Physical chemistry

PHYSICAL CHEMISTRY
ANDRÉS FELIPE LOAIZA CARREÑO
M. SC. QUIMICA UN
HELMHOLTZ ZENTRUM BERLIN FÜR MATERIALIEN UND ENERGIE

PHYSICAL CHEMISTRY BRANCHES
• THERMODYNAMICS: MACROSCOPIC SCIENCE THAT STUDIES THE
INTERRELATIONSHIPS OF THE VARIOS EQUILIBRIUM PROPERTIES OF A SYSTEM
AND THEIR CHANGES IN PROCESSES.
• QUANTUM CHEMISTRY: QUANTUM MECHANICS APPLIED TO ATOMIC
STRUCTURE, MOLECULAR BONDING AND SPECTROSCOPY.
• STATISTICAL MECHANICS: RELATES THE MOLECULAR (MICROSCOPIC)
PHENOMENA WITH MACROSCOPIC SCIENCE OF THERMODYNAMIC. (CAUSE-
CONSEQUENCE).
• KINETICS: STUDIES THE RATES OF PROCESSES SUCH AS CHEMICAL REACTIONS,
DIFFUSION, CHARGE FLOW IN AN ELECTROCHEMICAL CELL, ETC.

PHYSICAL CHEMISTRY, WHY?
• CHEMICAL ENGINEERS USE THERMODYNAMICS TO PREDICT THE EQUILIBRIUM
COMPOSITION OF REACTION MIXTURES, USE KINETICS TO CALCULATE HOW
FAST PRODUCTS WILL BE FORMED, AND USE PRINCIPLES OF THERMODYNAMIC
PHASE EQUILIBRIA TO DESIGN SEPARATION PROCEDURES SUCH AS FRACTIONAL
DISTILLATION.

THERMO
DYNAMICS
• GREEK WORDS FOR HEAT AND POWER
• STUDIES HEAT, WORK AND ENERGY AND THE CHANGES THEY PRODUCE IN THE
STATES OF SYSTEMS. TEMPERATURE IS A KEY PROPERTY.
• SOMETIMES IS DEFINED AS THE RELATION OF TEMPERATURE TO THE
MACROSCOPIC PROPERTIES OF A SYSTEM.

THERMODYNAMIC SYSTEM AND
SURROUNDINGS

THERMODYNAMIC SYSTEM
• A SYSTEM COULD BE:
o OPEN/CLOSED
o ISOLATED/NON-ISOLATED
• WALLS CONFINING THE SYSTEM COULD BE:
o RIGID/NON-RIGID (MOVABLE)
o PERMEABLE/IMPERMEABLE
o ADIABATIC/NON-ADIABATIC (THERMALLY CONDUCTING)

EQUILIBRIUM
• THE MACROSCOPIC PROPERTIES OF AN ISOLATED SYSTEM REMAIN CONSTANT
WITH TIME.
• THE MACROSCOPIC PROPERTIES OF A NON-ISOLATED SYSTEM
1. REMAIN CONSTANT WITH TIME.
2. REMAIN CONSTANT WHEN THE SYSTEM IS REMOVED FROM CONTACT WITH
ITS SURROUNDINGS.

THERMODYNAMIC EQUILIBRIUM
• MECHANICAL EQUILIBRIUM: THERE ARE NO UNBALANCED FORCES APPLIED ON
OR WITHIN THE SYSTEM; THE SYSTEM DOES NOT EXPERIMENT ACCELERATION,
NOR TURBULENCE.
• MATERIAL EQUILIBRIUM: THERE ARE NO CHEMICAL REACTIONS AND SYSTEM
AND THERE IS NO TRANSFER OF MATTER FROM ONE PART OF THE SYSTEM TO
ANOTHER OR BETWEEN IT AND ITS SURROUNDINGS. THE CONCENTRATIONS OF
CHEMICAL SPECIES IN THE VARIOUS PARTS OF THE SYSTEM ARE CONSTANT
WITH TIME
• THERMAL EQUILIBRIUM: THE PROPERTIES OF SYSTEM REMAIN CONSTANT WITH
TIME WHEN THERE IS A NON-ADIABATIC WALL BETWEEN IT AND ANOTHER PART
OR ITS SURROUNDINGS

THERMODYNAMIC PROPERTIES
• PROPERTIES THAT CHARACTERIZE A SYSTEM IN EQUILIBRIUM
 COMPOSITION
 VOLUME
 PRESSURE
 TEMPERATURE
 INTERNAL ENERGY
 ENTHALPY
 ENTROPY
 GIBBS FREE ENERGY
 HEMHOLTZ ENERGY (WORK FUNCTION)

EXTENSIVE AND INTENSIVE PROPERTIES
• REFRACTIVE INDEX
• MASS
• VOLUME
• MOLAR VOLUME
• SPECIFIC VOLUME
• ENTHALPY
• ENTROPY
• MOLAR ENTHALPY
• SPECIFIC ENTROPY
• TEMPERATURE
• PRESSURE
• DENSITY
• MOLAR FRACTION
• WEIGHT FRACTION
• SPECIFIC GRAVITY (RELATIVE DENSITY)
• SPECIFIC WEIGHT
If you sum the values of a property in every part of the system to obtain the to
of the property in the whole system, then the property is extensive
If all intensive porperties are constant throughout a system, the system is hom
An homogeneous part of as system is called a phase
A system composed of two or more phases is heterogenous
A thermodynamic property is also called a state function because a thermody
has a particular value for each thermodynamic property and the value of a sta
depends on the present state of the system and not on its past history

SPECIFIC GRAVITY OF SOME SUBSTANCES
AND COMPOUNDS

WHAT IS AN STATE?
• A SET OF PROPERTIES OF A GIVEN SYSTEM THAT MAKE IT DIFFERENT FROM ANY
OTHER SYSTEM. WE USE PROPERTIES TO SPECIFY THE STATE OF THE SYSTEM
• STATE POSTULATE:
THE STATE OF SIMPLE COMPRESSIBLE SYSTEM IS COMPLETELY SPECIFIED BY TWO
INDEPENDENT INTENSIVE PROPERTIES.

PROCESSES AND CYCLES• ANY PROCESS CAN BE USED TO CHANGE THE SYSTEM STATE TO ANOTHER,
THROUGHOUT A SERIES OF STATES THAT AS A SET ARE CALLED THE PATH.
• A REVERSIBLE OR QUASI-EQUILIBRIUM (QUASI-STATIC) PROCESS IS USED TO
CHANGE THE STATE OF A SYSTEM WITHOUT INHOMOGENEITY OF PROPERTIES
THROUGH THE SYSTEM VOLUME.
• A PROCESS COULD BE:
• ISOTHERMAL
• ISOBARIC
• ISOCHORIC (ISOMETRIC)
• CYCLIC

ZEROTH LAW OF THERMODYNAMICS AND
TEMPERATURE
• PRESSURE IS A PROPERTY THAT CAN BE USED TO EVALUATE MECHANICAL
EQUILIBRIUM
• THERMAL EQUILIBRIUM IS EVALUATED WITH A PROPERTY CALLED
TEMPERATURE
• TWO SYSTEMS THAT ARE EACH FOUND IN THERMAL EQUILIBRIUM WITH A
THIRD SYSTEM, THEY WILL BE FOUND TO BE IN THERMAL EQUILIBRIUM WITH
EACH OTHER.

MEASURING TEMPERATURE
• WE NEED A SCALE BASED ON A PROPERTY OF A REFERENCE SYSTEM WE CALL
THERMOMETER
• WE SUPPOUSE FIXED COMPOSITION AND PRESSURE FOR THE REFERENCE SYSTEM
SO THAT A CHANGE IN A THIRD PROPERTY (VOLUME FOR EXAMPLE) WILL MEAN A
CHANGE IN TEMPERATURE. BUT NOT EVERY SUBSTANCE CAN BE USED IN THE
REFERENCE SYSTEM.
• WE SET THE ICE TEMPERATURE AS 0*C AND THE STEAM
TEMPERATURE AS 100*C AND SUPPOSE A LINEAR BEHAVIOR
BETWEEN THE LENGTH OF MERCURY COLUMN AND TEMPERATURE

IDEAL GASES
• BOYLE’S LAW 1662
• CHARLE’S LAW 1787

IDEAL GASES MIXTURE
• DALTON’S LAW OF PARTIAL PRESSURES:

CONSTANT PROPERTIES AND PARTIAL
DERIVATIVES

EQUATIONS OF STATE
Real Gases
Solids and Liquids

FIRST LAW OF THERMODYNAMICS;
REVERSIBLE P-V
WORK

FIRST LAW OF THERMODYNAMICS; HEAT
• TRANSFER OF ENERGY BY USING HEAT BETWEEN TWO BODYS AT DIFFERENT
TEMPERATURES WHERE T2›T1.

FIRST LAW OF THERMODYNAMICS; INTERNAL
ENERGY
ENTALPHY AND HEAT CAPACITY• TRANSFER OF ENERGY BY USING HEAT BETWEEN TWO BODYS AT DIFFERENT
TEMPERATURES WHERE T2›T1.

SECOND LAW OF THERMODYNAMICS
• KELVIN PLANCK: IT IS IMPOSSIBLE FOR A SYSTEM TO UNDERGO A CYCLIC
PROCESS WHOSE SOLE EFFECTS ARE THE FLOW OF HEAT INTO THE SYSTEM
FROM A HEAT RESERVOIR AND THE PERFORMANCE OF AN EQUIVALENT AMOUNT
OF WORK BY THE SYSTEM ON THE SURROUNDINGS.
• CLAUSIUS STATEMENT: IT IS IMPOSSIBLE FOR A SYSTEM TO UNDERGO A CYCLIC
PROCESS WHOSE SOLE EFFECTS ARE THE FLOW OF HEAT INTO THE SYSTEM
FROM A COLD RESERVOIR AND THE FLOW OF AN EQUAL AMOUNT OF HEAT OUT
OF THE SYSTEM INTO A HOT RESERVOIR.

CARNOT CYCLE
• NO HEAT ENGINE CAN BE MORE EFFICIENT THAN A REVERSIBLE HEAT ENGINE
WHEN BOTH ENGINES WORK BETWEEN THE SAME PAIR OF TEMPERATURES TH AND
TC.

EXERCISE
• A MODERN STEAM POWER PLANT MIGHT HAVE THE BOILER AT 550°C AND THE
CONDENSER AT 40°C. IF IT OPERATES ON A CARNOT FIND THE EFFICIENCY OF
OPERATION.

ENTROPY
• ENTROPY IS EXTENSIVE

CALCULATION OF ENTROPY CHANGES
• IDENTIFY THE INITIAL AND FINAL STATES 1 AND 2.
• DEVISE A CONVENIENT REVERSIBLE PATH FROM 1 TO 2.
• CALCULATE S CHANGE.
1. CYCLIC PROCESS
2. ADIABATIC PROCESS
3. REVERSIBLE PHASE CHANGE AT CONSTANT T AND P

4. REVERSIBLE ISOTHERMAL PROCESS:
5. CONSTANT PRESSURE HEATING WITH NO PHASE CHANGE:
6.REVERSIBLE CHANGE OF STATE OF A PERFECT GAS

7. MIXING OF DIFFERENT INERT PERFECT GASES AT CONSTANT P AND T.

WHAT IS ENTROPY?
• PROBABILITY
• A PROCESS HAPPENS IF THE ENTROPY OF UNIVERSE IS TO BE MAXIMIZED
• FOR A SYSTEM IRREVERSIBLE PROCESS

THE GIBBS AND HELMHOLTZ ENERGY
• A=U-TS, CONSTANT VOLUME
• G=H-TS=U+PV-TS, CONSTANT PRESSURE

WORK FUNCTION AND GIBBS FREE ENERGY

STANDARD STATES OF PURE SUBSTANCES
• THE STATE WHEN THE FOLLOWING CONDITIONS ARE STABLISHED.

STANDARD ENTHALPY OF REACTION
• STANDARD P AT T

STANDARD ENTHALPY OF FORMATION
• 1 MOL OF SUBSTANCES IS FORMED FROM THE REFERENCE FORM OF ELEMENTS

DETERMINATION OF STANDARD ENTHALPIES
OF FORMATION AND REACTION
1. CALCULATE THE ENTHALPY OF FORMATION OF A REAL GAS FROM AN IDEAL
GAS
2. MEASURE THE ENTHALPY FOR MIXING THE PURE ELEMENTS
3. USE TO FIND CHANGE OF ENTHALPY OF
BRINGING THE MIXTURE FROM 1 BAR AND T TO THE EXPERIMENTAL
CONDITIONS
4. USE A CALORIMETER TO MEASURE THE ENTHALPY CHANGE OF REACTION.
5. FOLLOW INVERTED 3 AND 1 STEPS FOR THE COMPOUND FORMED IN STEP 4.
6. SUM ALL THE CHANGE ENTHALPIES INVOLVED FROM 1 TO 5

STEP 4: CALORIMETRY; FINDING Q.

RELATION BETWEEN U AND H CHANGES
• IN QUALITATIVE MANNER CHANGES IN U AND H ARE CONSIDERED THE SAME,
BUT:

HESS LAW
• IT IS NO POSSIBLE TO DO SUCH A REACTION, SO…

KIRCHHOFF’S LAW: T DEPENDENCE OF
REACTION HEATS

KIRCHHOFF’S LAW: T DEPENDENCE OF REACTION
HEATS

CONVENTIONAL ENTROPIES
• CONVENTIONAL OR RELATIVE ENTROPIES ARE TABULATED INSTEAD OF
ENTROPIES OF FORMATION.
• WHAT HAPPENS WITH COMPOUNDS….?
WE HAVE A PROBLEM…

THE THIRD LAW OF THERMODYNAMICS
• IN 1900 RICHARDS MADE EXPERIMENTS OF G CHANGE IN FUNCTION OF
TEMPERATURE FOR ELECTROCHEMICAL SYSTEMS
• THEN, NERNST NOTICED THAT THOSE EXPERIMENTS HAD A CLEAR TENDENCY:

DETERMINATION OF CONVENTIONAL
ENTROPIES
• AND FINALLY, WE HAVE TO CONSIDER THE IDEALITY OF STANDARD STATES OF
GASES

DETERMINATION OF CONVENTIONAL
ENTROPIES
• BUT HOW DO WE VALUATE THE FIRST INTEGRAL IF 0K CANNOT BE ATTAINABLE?

FINDING STANDARD ENTROPY CHANGES OF
REACTIONS

STANDARD GIBBS ENERGY OF REACTIONS

THERMOCHEMISTRY OF SOLUTIONS
• BONDS ARE BROKEN AND FORMED BETWEEN ATOMS AND MOLECULES DURING DE
SOLUTION FORMATION
• ENERGY IS REQUIRED TO BREAK BONDS AND ENERGY IS RELEASED WHEN BONDS
ARE FORMED
• ENERGY COULD BE TRANSFERRED BETWEEN SYSTEM AND SURROUNDINGS OR
COULD SIMPLY CHANGE DE SYSTEM TEMPERATURE (OR BOTH)
• FOR AN IDEAL MIXTURE:
• HEAT OF SOLUTION (SOLUTES ARE SOLIDS OR GASES) IS EQUIVALENT TO HEAT OF
MIXING (SOLUTES ARE LIQUIDS)
• HEAT OF SOLUTION AT INFINITE DILUTION (SOLVENT IS IN MUCH LARGER
PROPORTION)

CALCULUS OF HEAT OF SOLUTION
o WHAT IS THE ENTHALPY CHANGE FOR A PROCESS IN WHICH 2 MOL OF KCN IS
DISSOLVED IN 400 MOL OF WATER AT 18OC?
• THE COMMONLY REPORTED IS DEFINED RELATIVE TO THE PURE
SOLUTE AND SOLVENT AT T.
• WE COULD ALSO CHOICE THE PURE SOLVENT AND AN INFINITELY DILUTE
SOLUTION AT T AS THE REFERENCE CONDITIONS.
o EXAMPLE: CONSIDER A SOLUTION WHERE HCL(G) IS DISSOLVED IN H2O(L) AT 25OC
SO THAT R=10. FIND THE ENTHALPY OF SOLUTION RELATIVE TO H2O(L) AND A
HIGHLY DILUTE SOLUTION

THERMOCHEMISTRY OF SOLUTIONS:
STANDARD HEAT OF A NEUTRALIZATION
REACTION
• STANDAR HEAT OF FORMATION OF A SOLUTION:
• EXAMPLE

THERMODYNAMIC RELATIONS FOR A SYSTEM
IN EQUILIBRIUM
• VOLUME DEPENDENCE OF U
• TEMPERATURE DEPENDENC OF U
• TEMPERATURE DEPENDENCE OF H
• PRESSURE DEPENDENCE OF H
• TEMPERATURE DEPENDENCE OF S
• PRESSURE DEPENDENCE OF S
• TEMPERATURE DEPENDENCE OF G
• PRESSURE DEPENDENCE OF G

HEAT CAPACITY DIFFERENCE
• FOR A PERFECT GAS

HEAT CAPACITY DIFFERENCE
• IF AND
THEN

JOULE EXPERIMENT
• JOULE TRIED TO DETERMINE THE CHANGE OF U IN FUNCTION OF V AT
CONSTANT T BY MEASURING T DURING THE EXPANSION OF A GAS INTO
VACCUM.
• IT IS DEFINED THE JOULE COEFFICIENT AS
• THEN

JOULE THOMSON EXPERIMENT
• 10 YEARS LATER JOULE AND THOMSON TRIED TO DETERMINE THE CHANGE OF H
IN FUNCTION OF P AT CONSTANT T BY MEASURING T DURING A CHANGE OF
PRESSURE OF A GAS.
• IT IS DEFINED THE JOULE-THOMSON COEFFICIENT AS
• THEN

HEATING AND COOLING BY JOULE-THOMSON
EXPERIMENT
• THE FOR EACH T AND P VALUES IN A JOULE-THOMSON EXPERIMENT, IS
OBTAINED BY FITTING THE EXPERIMENTAL DATA TO AN EXPRESSION OF T IN
FUNCTION OF P CURVE, AND WE FIND THE DERIVATIVE OF THE EXPRESSION IN
POINTS OF INTEREST.
• TO HEAT A GAS USING THE JOULE THOMSON EXPERIMENT WE HAVE TO WORK IN
T-P REGIONS WHERE IS NEGATIVE
• TO COOL A GAS WE HAVE TO WORK IN REGIONS T-P REGIONS WHERE IS
POSITIVE

THE JOULE THOMSON COEFFICIENT IN
FUNCTION OF EASILY MEASURABLE SYSTEM
PROPERTIES

CALCULATION OF CHANGES IN STATE
FUNCTIONS IN A PROCESS
• CALCULATION OF ENTROPY CHANGE IN FUNCTION OF T AND P

CALCULATION OF CHANGES IN STATE
FUNCTIONS IN A PROCESS
• CALCULATION OF ENTHALPY CHANGE IN FUNCTION OF T AND P
• CALCULATION OF INTERNAL ENERGY CHANGE IN FUNCTION OF T AND P
• CALCULATION OF GIBBS ENERGY CHANGE IN FUNCTION OF T AND P
• CALCULATION OF HELMHOLTZ ENERGY CHANGE IN FUNCTION OF T AND P

REAL GASES; COMPRESSION FACTORS
• THE Z COMPRESSION FACTOR IS A MEASURE OF THE IDEALITY DEVIATION
• Z BECOMES 1 WHEN DENSITY IS IN THE LIMIT OF ZERO

REAL GASES; EQUATIONS OF STATE
• VAN DER WAALS
• REDLICH-KWONG EQUATION
• VIRIAL EQUATION OF STATE (FROM STATISTICAL MECHANICS)

• EXAMPLE: WHAT IS THE MOLAR VOLUME OF AR(G) AT 250,00K AND 1,0000ATM
• THE COMPRESSION FACTOR CAN BE EXPRESSED IN TERMS OF ATTRACTION AND
REPULSION FACTORS OF THE VAN DER WAALS EQUATION
b IS APPROXIMATELY THE MOLAR VOLUME OF THE LIQUID

• B IS APPROXIMATELY THE MOLAR VOLUME OF THE LIQUID SO AND WE
CAN EXPRESS THE FOLLOWING EXPANSION
• COMPARING WITH THE VIRIAL EQUATION OF STATE
• AND Z

REAL GASES MIXTURES
• TO RELATE A TWO PARAMETER EQUATION OF STATE WITH A REAL GAS MIXTURE
BEHAVIOR WE HAVE TO USE THE MIXING RULE:
• WE NOW REFER TO THE MEAN MOLAR VOLUME OF THE SYSTEM
• AND FOR THE LOW P VIRIAL EQUATION
• THE MIXING RULE FOR NON SIMILAR GASES

CONDENSATION OF GASES AND CRITICAL
PROPERTIES
• THE NORMAL TEMPERATURE BOILING POINT AND THE CRITICAL TEMPERATURE ARE BOTH
DEPENDENT ON INTERMOLECULAR FORCES, THEN, THEY ARE CORRELATED
• REMEMBER THAT THE AVERAGE MOLECULAR KINETIC ENERGY IS
• WHAT IS A FLUID? WHAT IS A LIQUID? WHAT IS A GAS? WHAT IS A SUPERCRITICAL FLUID?

CRITICAL PROPERTIES AND A, B PARAMETERS
RELATION
• THEN
Van der Waals
Redlich Kwong

CALCULATION OF LIQUID VAPOR EQUILIBRIA
• USING REDLICH-KWONG (EOS)
• The condition of liquid vapor equilibria is that a
molecule being transferred from the vapor to the liquid
phase (or visc.) must not change the Gibbs free energy
of the system.

CALCULATION OF LIQUID VAPOR EQUILIBRIA
• USING REDLICH-KWONG (EOS)

SOAVE REDLICH KWONG (SRK) EQUATION OF
STATE

THE LAW OF CORRESPONDING STATES
• THE VALUES OF CERTAIN PHYSICAL PROPERTIES OF A GAS DEPENDS ON THE
PROXIMITY OF THE GAS TO ITS CRITICAL STATE
• FOR HE AND H, ADJUSTED CRITICAL PROPERTIES
MUST BE USED

GAS MIXTURES AND COMPRESSIBILITY CHARTS
• THE KAY’S RULE

REAL GAS THERMODYNAMIC PROPERTIES
CHANGES RELATIVE TO IDEAL VALUES
• IT IS POSSIBLE TO USE ANY OF THE REAL GAS EQUATIONS OF STATE TO FIND
EXPRESSIONS FOR:

CHEMICAL POTENTIAL
• FOR A SYSTEM UNDERGOING A COMPOSITION CHANGE DUE TO AN IRREVERSIBLE
REACTION OR MASS TRANSFER (WITHIN THE PHASES OF THE SYSTEM OR
BETWEEN THE SYSTEM AND SURROUNDINGS) THE GIBBS FREE ENERGY IS ALSO A
FUNCTION OF COMPOSITION.
• NOW WE CAN CONSIDER WHAT HAPPENS WITH THE SYSTEM PROPERTIES DUE TO
THE IRREVERSIBLE CHANGE OF MATTER (REMEMBER THAT A CHANGE IN A STATE
BY AN IRREVERSIBLE PROCESS CAN BE CALCULATED SUPPOSING A REVERSIBLE
PROCESS)

CHEMICAL POTENTIAL IN ONE PHASE SYSTEM• FOR A REVERSIBLE PROCESS:

CHEMICAL POTENTIAL IN Α PHASE SYSTEMS• THE TOTAL FREE GIBBS ENERGY IS EXPRESSED AS:
• CONSIDERING AN INFINITESIMAL CHANGE IN G IN PHASE Α;
• IT IS POSSIBLE TO WRITE AN INFINITESIMAL CHANGE OF G IN THE SYSTEM AS:
• FINALLY

MATERIAL EQUILIBRIUM AND CHEMICAL
POTENTIAL
• MATERIAL EQUILIBRIUM
• REVERSIBLE PROCESS
• REMEMBER THAT WHEN EQUILIBRIUM IS REACHED UNDER CONDITIONS OF
CONSTANT T AND P, THEN G IS MINIMIZED AND WHEN THE SYSTEM REACHES THE
EQUILIBRIUM UNDER CONDITIONS OF CONSTANT T AND V, THEN A IS MINIMIZED.

WHAT IS CHEMICAL POTENTIAL?
• IT IS AN INTENSIVE PROPERTY
• IT DEPENDS ON T, P AND NI OR XI.
• THE CHEMICAL POTENTIAL OF SUBSTANCE I EXPRESS HOW IS THE CHANGE OF G
WHEN N MOLES OF I ARE ADDED TO THE SOLUTION.
• CHEMICAL POTENTIAL IS STILL DEFINED FOR A SUBSTANCE THAT IS ABSENT FROM
THE SOLUTION.
• FOR THE SIMPLEST SYSTEM:

PHASE EQUILIBRIUM
• IN A SEVERAL PHASE SYSTEM THAT IS IN EQUILIBRIUM, WHERE dnJ MOLES OF J ARE
FLOWING FROM PHASE Β TO PHASE Δ THE CONDITION OF PHASE EQUILIBRIUM IS
DEFINED BY:
• SUPPOSE THE SAME PHASE SYSTEM TO BE SPONTANEOUSLY REACHING THE
EQUILIBRIUM AT CONSTANT T AND P:
• ALSO:

PHASE EQUILIBRIUM
• IN A SEVERAL PHASE SYSTEM THAT IS IN EQUILIBRIUM, WHERE DNJ MOLES OF ARE
FLOWING FROM PHASE Β TO PHASE Δ THE CONDITION OF PHASE EQUILIBRIUM IS
DEFINED BY:
• SUPPOSE THE SAME PHASE SYSTEM TO BE SPONTANEOUSLY REACHING THE
EQUILIBRIUM AT CONSTANT T AND P:
• ALSO:

EXTENT OF REACTION ξ
• FOR ANY REACTION:
• WE DEFINE THE EXTENT OF REACTION Ξ AS THE PROPORTIONALITY CONSTANT
BETWEEN THE STOICHIOMETRIC COEFFICIENTS OF THE REACTION AND CHANGE
IN MOLES OF EACH SUBSTANCE.

REACTION EQUILIBRIUM
• THE CONDITION OF MATERIAL EQUILIBRIUM IS:
• IN TERMS OF EXTENT OF REACTION:

CHEMICAL POTENTIAL IN IDEAL GASES
• AS PRESSURE GOES TO ZERO, ENTROPY GOES TO INFINITY AND THAT FACT
DEFINES THE BEHAVIOR OF CHEMICAL POTENTIAL IN FUNCTION OF PRESSURE
FOR AN IDEAL GAS.
• AN IDEAL GAS MIXTURE MUST OBEY THE PURE-IDEAL
-GAS CONDITIONS AND ALSO THE LAW OF PARTIAL PRESSURES;
THEY ARE EQUAL TO THE PRESSURES OF PURE GASES AT THE
SAME CONDITIONS:

CHEMICAL POTENTIAL IN IDEAL GAS MIXTURE

IDEAL GAS REACTION EQUILIBRIUM
Standard Equilibrium
Constant
Equilibrium Constant

IDEAL GAS REACTION EQUILIBRIUM

CONCENTRATION AND MOLE FRACTION
EQUILIBRIUM CONSTANTS

TEMPERATURE DEPENDENCE OF EQUILIBRIUM
CONSTANT
• THE VANT’T HOFF EQ.
Constant enthalpy of reaction Constant delta(Cp)

TEMPERATURE DEPENDENCE OF EQUILIBRIUM
CONSTANT

PHASE EQUILIBRIUM; THE PHASE RULE
IT MAKE SENSE TO TRY SOLVING THE EQUATIONS THAT RELATE THE INTENSIVE
VARIABLES OF THE SYSTEM TO SPECIFY ITS INTENSIVE THERMODYNAMIC STATE.
IT MEANS TO KNOW ALL THE MOLAR FRACTIONS IN ALL PHASES, T AND P.
THE TOTAL INTENSIVE VARIABLES ARE:
IT IS POSSIBLE TO RELATE THE MOLAR FRACTIONS WITH ONE EQUATION IN EACH
PHASE, EG. SO WE CAN FORGET A NUMBER OF P
VARIABLES BECAUSE THEY ARE DEPENDENT.
IT IS POSSIBLE TO STATE C(P-1) PHASE EQUILIBRIUM CONDITION EQUATIONS, AND
EACH THEM ALLOW US TO FORGET ONE DEPENDENT COMPONENT.
THEN WE HAVE THE GENERAL PHASE RULE THAT LET US TO OBTAIN THE NUMBER
OF INDEPENDENT VARIABLES THAT NEED TO BE FIXED TO SPECIFY THE INTENSIVE

• WHEN THERE IS A REACTION HAPPENING IN THE SYSTEM WE CAN DROP A
NUMBER OF INTENSIVE VARIABLES EQUAL TO THE NUMBER OF CHEMICAL
REACTIONS (R) CONSIDERING THAT EACH OF THEM ALLOWS TO WRITE AN
EQUILIBRIUM CONDITION.
• ALSO WE CAN DROP A NUMBER OF INTENSIVE VARIABLES EQUAL TO SPECIAL
STOICHIOMETRIC OR NEUTRALITY CONDITIONS (A). Independent
Components

STOICHIOMETRIC OR NEUTRALITY CONDITIONS (A).

ONE COMPONENT, PHASE EQUILIBRIUM
STOICHIOMETRIC OR NEUTRALITY CONDITIONS (A).

ONE COMPONENT, PHASE EQUILIBRIUM
• OA AND AC SHOW THE BEHAVIOR OF SOLID VAPOR PRESSURE AND LIQUID VAPOR
PRESSURE IN FUNCTION OF TEMPERATURE

ENTHALPIES AND ENTROPIES OF PHASE
CHANGES
• STARTING FROM LIQUID VAPOR EQUILIBRIUM, BY LOWERING PRESSURES THE
VAPOR PHASE BECOMES MORE STABLE BECAUSE OF ITS GREAT DECREASING OF
GIBBS FREE ENERGY.
• INCREASING TEMPERATURE FAVORS THE ENTROPY CONTRIBUTION TO THE
MOLAR GIBBS FREE ENERGY AND GAS PHASE IS FAVORED.
• DECREASING TEMPERATURE FAVORS THE ENTHALPY CONTRIBUTION TO THE
MOLAR GIBBS FREE ENERGY AND LIQUID PHASE IS FAVORED.
• THE TROUTON’S RULE
• THE TROUTONS-HILDEBRAND-EVERETT’S RULE

ENTHALPIES AND ENTROPIES OF PHASE
CHANGES
• THE TROUTON’S RULE
• THE TROUTONS-HILDEBRAND-EVERETT’S RULE

THE CLAPEYRON EQUATION
• THE CLAPEYRON EQUATION PREDICTS THE BEHAVIOR OF THE SLOPE OF PHASE
EQUILIBRIA LINES.

• LIQUID-VAPOR AND SOLID-VAPOR EQUILIBRIUM
Take care!!!

• SOLID-LIQUID EQUILIBRIUM

THE ANTOINE EQUATION
• THE ANTOINE EQUATION IS AN EMPIRICAL EXPRESSION THAT WORKS VERY WELL
BETWEEN 10 AND 1500 TORR AND RELATES THE VAPOR PRESSURE OF A
SUBSTANCE WITH TEMPERATURE.

SOLUTIONS; PARTIAL MOLAR QUANTITIES
• A START ABOVE A PROPERTY MEANS THE PROPERTY OF A PURE SUBSTANCE OR THE
PROPERTY OF A COLLECTION OF PURE SUBSTANCES.
• BUT IN GENERAL THE PROPERTY OF A SOLUTION IS DIFFERENT TO THE PURE
SUBSTANCE PROPERTY SUM
• SO… WE KNOW THAT ALL PROPERTIES OF A SYSTEM ARE FUNCTIONS OF T, P AND NI:
• AND WE DEFINE THE PARTIAL MOLAR VOLUME OF J AS

• REMEMBER THAT FOR A PURE SUBSTANCE SYSTEM, Μ=GM. IN SIMILAR WAY BUT
IT DOES NOT MEANS THAT THE PARTIAL MOLAR VOLUME OF COMPONENT IN A
SOLUTION IS EQUAL TO THE MOLAR VOLUME OF PURE J.
• IF ALL INTENSIVE PROPERTIES ARE FIXED:
DIFFERENTIATION:
AND WE KNOW THAT: OR
SO OR

• SIMILAR TO THE PARTIAL MOLAR VOLUMES:
• IN GENERAL

RELATIONS BETWEEN PARTIAL MOLAR
QUANTITIES
• WE KNOW THAT G=H-TS SO:
• ALSO , THEN:
• IN SIMILAR WAY: AND

IMPORTANCE OF CHEMICAL POTENTIAL
• CHEMICAL POTENTIAL IS USED TO DEFINE REACTION AND PHASE EQUILIBRIA, BUT
ALSO IS USED TO FIND ALL OTHER PARTIAL MOLAR PROPERTIES AND ALL
THERMODYNAMIC PROPERTIES.

MIXING QUANTITIES
• IN MOST CASES WHEN YOU MAKE A SOLUTION, THERE IS DIFFERENCE BETWEEN THE
SUM OF THE PURE COMPONENT PROPERTIES AND THE REAL VALUE OF THE PROPERTY.
WE CALL SUCH A DIFFERENCE MIXING QUANTITIES.
Mixing properties relations

DETERMINATION OF MIXING QUANTITIES
• WE CAN FIND THE MIXING VOLUME BY MEASURING THE DEINSITIES OF THE SOLUTION
AND THE PURE COMPONENTS AT P, T AND X. OR WE CAN DIRECTLY MEASURE THE
CHANGE IN VOLUME WHEN A COMPONENT IS ADDED AT CONSTANT T. THE MIXING
ENTHALPY CAN BE FOUND WITH A CONSTANT PRESSURE CALORIMETER
• FOR MIXING GIBBS FREE ENERGY WE HAVE:

DETERMINATION OF PARTIAL MOLAR
QUANTITIES

INTEGRAL AND DIFFERENTIAL HEATS OF
SOLUTIONS
At infinite dilution

IDEAL SOLUTIONS
• SOME OF THE MIXTURES THAT CAN BE CONSIDERED IDEAL ARE
• ISOTOPIC MIXTURE
• BENZENE-TOLUENE
•
•
•

THERMODYNAMIC FUNCTIONS OF IDEAL
SOLUTIONS
• MIXING GIBBS FREE ENERGY
CYCLOHEXANE-CYCLOPENTANE
BENZENE-DEUTERATED BENZENE
• MIXING ENTROPY

CHEMICAL POTENTIAL OF IDEAL SOLUTIONS
• AS NOTED EARLIER
AND WE CAN WRITE
SO
THAT HOLDS ONLY IF
• NOTE THAT ΜI INCREASES AS XI INCREASES
• IN SUMMARY

VAPOR PRESSURE OF IDEAL SOLUTIONS
(RAOULT’S LAW)
• THE CONDITION OF PHASE EQUILIBRIUM IS:
• SUPPOSING A PURE SUBSTANCE SYSTEM:
• USING THE SECOND AND THIRD EQUATIONS:
• REMEMBER THAT THE PROPERTIES OF A LIQUID VARY SLOWLY WITH PRESSURE, SO:
• AND THE RAOULT’S LAW:

(RAOULT’S LAW)
• OTHER USEFUL FORM OF THE ROULT’S LAW IS:
• AND FOR TWO COMPONENTS:
• THE LAST FORM MEANS THAT
THE TOTAL VAPOR PRESSURE OF
AN IDEAL SOLUTION VARIES
LINEARLY WITH THE MOLE
FRACTION OF A COMPONENT
IN A TWO COMPONENTS SYSTEM.

(RAOULT’S LAW)
• OTHER USEFUL FORM OF THE ROULT’S LAW IS:
• AND FOR TWO COMPONENTS:
• THE LAST FORM MEANS THAT
THE TOTAL VAPOR PRESSURE OF
AN IDEAL SOLUTION VARIES
LINEARLY WITH THE MOLE
FRACTION OF A COMPONENT
IN A TWO COMPONENTS SYSTEM.
Note that an ideal gas mixtu
Is an ideal solution, so:

IDEALLY DILUTE SOLUTIONS
• IN AN IDEALLY DILUTE SOLUTIONS, SOLUTE MOLECULES INTERACT ESSENTIALLY
ONLY WITH SOLVENT MOLECULES BECAUSE OF THE HIGH DILUTION OF SOLUTES
At low
concentrations

VAPOR PRESSURE IN IDEALLY DILUTE
SOLUTIONS (HENRY’S LAW)
• IN AN IDEALLY DILUTE SOLUTIONS, SOLUTE MOLECULES INTERACT ESSENTIALLY
ONLY WITH SOLVENT MOLECULES BECAUSE OF THE HIGH DILUTION OF SOLUTES

VAPOR PRESSURE IN IDEALLY DILUTE
SOLUTIONS (HENRY’S LAW)
• SOLVENTS OBEY RAOULT’S LAW AND SOLUTES HENRY’S LAW

SOLUBILITY OF GASES IN LIQUIDS
• FOR GASES THAT ARE SOLUBLE IN A GIVEN LIQUID THE CONCENTRATION OF THE
GAS IS LOW ENOUGH TO CONSIDER THE SOLUTION AS IDEALLY DILUTED. SO HENRY
LAW HOLDS WELL
At low concentrations

VAPOR PRESSURE LOWERING
• IT HOLDS IN SOLUTIONS WHERE THE SOLUTES ARE NON-VOLATILE (SOLID SOLUTES)
Equal to 1 for ideally diluted solutions
Elevation of boling point

FREEZING POINT DEPRESSION
• IT HOLDS IN SOLUTIONS WHERE THE SOLUTES ARE NON-VOLATILE (SOLID SOLUTES)

OSMOTIC PRESSURE
• CHEMICAL POTENTIAL IS LOWER IN THE SOLUTION SO SOLVENT TENDS TO FLOW
THROUGH THE SEMIPERMEABLE MEMBRANE TO EQUATE THE CHEMICAL POTENTIALS

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