Electrolyte Solutions

From JM Prausnitz, RN Lichtenthaler, and E Gomes de Azevedo

“Molecular Thermodynamics of Fluid Phase Equilibria” Prentice Hall

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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

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Activity coefficients

• Non-volatile solute + volatile solvent:

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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)

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Chemical potential of the solute

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Activity of non-dissociating solute

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Units

• Molarity (moles of solute/liter of solution),ci

• Molality (moles of solute /kg solvent), mi

• Mole fraction, xi

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Activity of the solvent

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Osmotic pressure

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Van’t Hoff equation

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At finite concentrations

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Osmotic coefficient

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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

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Chemical potential of an electrolyte

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mean ionic molality and mean ionic activity coefficient

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examples

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examples

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Experimental mean activity coefficients

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Standard state for a dissociating electrolyte

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Osmotic coefficient of the solvent and mean ionic activity coefficient

An electrolyte MX completely dissociated in solvent S

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Osmotic coefficient of the solvent and mean ionic activity coefficient

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Osmotic coefficient of the solvent and mean ionic activity coefficient

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Debye-Hückel limiting law

Ionic strength

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Forces among ions

Long-range electrostatic attractions and repulsions

Short-range interactions between ions and ion-solvent

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Debye-Hückel limiting law

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Debye length– Screening of charges

To account for shielding,

Shielding length,

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Debye length– Screening of charges

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Activity coefficient of ions

According to Debye-Hückel theory,

Mean activity coefficient

Osmotic coefficient

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Mean activity coefficient for strong electrolytes

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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

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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

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Semi-empirical corrections to Debye-Hückel

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

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Setchenov equation

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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

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Application of Setchenov’s equation to organic molecules

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Effect of salt on VLE

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Salt effects on VLE

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Concentrated ionic solutions

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For a binary

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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

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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.

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

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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