phychem lecture 1

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Powerpoint Templates Powerpoint Templates

Physical Chemistry Lecture no. 1

ChE Course Integration 1 Review

Sherrie Mae S. Medez

Powerpoint Templates Page 2

OUTLINE

• BASIC CONCEPTS • integration and differentiation • partial derivatives • functions of multiple variables

• GASES • definition and properties • ideal gases • kinetic molecular theory of gases • mixture of ideal gases • real gases

• THERMODYNAMICS

• basic concepts • laws

http://www.powerpointstyles.com/



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OUTLINE

•LIQUIDS • characteristics • physical properties

• SAMPLE PROBLEMS


GASES



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GASES

• Simplest forms of matter

• Properties:

– Fill the volume of the container

– Less dense than solids or liquids

– Have highly varying densities, depending on the condition

– Readily mix with other gases

– Have volumes that change with

change in temperature

Source: http://www.phy.cuhk.edu.hk/contextual/heat/tep/trans01_e.html


The Perfect / ideal gas

• a collection of atoms or molecules having continuous random motion

• speeds of the molecules are increased as temperature is raised

• differs from liquids because except during collisions, molecules are far from one another and are not significantly affected by intermolecular forces


http://www.phy.cuhk.edu.hk/contextual/heat/tep/trans01_e.html


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The ideal gas law

• Defines the state of a PURE GAS

• Equation of state – interrelates the 4 variables that define the state of a gas

P = f(n,V,T)

PV nRT


The ideal gas law

where P = pressure

V = volume

n = no. of moles

T = temperature

R = universal gas constant

= 0.08206 atm L/ (mol-K)

= 8.314 J/(mol-K)

PV nRT



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The ideal gas law variables

1) PRESSURE

- the force comes from the ceaseless motion of the gases onto the walls of the container

- these collisions are numerous that they exert an EFFECTIVE STEADY FORCE, and therefore an EFFECTIVE STEADY PRESSURE

Force (can also be weight)

Area to which the force is

applied

FP

A



1) PRESSURE

- units: atm, Torr, bar, mmHg, Pascal, psi

1 atm = 760 Torr

= 760 mmHg

= 101325 N/m2

= 1.01325 bar

= 14.7 psi

FP

A

Force (can also be weight)

Area to which the force is

applied



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1) PRESSURE

Physical Illustration of pressure: Consider:

- movable wall will continue to move until Pleft = Pright

- when movable wall stops moving, then

MECHANICAL EQUILIBRIUM (equality of pressure) is achieved



1) PRESSURE

* Manometer – used to measure the pressure of a gas inside a container

Source: http://www.efunda.com/formulae/fluids/images/Manometer_A.gif



http://www.efunda.com/formulae/fluids/images/Manometer_A.gif

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2) TEMPERATURE

- physical change that can be observed when 2 objects come into contact with one another

units: Celsius, Fahrenheit

Kelvin, Rankine

* Temperature is a property that indicates the

direction of the flow of energy through a thermally

conducting rigid wall

Physical Illustration of temperature:

- if no change is observed, then there is an

ADIABATIC WALL

* Diathermic wall – exists when 2 objects of

different temperatures come into contact

and change is observed



2) TEMPERATURE

*When the diathermic wall stops transferring heat, then THERMAL EQUILIBRIUM (equality of temperature) is achieved



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2) TEMPERATURE Zeroth Law of Thermodynamics

A

C B

If A is in thermal equilibrium with B,

and B is in thermal equilibrium with

C, then A is in thermal equilibrium

with C.

-This law allows for the consideration of temperature

as a state function.

-Basis of thermometers – systems that contain

substances which expand when heated (e.g.

mercury)


The gas laws

1) Boyle’s Law

PV = constant

P1 V1 = P2 V2

2) Charles’ Law / Gay-Lussac’s Law

V = constant x T

3) Alternative to Charles’ Law

P = constant x T

1 2

1 2

V V

T T

1 2

1 2

P P

T T



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The gas laws


The gas laws 4) Avogadro’s Principle

V = constant x n

- at a given temperature and pressure, the volume per mole of a gas is the same regardless of the identity of the gases

5) The ideal gas law

PV = constant x nT

- gases obey this at low pressure and high temperature

6) Combined gas equation – at constant n

m

VV

n

PV nRT

1 1 2 2

1 2

PV PV

T T



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The gas laws


Conditions:

• STANDARD AMBIENT TEMPERATURE AND PRESSURE (SATP)

= 298 K, 1 bar

Vm = 24.789 L/mol

• STANDARD TEMPERATURE AND PRESSURE

= 00 C or 273.15 K, 1 atm

Vm = 22.414 L/mol



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Mixtures of ideal gases

• In a mixture of ideal gases, each component contributes to the total pressure of the system



• DALTON’S LAW OF PARTIAL PRESSURES The pressure exerted by a mixture

of gases is the sum of the partial pressure of the gases.

where pT = total pressure

T A B C

ii

p p p p

n RTp

V



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• DALTON’S LAW OF PARTIAL PRESSURES

– in terms of molar fraction:

– for a mixture

– partial pressure can be expressed as:

...ii T A B

T

nx n n n

n

... 1.0A B cx x x

i i Tp x pthe pressure that will be

exerted by a gas if it were

alone in a container

... ....( )A B A B T Tp p x x p p



• GRAHAM’S LAW

– Obtained from the experiment:

NH3(g) + HCl(g) NH4Cl(s)

21 1

2 2 1

gg avg

g avg g

MWd u

d u MW



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• AMAGAT’S LAW OF COMBINING VOLUMES – The total volume occupied by a mixture of

gases is equal to the sum of the volumes which would be occupied by each constituent at the same temperature and pressure as the mixture.

... iT A B i

i

T

n RTv v v v

P

n RTv

P



• AMAGAT’S LAW OF COMBINING VOLUMES

for gases,

1

if

m

i

ft

m

fi i

vv

v

vv

v

v x



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Variation of atmospheric pressure with altitude

p = po eh/H

Where p0 – pressure at sea level

h – altitude

H – RT/Mg

p – pressure at altitude h


Kinetic molecular theory of gases

• Is the theoretical means of displaying the behavior of gases and all assumptions associated with them

• First proposed by Bernoulli in 1738



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POSTULATES:

1) Gases are composed of minute discrete particles called molecules. All molecules of 1 gas are of the same mass and size, but differ from gas to gas.

2) The molecules within a container are believed to be in ceaseless, chaotic motion during which they collide with each other and with the walls of the container.



POSTULATES:

3) The bombardment of the container walls by the molecules gives rise to the phenomenon we call PRESSURE. (The average force on the walls per unit area is the average force per unit area which the molecules exert in their collisions with the walls).

4) Inasmuch as the pressure of a gas within a container does not vary with time at any given pressure and temperature, the molecular collisions must involve no energy loss due to friction. In other words, all molecular collisions are elastic.




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POSTULATES:

5) The absolute temperature is a quantity proportional to the average kinetic energy of all the molecules in a system.

6) At relatively low pressures, the average distances between molecules are large compared with the molecular diameters, and hence the attractive forces between molecules, which depend on the distance of molecular separation, may be considered negligible.



POSTULATES:

7) Since molecules are small

compared with the distances

between them, their volume may be

considered to be negligible

compared to the volume of the gas

* Postulate nos. 6 and 7 make the theory limited to IDEAL GASES.




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Speeds of gas molecules

• Most probable speed, Vp

• Mean speed, V

• Root mean squared speed, Vrms

2p

RTv

MW

8

( )

RTv

MW

3rms

RTv

MW

*In reality, speeds of molecules span over a wide range ,

given by the MAXWELL SPEED DISTRIBUTIONS.


Maxwell speed distrIbutions



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Maxwell speed distrIbutions

• The Maxwell Speed Distributions depend on the temperature or molecular weight

Low T or high MW

Intermediate T or MW

High T or low MW


Collision frequency

Where

σ = collision cross section

vrel = (√2)v

V=volume

N = no. of molecules

relv Nz

V

Mean Free Path

v

z

Where

v = mean speed

z = collision frequency



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Kinetic energy of translation

3

2KE nRT

Where

k = 1.38066 x 10-23 J/K

= R/N

(Boltzman Constant)

N = Avogadro’s number

3

2KE RT

3

2KE kT


Real gases

• Gases that do not obey ideal gas laws

• exist at low temperature and high pressure, especially when gases are at the point of condensing to a liquid

• INTERMOLECULAR FORCES

– REPULSIVE FORCES – assist expansion

- Very significant at high pressures

– ATTRACTIVE FORCES – assist compression

- Very significant at moderate pressures

Low pressure: no significance, volume is high

Moderate pressures: AF > RF

High pressures: RF > AF



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Compression factor, z

• At given T and P,

0

m

m

VZ

V

Molar volume

Molar volume of perfect gas

mPV RTZ

Low P: Z=1

Moderate P: Z<1

High P: Z>1


Van der waals equation of state

• Applies to real gases

• Considers the volume occupied by the molecules themselves and the attractive forces between them

2

2

2 227

64 8

c c

c c

nRT n aP

V nb V

where

R T RTa b

P P

The Van der Waals equation:

Where Tc and Pc,

are critical

constants



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OTHER EQUATIONS OF STATE

1) Kamerlingh Onnes Equation

- expresses PV as a function of a power series of the pressure at any given temperature

where A, B, C, and D are virial coefficients at low P, only A is significant (A=RT)

2) Berthelot Equation

- applicable for gas pressures <= 1 atm

2 3 .....mPV A BP CP DP

2

2

9 61 (1 )

128

c c

c

PT TPV nRT

PT T



3) Beattie- Bridgeman Equation - for wide ranges of temperature (up to -1500 C and 100 atm)

where

2 3 4

m m m m

RTP

V V V V

2

2 3( ) ( )m

RT P PV

P RT RT RT

2 2

2

c c oo o o o

c

o

R R BRTB A RTB b A a

T T

RB bc

T



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4) Virial Equation

Where B, C, …. Are virial coefficients

* the terms in the parenthesis can be identified with the compression factor Z

...)1(2

mm

mV

C

V

BRTPV


CONDENSATION

Critical Temp, Tc: 31.40 C

Critical Pressure, Pc : 72.9 atm

Critical Molar Volume, Vc :0.094 L/mol

Below Tc : condensation

occurs



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Vapor pressure

• Established between the liquid and vapor

phases contained in a sealed volume

• the pressure of a vapor above the liquid that

evaporated from the liquid and remains

above the sample in a sealed container

• Saturated Vapor Pressure: established at

equilibrium

- increases constantly with temperature

- H2O: 23.76 mmHg at 250C; 760 mmHg at

1000C


Critical constants

• Critical constants are constants for different gases.

– At critical conditions, the physical properties of the liquid and vapor become identical, and there is no distinction between the 2 phases

– At the critical point, T=Tc , V=Vc, and P = Pc

– At points above and at Tc , the substance remains as a gas.

– If T>Tc , a single phase, denser fluid is present, known as a supercritical fluid.



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Principle of corresponding states

r r r

C C C

P V TP V T

P V T

• At any given values of Tr and Pr , all

liquids should have the corresponding

volumes Vr

•substituting into the VDW equation of

state:

2

33 1 8r r r

r

P V TV


THERMODYNAMICS



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Thermodynamics

• “power developed from heat”

• the physical science concerned with the transformation of energy

• concerned with heat transfer

e.g. energy released Provide heat

Provide mechanical work

Provide electricity


Thermodynamics

• The 1st and the 2nd laws have no mathematical sense; their validities are due to no contradictory principles

• Thermodynamics can be used for:

1) prediction of the possibility of the process taking place

2) quantification of needed energy and maximum yield



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Thermodynamic variable?

YES

NO

Thermodynamics

• Thermodynamics cannot be used for:

1) establishing reaction rates

2) revealing microscopic aspects since it is macroscopic in nature

tan

driving force

resis cerate


Basic concepts

1) SYSTEM – body of matter that serves as the focus of attention

- types depend on the quantity allowed to be exchanged through its boundary

* Adiabatic – system that is thermally isolated from the

surroundings 2) SURROUNDINGS – the region outside the system

3) BOUNDARY – portion separating the system from the

surroundings

TYPE ENERGY MATTER

OPEN / /

CLOSED / X

ISOLATED X X



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Basic concepts

4) CONTACT a) MECHANICAL CONTACT - present between a system

and its surroundings if a change in pressure in the surroundings results to a change in the system

b) THERMAL CONTACT - present if a change in the

temperature of the surroundings results to a change in the temperature of the system


Basic concepts

5) WORK - fundamental physical property in

thermodynamics where F = opposing force d = distance

6) ENERGY - capacity to do work * INTERNAL ENERGY- motions, interactions,

bonding of molecules * KINETIC ENERGY * POTENTIAL ENERGY

W F d



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Basic concepts

7) EQUILIBRIUM -’static condition’ or the absence of any

tendency towards change CHARACTERISTICS: a. the system does not vary with time b. the system is uniform (no change in P,

V, T, and concentration c. the mass, heat, and work flows

between the systems and the surroundings are equal to zero

d. the rate of all chemical reactions is zero


Basic concepts

7) EQUILIBRIUM

-’static condition’ or the absence of any tendency towards change

i) MECHANICAL EQUILIBRIUM

- between 2 subsystems of equal pressure

ii) THERMAL EQUILIBRIUM

- between 2 subsystems of equal temperature



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Basic concepts

8) PHASE -homogenous, physically distinct,

mechanically separable portion of a system

- may or may not be continuous * Heterogenous – 2 or more phases * Phase rule – used to treat heterogenous

equilibria - “fix” the number of variables involved


Basic concepts

8) PHASE Gibbs’ Phase Rule - applies to systems in equilibrium where F - degrees of freedom - the number of intensive variables

that can be changed without disturbing the number of phases in equilibrium

- no. of phases N – no. of components / species

2F N



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Basic concepts

9) EXTENSIVE vs INTENSIVE PROPERTY

a) Extensive property – dependent on the amount of substance present

e.g. mass, volume

b) Intensive property – independent on the amount of substance present

e.g. density, molar volume, temperature


Basic concepts

10) STATE vs PATH FUNCTIONS

a) State functions – variables that do not depend on the undertaken from the initial to the final state

b) Path functions – variables that are dependent on the path taken from the initial to the final states



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Zeroth law of thermodynamics

• “If A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A and C are in thermal equilibrium.”


Definition and mathematical statement of the First law

• Law of conservation of energy

• “The energy of the universe is constant.”

• “Energy can neither be created no destroyed, only transformed from one form to another.”

• MATHEMATICAL STATEMENT

For a closed system:

U Q W



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MATHEMATICAL STATEMENT For a closed system: where Q – heat (+) – absorbed by the system (-) – absorbed by the

surroundings W – work (+) – done on the system (-) – done by the system ΔU – change in internal energy Units: 1 calorie (cgs) = 4.184 J (SI)

U Q W

Path functions State function

Definition and mathematical statement of the First law


• The total energy of a system

• Sum of the total kinetic and potential energies of the system

• State function, extensive property

Internal Energy, U

ΔU = Uf - Ui



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WORK

• Defined as mechanical or P-V work

• The transfer of energy that makes use of organized motion

Source: Physical Chemistry 8th ed by Atkins


Work, W

1) By free expansion

pex = 0, therefore W =

2) Against constant external pressure, pex

Source: Physical Chemistry 8th ed by Atkins



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Enthalpy

• The thermal changes at constant pressure

• A state function, since U and PV are also state functions

H U PV

2 1H H H

H U P V

pH nC dT


Specific Heat

• The heat required to raise the temperature of a unit mass of a substance by 1 degree of temperature

At constant volume:

At constant pressure:

For ideal gases, Cp = Cv + R

V

vT

UC

p

pT

HC



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Processes

1) Isothermal – constant temperature

2) Isochoric – constant volume

3) Isobaric – constant pressure

4) Adiabatic – no exchange of heat between the system and the surroundings


Thermochemistry

• Branch of thermodynamics concerned with the heat produced or required by chemical reactions

• A reaction vessel and its contents form a system, and the chemical reactions result in the exchange of energy between the system and the surroundings



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Calorimetry

• Study of heat transfer during physical and chemical reactions

• CALORIMETER – device used in calorimetry to measure energy transferred as heat

– thermally isolated / adiabatic


Calorimetry

• For a calorimeter: • To get heat produced or absorbed: where Q = heat produced / absorbed

by the reaction n – amount of substance C - specific heat ΔT – change in temperature;

proportional to Q

cal calQ C T

Q nC T



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Calorimetry

Types: 1) Open Type – constant pressure; 2) Bomb Type – constant volume; For reactions: ΔH is (-) when heat is

produced/exothermic (+) when heat is

absorbed/endothermic

pQ H

vQ U


Bond enthalpy

• The change in enthalpy required to break a bond between 2 atoms in an isolated gaseous molecule, producing dissociated fragments in the gaseous state

– Only applicable to gaseous molecules having covalent bonds

e.g.: HCl(g) H(g) + Cl(g)



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Standard enthalpy changes

• Change in enthalpy for a process in which the initial and final substances are in their standard states

a) ENTHALPIES OF PHYSICAL CHANGE

- changes that do

not cause any

change in the

temperature

- enthalpy of transition -50

0

50

100

150

200

250

1

2

3

4

5


Standard enthalpy changes

b) ENTHALPIES OF CHEMICAL CHANGE

- thermochemical equations or combinations of chemical reactions and their corresponding change in standard enthalpy

e.g.: CH4(g) + O2(g) CO2(g) + H2O(l)

Pure, unmixed

reactants in their

standard states

Pure, separated

products in their

standard states

ΔH= -890 kJ



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Standard enthalpy / heat of formation, ΔHF

0

- reaction enthalpy for the formation of a compound from the elements in their reference states

- T = 298 K; P = 1 bar most stable state

e.g.: formation of benzene

6C(s,graphite) + 3H2(g) C6H6 (l)

ΔH0f, C6H6 = 49.0 kJ/mol

ΔH0f, elements = 0


Standard enthalpy / heat of reaction, ΔH0

rxn

e.g. Calculate the standard reaction enthalpy of the following:

2HN3 (l) + 2NO(g) H2O2(l) + 4N2(g)

0 0 0

, , tan( ) ( )rxn f products f reac tsH n H n H



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Heats of reaction

1) Heat of combustion – standard reaction enthalpy for the complete oxidation of an organic compound to CO2 gas and liquid water (if N is present, also to N2)

e.g.: combustion of glucose


Heats of reaction

2) Heat of solution – standard reaction enthalpy when solute is dissolved in a solvent

3) Heat of neutralization

H+ + OH- H2O

4) Heat of dilution



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Hess’s law of heat summation

• The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions in which the reaction may be divided

e.g. Calculate the standard enthalpy of the combustion of propene, C3H6, given:


Temperature dependence of enthalpy

• The standard enthalpies of many reactions can be computed at different temperatures using Cp

KIRCHHOFF’S LAW: 2

1

0 0 0

2 1

0 0 0

, , , , tan

( ) ( )

( ) ( )

T

rxn rxn rT

r p m products p m reac ts

H T H T Cp dT

Cp n C n C



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SPONTANEITY

• The natural occurrence of processes

• A spontaneous direction of change does not require work to be done to bring it about.

> the spontaneous flow of heat is always unidirectional from the higher to the lower temperature

• All naturally occurring processes always tend to change

spontaneously in a direction which will lead to equilibrium


SPONTANEITY

• performing a non-spontaneous process can be possible, but only if a certain amount of work is done



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The 2nd law of thermodynamics

• Recognizes between the spontaneous and non-spontaneous processes

• Places a limitation to the 1st law, which does not have any restrictions on the source of the heat or direction of its flow

• Statements:

1) Clausius Statement

It is impossible for a self-acting machine unaided by an external agency to move heat from one body to another at a higher temperature.



• Statements:

2) Kelvin-Planck Statement It is impossible to construct a heat

engine which, while operating in a cycle, produces no effects except to do work and exchange heat with a single reservoir.

3) Kelvin statement No process is possible in which the

sole result is the absorption of heat from a reservoir and its complete conversion into work.

H

CH

H

CH

Q

QQ

Q

Weff

WQQ

Qc

QH

QH



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• Statements:

4) The entropy of an isolated system never decreases.


Entropy, S

• Measure of energy dispersed in a process

• A state function; a change in entropy occurs as a result of a physical or a chemical change, this change is at the extent to which energy is dispersed in a disorderly manner



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Entropy, S

The 2nd law statement in terms of entropy:

A spontaneous change is directed towards a more disorderly dispersal of the total energy of the isolated system. ΔStot>0

where ΔStot - total entropy of the system and the surroundings

The thermodynamic definition of entropy:

f

i

rev

rev

T

dQS

T

dQdS


Entropy, S

• For the surroundings:

• For an adiabatic change: ΔSsur = 0

• Clausius Inequality: ΔS >= 0

sur

sur

sur

sursurr

T

QS

T

dQdS



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USEFUL EQUATIONS FOR REVERSIBLE PROCESSES


Isothermal mixing of gases

A

pAo, nA

B

pBo, nB

A

pA, nA

B

pB, nB

ΔSA ΔSB nA + nB = nT

pA = xApT

pB = xBpT



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Entropy during phase changes

• Phase changes under 1 atm pressure are reversible processes

trans

trans

HS

T


Trouton’s Rule

• Many normal liquids have approximately the same standard entropy of vaporization which is 85 J/(K-mol).

trans

trans

HS

T

)/(85 molKJxTH transtrans



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Carnot cycle

• Cycle – a series of operations so conducted that at the end, the system is back to its original state

• Named after the French engineer Sadi Carnot

• Consists of 4 stages


Carnot cycle

1: reversible isothermal expansion from A to B at Th

2: reversible adiabatic expansion from B to C until temperature decreases from Th to Tc

3: reversible isothermal compression from C to D until temperature increases from Tc to Th

4: reversible adiabatic compression from D to A until temperature increases from Tc to Th



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Third Law of Thermodynamics

1. It is impossible to attain the absolute zero of temperature

2. In an isothermal process involving condensed pure substances in equilibrium, the entropy change approaches zero as the absolute temperature approaches zero and equals zero when the temperature is zero. (NERNST HEAT THEOREM)


Third Law of Thermodynamics 3. At absolue zero temperatures, the entropy of

all pure perfect crystalline structures may be taken to be zero.

*3rd law entropy: entropies reported on the basis that S0 = 0

- allows for the computation of pure substances

- S298 K - standard state entropy



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Third Law of Thermodynamics

• Debye’s Law - can be used to calculate for the molar entropy of substances at temperatures close to absolute zero

C = bT3

Sm = 1/3(bT3)


Absolute Entropies of Liquids and Gases

• The total absolute entropy of a substance in a particular state at a given temperature will be the sum of all the entropy changes that the substance has to undergo in order to reach the particular state from the crystalline solid to absolute zero



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LIQUIDS


Liquids

• Liquids have the following properties:

– Higher densities than gases

– Have definite volume but takes the shape of the container

– Are less compressible than gases

– Movement is constant (vibrating) and by mode of sliding past one another



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Critical phenomena

At critical conditions, the physical properties of the liquid and vapor become identical, and there is no distinction between the 2 phases

At the critical point, T=Tc , V=Vc, and P = Pc

At points above and at Tc , the substance remains as a gas.

If T>Tc , a single phase, denser fluid is present,

known as a supercritical fluid. *Saturated vapor pressure – vapor pressure at

equilibrium of a liquid-gas system


Properties of liquids

1) Density (ρ) Just like for gases, the density of liquids are

affected by pressure and temperature. Recall: *Specific gravity – the ratio of the density of

a compound / substance to a reference compound / substance

S.G. =

m

V

tan

tan

subs ce

ref subs ce

Reference substances:

For liquids: water at 40C

(ρ=1 g/mL)

For gases: usually air



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2) Viscosity (μ) - defined as the resistance of a fluid to flow - in gases, as temperature increases, μ also

increases - unit: Poise (P) 1 cP = 0.001 Pa-s - for liquids, 2 equations can be used: a) Pouiseuille’s equation b) Stokes’ Law



Ostwald viscometer Falling sphere viscometer



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2) Viscosity (μ)

a) Pouiseuille’s equation

– used by the Ostwald viscometer

4Pr

8

t

LV

Where P – pressure head

r – radius of the capillary tube

t – time of flow

L – length of capillary tube

V – volume of the fluid (absolute viscosity)



2) Viscosity (μ)

a) Pouiseuille’s equation – used by the Ostwald viscometer

Using the same viscometers, the relative viscosities can also be obtained:

1 1

2 2

( )

( )

liqd liqd

liqd liqd

t

t



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2) Viscosity (μ)

b) Stokes’ Law – used by the falling sphere viscometer

- applicable when the radius of the falling body is greater than the distance between the molecules of the fluid

22r ( )

9

m g

v

Where ρm – density of the fluid inside

the cylinder

ρ – density of the steel ball

r – radius of steel ball

v – velocity of the steel ball

(absolute viscosity)

1 1

2 2

( )

( )

liqd m liqd

liqd m liqd

t

t

(relative viscosity)



3) Surface Tension

- the amount of work required to increase the surface area of the liquid

- as liquid molecules at the surface come into contact with gas molecules:

> they encounter less attractive forces since they are surrounded by less liquid molecules compared to those at the bulk section

> they are at a higher energy state than those at the bulk section



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3) Surface Tension

- as liquid molecules at the surface come into contact with gas molecules:

> the tendency of the molecules is to decrease the energy state (to a more stable state). It forms the shape with the least surface area that it can assume for a certain volume: sphere

- the “teardrop shape” is a spherical drop affected by gravity



3) Surface Tension

- as liquid molecules at the surface come into contact with solid surfaces:

* cohesion – the interaction of liquid molecules with one another

* adhesion – the interaction of liquid molecules with solid molecules

- The relative strengths of these 2 dictate the shape of the surface (meniscus)



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3) Surface Tension - as liquid molecules at the

surface come into contact with solid surfaces:



3) Surface Tension

- 2 methods of measuring surface tension:

a) capillary rise method

2

h gr Where h - height

ρ – density

g - gravity

r – radius of the capillary

tube



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2

mg

L

Where m – weights used to restore

the tensiometer’s horizontal

position

L – mean circumference of the

ring

α – correction factor


3) Surface Tension

- 2 methods of measuring surface tension:

b) De Nuoy ring method / tensiometer


EQUILIBRIUM

• A condition of maximum stability appropriate with the state of each system

• All changes in nature tend to go towards equilibrium

• WORK results when the tendencies of systems to reach equilibrium are harnessed in some way; therefore NO WORK can be harnessed from a system in equilibrium



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EQUILIBRIUM

• For Reversible processes: Maximum work is obtained

• For Irreversible processes: work is always less than the maximum; the difference is yielded as heat


Free energies

• Energies produced as the system approaches equilibrium

• Helmholtz Free Energy, A

– Since U and S are state functions,

– Under isothermal and reversible conditions,

– Therefore “maximum work function”

A U TS

A U T S

Q T S

maxA W



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Free energies

• Gibbs Free Energy, G

– Since H and S are state functions, under isothermal and reversible conditions,

or

G H TS

G H T S

G A P V

maxaddG W Maximum additional non-

expansion work


Free energies

• Gibbs Free Energy, G

– From the Helmholtz free energy, the maximum work is quantified, but a part of this work will be used for mechanical / P-V work against the atmosphere (W=PΔV), therefore ΔG can also be expressed as:

– Where net energy is the available energy after doing mechanical work, or the maximum net energy at constant non-expansion work

maxnet energy G W P V



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Standard Gibbs energy of reaction

r r rG H T S

, ,r f pdts f reactG n G n G

• 3 possible conditions for free

energy change:

A + B C + D ΔG=

A + B C + D ΔG=

A + B C + D ΔG=


Calculation of Gibbs energy of reaction

• At constant temperature

– Since for gases, V = nRT/P,

– For solids and liquids

dG VdP

nRTdPdG

P

2

1

lnP

G nRTP

2 1( )G V P P



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REFERENCES

• http://www.chem.purdue.edu/gchelp/liquids/vpress.html

• http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Bond-Enthalpies-718.html


http://www.chem.purdue.edu/gchelp/liquids/vpress.html

http://www.chem.purdue.edu/gchelp/liquids/vpress.html

http://chemed.chem.wisc.edu/chempaths/GenChem-Textbook/Bond-Enthalpies-718.html








phychem lecture 1

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