Solid-vapor equilibrium (SVE) and Solid-liquid equilibrium (SLE) Chapter 14-Part VIII Solid-vapor equilibrium (SVE) and Solid-liquid equilibrium (SLE)

A solid can vaporize at T < T triple point; pressures along the sublimation curve are called saturation pressures of the solid

Lets consider SVE of a pure solid (1) and a vapor mixture Species 2 does not dissolve in the solid phase; In the vapor phase usually 2 is the solvent; 1 is the solute Vapor mixture of 1 and 2 Solid 1 We want to calculate the solubility of 1 in the vapor phase as a function of T and P

SVE for component 1: We model the solid phase with the same equation of the liquid (is a condensed phase)

Solubility of 1 in the vapor phase How this expression may reduce at low pressures?

Simplifications to the equation Solubilities of solids in fluids at high pressures important for separation processes Examples: extraction of caffeine from coffee, separation of asphaltenes from heavy petroleum fractions Usually P1sat is very small; Saturated vapor can be considered ideal gas Also if y1 is very small,

Simplified equation The fugacity coefficient at infinite dilution can be calculated from an EOS Where aij is calculated as aij =(1-lij)(aiaj)1/2 lij is a cross-coefficient for the mixture

Solubility of a solid in a gas Estimate the solubility of naphthalene in carbon dioxide at 1 bar and temperatures of 35 and 60.4 oC assuming that the solid is incompressible, and the solid and fluid phases may be considered ideal.

Solving at each temperature T = 35 oC; Pnsat = 2.789 x10-4 bar; yN =0.00028 T = 60.4 oC; Pnsat = 2.401 x10-3 bar; yN =0.0024

Lets consider the effect of pressure Estimate the solubility of naphthalene in carbon dioxide at 1 bar and temperatures of 35 oC and pressures from 1 bar to 60 bar using the virial equation of state with the following values for the second virial coefficient B(CO2-naphthalene) = -345 cc/mol B (CO2-CO2) = -96.5 cc/mol B(naphthalene-naphthalene) = -1850 cc/mol Assume that CO2 is insoluble in solid naphthalene, and therefore only equate the fugacities of naphthalene in the solid and vapor phases. Since the fugacity coefficient is a function of y1 iterate

SLE: solid-liquid equilibria

Solid-liquid equilibria (SLE)

Solid-Liquid Equilibria (SLE)

SLE-cont. T-effect on fugacity

SLE-cont. The enthalpies are functions of T (through the Cp dependence on T)

SLE (cont.)

Simplifications Triple integral I is usually neglected Heat capacity change of melting usually not available Therefore For all components

SLE-Typical cases A) Assume ideal-solution behavior for both phases for all T and compositions Gives a normal T-x phase diagram

SLE-typical cases B) Assume ideal behavior for the liquid phase and complete immiscibility for all species in the solid state=>

For case B: Liquid + solid 1 Liquid + solid 2 Both equations apply at the eutectic point

Example: SLE Estimate the solubility of solid naphthalene in liquid n-hexane at 20 oC. Data Naphthalene MW = 128.19 Melting point: 80.2 oC Heat of fusion: 18.804 kJ/mol Density of the solid: 1.0253 g/cc at 20oC Density of the liquid: 0.9625 g/cc at 100 oC Vapor pressure of the solid: log P (bar) = 8.722 -3783/T (T in K) The heat capacities of liquid and solid naphthalene may be assumed to be equal If DCp =0, The result is x1 = 0.269, the experimental result is x1 = 0.09 How can we correct the answer?

Same example using UNIFAC to estimate the naphthalene activity coefficient Naphthalene has 8 aromatic CH (subgroup 10) and 2 aromatic C (subgroup 11) N-hexane has 2 CH3 (subgroup 1) and 4 CH2 (subgroup 2) groups.

Since g1 is a function of x1, we need to iterate in x1 Solving for x1 yields x1 =0.124, 38% larger than the experimental value

Calculation of activity coefficient from solubility data The following data has been reported for benzo-pyrene and its solubility in water at 25 oC: Melting point: 178.1 oC Heat of fusion: 15.1 kJ/mol Solubility in water: xBP =3.37x10-10 Estimate the activity coefficient of benzo-pyrene in water at 25 oC

Calculation is similar to previous example Note that in this case the correction given by the activity coefficient is HUGE !!!! Important in applications when we are interested in the distribution of a chemical species between air, water, soil. Since the concentration of benzopyrene is small, the calculated activity coefficient is the infinite diluted activity coefficient.