# UNIQUAC

Activity coefficient en regression with UNIQUAC ( chloroform / methanol mixture)

UNIQUAC (Abbr. For English Universal Quasi Chemical ) is an activity coefficient model , the activity coefficient γ of the components in a chemical mixture with the compositions, expressed in terms of mole fractions correlated. ${\ displaystyle x _ {\ text {i}}}$

## Equations

In UNIQUAC, the activity coefficient of component i is made up of two components, the remaining component, which describes intermolecular forces, and the combinatorial component, the size and shape of the components:

${\ displaystyle \ ln \ gamma _ {\ text {i}} = \ ln \ gamma _ {\ text {i}} ^ {C} + \ ln \ gamma _ {\ text {i}} ^ {R}}$

### Combinatorial part

The combinatorial portion is calculated exclusively from substance-specific quantities, the relative van der Waals volumes and surfaces of the pure substances. ${\ displaystyle \ gamma ^ {C}}$${\ displaystyle r _ {\ text {i}}}$${\ displaystyle q _ {\ text {i}}}$

${\ displaystyle \ ln \ gamma _ {\ text {i}} ^ {C} = 1-V _ {\ text {i}} + \ ln V _ {\ text {i}} - 5q _ {\ text {i}} \ left (1 - {\ frac {V _ {\ text {i}}} {F _ {\ text {i}}}} + \ ln {\ frac {V _ {\ text {i}}} {F _ {\ text {i}}}} \ right)}$

with the volume fraction per mole fraction of component i ${\ displaystyle V _ {\ text {i}}}$

${\ displaystyle V _ {\ text {i}} = {\ frac {r _ {\ text {i}}} {\ sum _ {j} r _ {\ text {j}} x _ {\ text {j}}}} }$

and the surface area per mole fraction of component i ${\ displaystyle F _ {\ text {i}}}$

${\ displaystyle F _ {\ text {i}} = {\ frac {q _ {\ text {i}}} {\ sum _ {j} q _ {\ text {j}} x _ {\ text {j}}}} }$

### Remainder

The remainder, on the other hand, contains interaction parameters that are adapted to experimental and sometimes also estimated activity coefficients.

${\ displaystyle \ ln \ gamma _ {\ text {i}} ^ {R} = q _ {\ text {i}} \ left (1- \ ln {\ frac {\ sum _ {j} q _ {\ text { j}} x _ {\ text {j}} \ tau _ {\ text {ji}}} {\ sum _ {j} q _ {\ text {j}} x _ {\ text {j}}}} - \ sum _ {j} {\ frac {q _ {\ text {j}} x _ {\ text {j}} \ tau _ {\ text {ij}}} {\ sum _ {k} q _ {\ text {k}} x _ {\ text {k}} \ tau _ {\ text {kj}}}} \ right)}$

With

${\ displaystyle \ tau _ {\ text {ij}} = e ^ {- \ Delta u _ {\ text {ij}} / {RT}}}$

${\ displaystyle \ Delta u _ {\ text {ij}}}$ are the adjustable interaction parameters between components i and j.

## use

Activity coefficients make it possible to calculate phase equilibria (gas-liquid, liquid-liquid, solid-liquid) and some other thermodynamic quantities using simple relationships. Models such as UNIQUAC now make it possible, for example, in process simulation to perform complex calculations for any composition of a chemical mixture with only a few known parameters, without having to know experimental data for all the required points.

## parameter

UNIQUAC knows two fundamentally different parameters.

1. Relative van der Waals surfaces and volumes are material constants that must be known for all substances involved.
2. Interaction parameters between two components that describe the intermolecular forces. These parameters must be determined for all binary pairs in a mixture. In a quaternary mixture there are already six parameter sets (1-2, 1-3, 1-4, 2-3, 2-4, 3-4) and this number increases sharply with further components. The interaction parameters themselves are adapted to experimental activity coefficients or to phase equilibrium data from which activity coefficients can be derived. Another alternative is to determine activity coefficients with an estimation method such as UNIFAC and to adapt UNIQUAC parameters to these estimated activity coefficients. The advantage of the UNIQUAC parameters is the significantly simpler and therefore faster calculation compared to the direct use of the rather complex prediction method.

## Recent developments

UNIQUAC is being further developed in many working groups. Some selected derivatives are

• UNIFAC : A method that allows the volumes and surfaces as well as, in particular, the interaction contributions to be estimated. This eliminates the need to use experimental data to adjust the UNIQUAC parameters.
• Extensions for the calculation of activity coefficients in mixtures containing electrolytes
• Enhancements to better describe the temperature dependence of activity coefficients
• Extensions for polymer systems

## Individual evidence

1. Denis S. Abrams, John M. Prausnitz: Statistical thermodynamics of liquid mixtures: A new expression for the excess Gibbs energy of partly or completely miscible systems . In: AIChE Journal . tape 21 , no. 1 , 1975, p. 116-128 , doi : 10.1002 / aic.690210115 .
2. Maria C. Iliuta, Kaj Thomsen, Peter Rasmussen: Extended UNIQUAC model for correlation and prediction of vapor-liquid-solid equilibria in aqueous salt systems containing non-electrolytes. Part A. Methanol-water-salt systems . In: Chemical Engineering Science . tape 55 , no. 14 , 2000, pp. 2673-2686 , doi : 10.1016 / S0009-2509 (99) 00534-5 .
3. ^ Barbara Wisniewska-Goclowska, Stanislaw K. Malanowski: A new modification of the UNIQUAC equation including temperature dependent parameters . In: Fluid Phase Equilibria . tape 180 , no. 1-2 , 2001, pp. 103-113 , doi : 10.1016 / S0378-3812 (00) 00514-8 .
4. João AP Coutinho, Fernando LP Pessoa: A modified extended UNIQUAC model for proteins . In: Fluid Phase Equilibria . tape 222-223 , 2004, pp. 127-133 , doi : 10.1016 / j.fluid.2004.06.030 .