1. G.H. Patel College of Engineering and Technology
Chemical Engineering Thermodynamics – ( )
TOPIC :-Excess Gibbs Free Energy And Activity co-efficient and model for
The Excess Gibbs Free Energy

2. PREPARED BY Guided By PATEL JAY (130110105027)
PATEL KUNDANIKA ( )
PATEL KUNJAN ( )
PATEL MITESH ( )
PATEL NILKANTH ( )
Guided By
Prof. Harish. K .Dave

3. Content Gibbs Free Energy Activity Co-efficient Ionic Strength(I or µ)
calculation of Ionic Strength(I or µ)
Relation Between Excess Free Energy And Activity coefficient
Gibbs free energy change of mixing

4. Gibbs Free Energy
The combination of Entropy, Temperature and Enthalpy explains whether a reaction is going to be spontaneous or not.
The symbol ∆G is used to define the Free Energy of a system. Since this was discovered by J.
Willard Gibbs it is also called the Gibbs Free Energy.

5. “Free energy” refers to the amount of energy available to do work once you have paid your price to entropy. Note that this is not given simply by ∆H, the heat energy released in a reaction.
∆Go =  ∆Ho - T∆So
Where,
∆Go = Excess Gibbs Free Energy
∆Ho = Enthalpy
∆So = Entropy
T = Temperature

6. When ∆G is Negative, it indicates that a reaction or process is spontaneous. A Positive ∆G indicates a non-spontaneous reaction.
∆G = ∆H - T∆S
Entropies are given in units of J/K.mol
Enthalpies and Free Energies are in kJ/mol.
DON'T forget to convert all units to kJ or J when using both ∆S and ∆H in the same equation!!

7. The Effect of Temperature on the Free Energy of a Reaction
Reactions are classified as either Exothermic (H < 0) or Endothermic (H > 0) on the basis of whether they give off or absorb heat. Reactions can also be classified as Exergonic (G < 0) or Endergonic (G > 0) on the basis of whether the free energy of the system decreases or increases during the reaction.
The Effect of Temperature on the Free Energy of a Reaction
Practice Problem
Use the values of   ∆H and  ∆S to predict whether the following reaction is spontaneous at 25C:

8. N2(g) + 3 H2(g) 2 NH3(g) ∆ H = -92.22 kJ (favourable)
∆ S = J/K    (unfavourable)
Before we can compare these terms to see which is larger, we have to incorporate into our calculation the temperature at which the reaction is run:
TK = 25o C = K
We then multiply the entropy of reaction by the absolute temperature and subtract the T∆So term from the  ∆Ho term:
∆Go =  ∆Ho - T∆So
            = -92,220 J - ( K x J/K)
        = -92,220 J + 59,260 J
= -32,960 J
∆Go = kJ

9. Activity Co-efficient
An activity coefficient is a factor use in thermodynamics to account for deviations from ideal behaviour in a mixture of chemical substances.
In an ideal mixture, the microscopic interactions between each pair of chemical species are the same (or macroscopically equivalent, the enthalpy change of solution and volume variation in mixing is zero) and, as a result, properties of the mixtures can be expressed directly in terms of simple concentrations or partial pressures of the substances present e.g. Raoult's law.

10. Deviations from ideality are accommodated by modifying the concentration by an activity coefficient.
Activity and concentration are related through the activity coefficient according to :
ai = ϓi . Mi
Activity coefficient different from unity arise because of the interaction of ions as concentration rises.
The degree of ion interaction depends on ionic charge as well as concentration.

11. Ionic Strength(I or µ)
ionic strength is a measure of the total ion concentration in solution but ions with more charge are counted more due to stronger electrostatic interactions with other ions.
Where,
ci is conc. of ith species
zi is the charge on ith species

12. Calculation of ionic strength
What is ionic strength of 0.01 M NaCl solution?
µ = 1/2 ([Na+]zNa2 + [Cl-]zCl2 )
= 1/2 (0.01 (1) (-1)2)
= 0.01 M
Once you know ionic strength of a solution you can calculate the Activity Coefficients ( γi ) of ions in that solution

13. Activity = ai = γi[i]
Activity is simply the concentration of the species times the activity coefficient.
For all chemical equilibria strictly speaking we should write in terms of activity units not concentration of species
for A + B <------> C + D ;
for solubility products: Ksp(AB) = [A]γA [B]γΒ
So if solubility increases with ionic strength, meaning that concentrations increase, then activity coefficients decrease as you increase ionic strength.

14. Relation Between Excess Free Energy And Activity coefficient
Relationship Between Excess Free Energy And Activity coefficient can be represent by three Equations
WHOL’S THREE SUFFIX EQUATION
MARGULES EQUATION
VAN LAAR EQUATION

15. WHOL’S THREE SUFFIX EQUATION
Most of the equations relating the activity co-efficient γi and composition of the solution where derived from the excess free energy relationship.
Whol proposed, statistically a general method for expressing excess free energy and provided some rough physical significance to the various parameters appearing in the equations.

16. WHOL’S THREE SUFFIX EQUATION

17. When the term is unity then the co-relation between Z &q may reduce to,
Similarly,

18. This equation for excess free energy contained terms for composition, effective molar volumes and effective volumetric fractions of the separate constituents of a solution.

19. MARGULES EQUATION
Similarly we can find

20. The Margules equation adequately represents the V. L. E
The Margules equation adequately represents the V.L.E. data of the systems like acetone-methanol, acetone-chloroform, chloroform-methanol etc.
The V.L.E. data of argon-oxygen, benzene-cyclohexane etc. are well represented by Margules Two Suffix Equation.

21. VAN LAAR EQUATION

22. The Van Laar equation may be rearrange to the following forms which are very convenient for the evaluation of constants A & B.

23. Gibbs free energy change of mixing
Gibbs free energies of mixing for a hypothetical binary solution. Negative free energy of mixing (a) mean that there is a thermodynamic driving force for mixing to occur (i.e. it will occur spontaneously), while a positive free energy of mixing (b) mean that the pure components will not mix.

24. For given temperature and pressure, the gibbs energy of a real mixture differ from the Gibbs energy of the hypothetical ideal mixture of the same components. Difference between the two is the excess gibbs energy.

25. Depending on the relative values of ∆Hmix and -T∆Smix, the free energy of mixing may be negative throughout the whole composition range if the enrropic energy contribution outweighs the enthalpy increase: this is e likely at higher temperature.

26. THANK YOU!!!