1. Electrolyte Solutions
From JM Prausnitz, RN Lichtenthaler, and E Gomes de Azevedo “Molecular Thermodynamics of Fluid Phase Equilibria” Prentice Hall

2. Relevance Partitioning processes in biochemical systems
Precipitation and crystallization in geo-thermal energy
Desalination of water
Water-pollution control
Salting-in and slating-out effects in extraction and distillation
Food processing
Production of fertilizers

3. Activity coefficients
Non-volatile solute + volatile solvent:

4. Standard states
For a simple liquid mixture (of volatile nonelectrolytes), standard state could be the pure liquid at T and P
For the mixture of a nonvolatile solute and a solvent, we use the same standard state for the solvent, but not for the solute (typically does not exist as a liquid at T&P)

5. Chemical potential of the solute

6. Activity of non-dissociating solute

7. Units Molarity (moles of solute/liter of solution),ci
Molality (moles of solute /kg solvent), mi
Mole fraction, xi

8. Activity of the solvent

9. Osmotic pressure

10. Van’t Hoff equation

11. At finite concentrations

12. Osmotic coefficient

13. Solution of an electrolyte
Solute dissociates into cations and anions.
Example: 1 mol of NaCl is dissolved in 1 kg of water gives 1 molal solution of NaCl that is fully dissociated into 1m of Na+ ions and 1 m of Cl- ions.
Condition of electroneutrality applies: the number of moles of cations and anions cannot be varied independently

14. Chemical potential of an electrolyte

15. mean ionic molality and mean ionic activity coefficient

16. examples

17. examples

18. Experimental mean activity coefficients

19. Standard state for a dissociating electrolyte

20. Osmotic coefficient of the solvent and mean ionic activity coefficient
An electrolyte MX completely dissociated in solvent S

21. Osmotic coefficient of the solvent and mean ionic activity coefficient

22. Osmotic coefficient of the solvent and mean ionic activity coefficient

23. Debye-Hückel limiting law
Ionic strength

24. Forces among ions Long-range electrostatic attractions and repulsions
Short-range interactions between ions and ion-solvent

25. Debye-Hückel limiting law

26. Debye length– Screening of charges
To account for shielding,
Shielding length,

27. Debye length– Screening of charges

28. Activity coefficient of ions
According to Debye-Hückel theory,
Mean activity coefficient
Osmotic coefficient

29. Mean activity coefficient for strong electrolytes

30. Conclusions about Debye-Hückel
Valid only for very low concentrations, mainly because of
Ion-ion repulsion (size effects)
Dispersion forces
Solvent is not a continuum

31. Semiempirical corrections to Debye-Hückel
Zemaitis et al, 1986
For aqueous solutions with I < 0.1 mol/kg
For I up to 1 mol/kg

32. Semi-empirical corrections to Debye-Hückel

33. Salting-out: decrease of gas solubility in a salt solution

34. Setchenov equation

35. Setchenov constants
If kMX is positive, “salting-out”, gas solubility decreases in salt solution
If kMX is negative, “salting-in”, gas solubility increases in salt solution

36. Application of Setchenov’s equation to organic molecules

37. Effect of salt on VLE

38. Salt effects on VLE

39. Concentrated ionic solutions

41. For a binary

46. Solubility product
If we know Ksp, and we can estimate the mean ionic activity coefficient and the activity of water, for example from Pitzer’s model, we can calculate the molalities of the individual species in solution

47. Estimates of Ksp
Ksp at a reference temeprature (for example 298 K) can be obtained from the standard Gibbs free energies of formation of the solid and aqueous species at the T of the solution (generally found in tables)
To obtain Ksp at a different T, we use the T-dependence of an equilibrium constant and integrate to the desired T. Usually we need enthalpy and Cp data for each species at the reference temperature.

48. Results for two solid salts in an aqueous ternary mixture (see procedure next slide)

49. To obtain molalities calculate Ksp at the appropriate T
fix m of one of the non-common ions and calculate m for the other ion; the procedure is iterative because both the mean activity coefficient and the solvent activity depend on the molalities
the intersection between the two curves gives points of equilibrium of two solids with an aqueous solution