**Activity, excess functions and Activity Coefficients**

**Student: Isis Hernández R.**

Proffesor: Rigoberto Rios

Proffesor: Rigoberto Rios

**Advanced Thermodynamics**

The function Activity...

It´s auxiliary thermodynamic property

related to the Gibbs energy, applicable primarily to:

Liquid and Solid phases

Activity Coefficient...

These is a measure of the nonideality. Represent the deviations from the ideal behavior, and act as correction factors Raoult's law modificated.

Excess property...

It´s a deviation of mixture (real value) from ideal dilution behavior at same P, T and X.

tendency to escape

This functions are able to express the Gibbs free energy (and thus the conditions of phase equilibrium and chemical equilibrium) as a function of the thermodynamic variables of the gas.

Using for component of solution

Activity Coefficient

Van Laar

Without many different chemical components, except for the size of their molecules

Margules

Solution binary whose components are not very different in molecular size.

Wilson

NTRL

Applicable to systems partial miscibility. Strongly nonideal

UNIFAC

UNIQUAC

By binary sistem

References

Gamero R. Termodinámica Avanzada. Termodínamica del equilibrio. Mezclas Líquidas. En línea: http://www.sarec-fiq.edu.ni/pmciq/che570/pdf/3g.pdf

Valid for simple solutions preferably non-polar

Empirical

If constant of Van Laar A´ and B´ is equal, so...

http://www.slideshare.net/cruizgaray/coeficientes-de-actividad

http://dspace.ubu.es:8080/tesis/bitstream/10259/155/1/Aguilar_Romero.pdf

http://depa.fquim.unam.mx/amyd/archivero/soluciones_reales_5181.pdf

http://www.uib.es/facultat/ciencies/prof/juan.frau/qfI/teoria/tema12.pdf

The parameters have physical meaning:

Effective volume of the molecules (as the size of the molecule).

Interaction parameters similar to the virial coefficients

a

b

Reason A´, B´ it´s same q1 and q2 and Activity coefficient at infinite dilution

q1 =q2

Gibbs Energy in excess associated with the molar fractions. Using for solutions polar compounds or solvents no polar.

Activity Coefficients

parameters

Limit condition:

GE=0 if x1 or x2

Can be easily extended to multicomponent mixtures.

Doesn´t apply to Liquid-liquid equilibrium.

Wilson parameters report to binary, ternary and quaternary system

Difference

Characteristic

Energy

Parameter alpha related non random in mixture. The components fallow pattern defined by the

local composition.

If

Mixture is random (Equal Margules)

Wilson...

Thanks!

**Property relationships for mixtures:**

Molar Excess:

Molar Partial:

For liquid disolutions:

Integrate from the pure state to its state in the solution at a molar fraction x

The necessary condition for that a liquid phase is in equilibrium is that it behaves like an ideal solution.

The activity coefficient can related to the excess Gibbs energy since ln(lamba) is a partial property regarding GE/ RT

Using Euler Theorem for homogeneous functions:

Dividing by n (moles)

Additionability equation

M of a mixture it´s obtained by aggregation of partial properties of its components with a weight proportional to amount present

EXAMPLE:

For binary solution:

Thermody. Functs:

Raoult´s law

Modified

Data and results

Show that:

Graphic:

Smith And Van Ness, Introducción a la Termodinámica en Ingenieria Química

Tester J, Modell M, Thermodynamics and its applications

Reference state

Gibbs molar

Replace:

where:

The reference State could be:

Pure

For most solutions a/x is not unit.

If M = (V, U, S or G)

By analogy, excess mixing functions: Whit M=B

use if one of the components doesn´t exist at pure liquid at T and P in question.

}

Pure component standard state, rational basis at T and P of mixture

Unit molality

Infinity dilution

Variation a miscible A-B solution

For Solute A, there are two different states:

Henry

For Solvent B, only one:

Rational

Base in mole fractions. In place of mole fractions we introduce molality (m) as composition parameter

Reference stady, at same P, T and sate aggregation as the mixture.

molality based (activity coefficients)

Limit by:

This relationship allows to obtain the effects to T and P

Properties for Methyl Ethyl Cetone(1)/Toluene(2)

others....

Lewis Randall

CALCULATION...