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# UNIQUAC

UNIQUAC (short for UNiversal QUAsiChemical) is an activity coefficient model in which the activity coefficients, γ, of the components in a chemical mixture can be related through their molar fraction, xi.

## Equations

In UNIQUAC the activity coefficients of the ith component of a two component mixture are modelled, with the intermolecular forces are described by a residual and combinatorial parts.

$ln ; gamma_i = gamma^C_i;+;gamma^R_i$

### Combinatorial component

The combinatorial component γC is calculated exclusively from the pure chemical parameters, using the relative Van der Waals volumes ri and surface areas qi of the pure chemicals.

$ln ; gamma_i^C = 1 - V_i + ln ; V_i - 5 q_i left\left(1 - frac\left\{V_i\right\}\left\{F_i\right\} + ln frac\left\{Vi\right\}\left\{Fi\right\}right\right)$

With the volume fraction per mixture mole fraction, Vi, for the ith component given by:

$V_i = frac\left\{r_i\right\}\left\{sum_j r_j x_j\right\}$

And the surface area fraction per mixture molar fraction, Fi, for the ith component given by:

$F_i = frac\left\{q_i\right\}\left\{sum_j q_j x_j\right\}$

### Residual

The residual term contains an empirical parameter, which is derived from experimental, or occasionally estimated, activity coefficients.

$ln ; gamma_i^R = q_i left\left(1 - ln ; frac\left\{sum_j q_j x_j tau_\left\{ji\right\} \right\}\left\{ sum_j q_j x_j\right\} - sum_j \left\{frac\left\{q_j x_j tau_\left\{ij\right\}\right\}\left\{sum_k q_k x_k tau_\left\{kj\right\}\right\}\right\} right\right)$

with

$tau_\left\{ij\right\} = e^\left\{-Delta u_\left\{ij\right\}/\left\{RT\right\}\right\}$

Δuij [J/mol] is the estimated binary parameter between two components, i and j.

## Uses

Activity coefficients can be used to predict simple phase equilibria (vapour-liquid, liquid-liquid, solid-liquid), or to estimate other important thermodynamic parameters. Models such as UNIQUAC allow for the calculation of chemical mixtures that are commonly used in process simulation. This can be achieved by interpolation from only a few known parameters, without requiring experimental data from all desired points.

## Parameters

UNIQUAC requires two basic underlying parameters.

1. Relative surface and volume fractions are chemical constants, which must be known for all chemicals.
2. An empirical parameter between components that describes the intermolecular behaviour. This parameter must be known for all binary pairs in the mixture. In a quaternary mixture there are six such parameters (1-2,1-3,1-4,2-3,2-4,3-4) and the number rapidly increases with additional chemical components. The empirical parameters are derived from experimental activity coefficients, or from phase diagrams, from which the activity coefficients themselves can be calculated. An alternative is to obtain activity coefficients with a method such as UNIFAC, and the UNIFAC parameters can then be simplified by fitting to obtain the UNIQUAC parameters. This method allows for the more rapid calculation of activity coefficients, rather than direct usage of the more complex method.

UNIQUAC has been extended by several research groups. Some selected derivatives are:

• UNIFAC : A method which permits the volume, surface and in particular,the binary interaction parameters to be estimated. This eliminates the use of experimental data to calculate the UNIQUAC parameters.
• Extensions for the estimation of activity coefficients for electrolytic mixtures.
• Extensions for better describing the temperature dependence of activity coefficients