKRTG[B][A]

[D][C] wherelnor ln


40

Equilibrium Constant (6) The equilibrium constant, K, is a function of temperature

The effect of inert on the equil. composition - depending on the reaction stoichiometry

v = vC + vD - vA - vB

When v>0, 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 vCC + vDD

vCC + vDD vAA + vBB

For reaction equation written with different stoichiometery coefficient

2NO(g) + O2(g) 2NO2(g) NO(g) + ½ O2(g) NO2(g)


- adding an inert cause the equilibrium to shift to more reactants

- adding an inert has no effect on the equilibrium composition

- adding an inert push the the equilibrium to shift to more products

0

0

0

)exp(- lnor )exp(- lnRT

KKRTRT

GKKRTG

BA

DC

vB

vA

vD

vC

forward,pPP

PPK 1

1

forward,pv

Bv

A

vD

vC

vD

vC

vB

vA

reverse,p KPP

PP

PP

PPK

BA

DC

DC

BA

2

2

2

2

ONO

NOp PP

PK 2

121

2

2

21

2

2

2

2

pONO

NO

ONO

NOp K

PP

P

PP

P'K


41

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

Chemical Reaction - The Rate


42

Definition of Reaction RateFor 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.

Reaction kinetics

Adt

dreactant on based

[A]rate

dt

d

dt

d

dt

d [D]rateor

[C]rateor

[B]rate

dt

d

vdt

d

vdt

d

vdt

d

v DCBA

[D]1[C]1

[B]1

[A]1rate

dt

d

dt

d

dt

d ][NH

2

1

][H

3

1

][N

1

1rate 322


43

Rate Equations (or Rate Laws) (1)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 [A][B] (2a)

Reactant A molecules may differ from B molecules in leading to reaction, this may be written as:

rate [A][B] (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 [C][D] or rate [C][D] = [C]-[D]- (3)

Considering the effectiveness of product C and D molecules in causing the reverse reaction, we have: rate [C] [D]

Reaction rate, ri, in relation to reactant/product i, in general form:

where k is reaction rate constant

Reaction kinetics

[D][C][B][A]][

k dt

idri


44

Rate Equations (2) 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?

Reaction kinetics

k dt

idri

][

[B][A]][

k dt

idri

[B][B] [A]][

'kk dt

idri


45

Reaction Order 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 , the order w.r.t. B is , the order w.r.t. C is , etc….

Overall Reaction order - is the sum of orders of all reactants & products

The overall order of the above reaction is: N=(+ ++)

Note: 1) A reaction order do not have to be an integral, it can be a fraction.

e.g. C4H10+3.5O2=C4H2O3+4H2O

2) Some rate eqns. are very complicated - we do not use the term ‘reaction order’.

e.g. CO+H2O=CO2+H2

Reaction kinetics

[D][C][B][A]][

k dt

idri

58004

2

110610941 .

OnBMA P)PRT

.(exp.r

22

2

21 HOH

OH

P/PK

kPr


46

Reaction Rate ConstantFor 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

Reaction kinetics

[D][C][B][A]][

k dt

idri

5800

2

.OnBMA PkPr

0.58-1-1-0.58

-1-1

0.58O

0nB

MA barhmolg ][bar

]h[molg

]][P[P

][r

2

k

RT/EAek

RT

EAk aexp


47

Rate Constant & Arrhenius Equation 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

Reaction kinetics

RT

EAk aexp

Arrhenius parameters

reaction process

Ea reactant

producten

ergy


48

Exp. Determination of Arrhenius Parameters

From the Arrhenius Equation(1)

To determine A and Ea

Take log:

Compare with linear equation: y=a+bx, where y=lnk, a= lnA, b=-Ea/R and x=1/T

If when can measure k at various temperature T’s

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 T’s applied.

Reaction kinetics

RT

EAk aexp

RT

EAk a lnln

1/T

slope=-Ea/Rintersect=ln A

lnk


Physical Chemistry 2 CH4003 Dr. Erzeng Xue CH4003 Lecture Notes 1 (Erzeng Xue)

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Transcript of Physical Chemistry 2 CH4003 Dr. Erzeng Xue CH4003 Lecture Notes 1 (Erzeng Xue)