MOSCED

Basic principle

MOSCED uses component-specific parameters describing electronic properties of a compound. These five properties are partly derived from experimental values and partly fitted to experimental data. In addition to the five electronic properties the model uses the molar volume for every component.

These parameters are then entered in several equations to obtain the limiting activity coefficient of an infinitely diluted solute in a solvent. These equations have further parameters which have been found empirically.

The authors found an average absolute deviation of 10.6% against their database of experimental data. The database contains limiting activity coefficients of binary systems of non-polar, polar and hydrogen compounds, but no water. As can be seen in the deviation chart, the systems with water deviate significantly.

Equations

ln ⁡ γ 2 ∞ = ν 2 R T [ ( λ 1 − λ 2 ) 2 + q 1 2 q 2 2 ( τ 1 T − τ 2 T ) 2 ψ 1 + ( α 1 T − α 2 T ) ( β 1 T − β 2 T ) ξ 1 ] + d 12

d 12 = ln ⁡ ( ν 2 ν 1 ) a a + 1 + ( ν 2 ν 1 ) a a

a a = 0.953 − 0.002314 ( ( τ 2 T ) 2 + α 2 T β 2 T )

α T = α ( 293 K T ) 0.8 , β T = β ( 293 K T ) 0.8 , τ T = τ ( 293 K T ) 0.4

ψ 1 = P O L + 0.002629 α 1 T β 1 T

ξ 1 = 0.68 ( P O L − 1 ) + [ 3.4 − 2.4 exp ⁡ ( − 0.002687 ( α 1 β 1 ) 1.5 ) ] ( 293 K / T ) 2

P O L = q 1 4 [ 1.15 − 1.15 exp ⁡ ( − 0.002337 ( τ 1 T ) 3 ) ] + 1

with

Important note: The value 3.4 in the equation for ξ is different from the value 3.24 in the original publication. The 3.24 has been verified to be a typing error.

The activity coefficient of the solute and solvent can be extended to other concentrations by applying the principle of the Margules equation. This gives:

ln ⁡ γ 2 = ( ln ⁡ γ 2 ∞ + 2 ( ln ⁡ γ 1 ∞ − ln ⁡ γ 2 ∞ ) Φ 2 ) Φ 1 2

ln ⁡ γ 1 = ( ln ⁡ γ 1 ∞ + 2 ( ln ⁡ γ 2 ∞ − ln ⁡ γ 1 ∞ ) Φ 1 ) Φ 2 2

where

Φ i = x i ν i ∑ j ν j x j

is the volume fraction and x i the mole fraction of compound i. The activity coefficient of the solvent is calculated with same equations, but interchanging indices 1 and 2.

Model parameters

The model uses five component specific properties to characterize the interaction forces between a solute and its solvent. Some of these properties are derived from other known component properties and some are fitted to experimental data obtained from data banks.

Liquid molar volume

The molar liquid volume ν is given in cm³/mol and assumed to be temperature-independent.

Dispersion parameter

The dispersion parameter λ describes the polarizability of a molecule.

Polarity parameter

The polarity parameter τ describes the fixed dipole of a molecule.

Induction parameter

The induction parameter q describes the effects of induced dipoles (induced by fixed dipoles). For structures with an aromatic ring the value is set to 0.9, for aliphatic rings and chains this value is set on 1. For some compounds the q-parameter is optimized between 0.9 and 1 (e.g. hexene, octene).

Acidity and basicity parameters

These parameters describe the effects of hydrogen-bonding during solving and association.