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

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

Activity coefficients Non-volatile solute + volatile solvent:

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)

Chemical potential of the solute

Activity of non-dissociating solute

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

Activity of the solvent

Osmotic pressure

Van’t Hoff equation

At finite concentrations

Osmotic coefficient

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

Chemical potential of an electrolyte

mean ionic molality and mean ionic activity coefficient

examples

examples

Experimental mean activity coefficients

Standard state for a dissociating electrolyte

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

Osmotic coefficient of the solvent and mean ionic activity coefficient

Osmotic coefficient of the solvent and mean ionic activity coefficient

Debye-Hückel limiting law Ionic strength

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

Debye-Hückel limiting law

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

Debye length– Screening of charges

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

Mean activity coefficient for strong electrolytes

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

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

Semi-empirical corrections to Debye-Hückel

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

Setchenov equation

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

Application of Setchenov’s equation to organic molecules

Effect of salt on VLE

Salt effects on VLE

Concentrated ionic solutions

For a binary

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

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.

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

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