Section 1.2.2: Binary Vapour-Liquid Phase Equilibrium

Recall that for systems that approximate to ideal mixtures in the liquid phase, vapour-liquid equilibrium may be determined from pure component vapour pressure P^*_i data for each species i.

This is a function only of temperature T, as implied by the general equation:

P^*_i = P^*_i(T)

There are a range of function forms for this equation which may be used to calculate vapour pressure. One such approximates the vapour pressure in bara or atmospheres:

ln P^*_i = 11(1- T _Bi / T)

where T_Bi is the one atmosphere boiling point of the pure species and all temperatures are in Kelvin. (This equation results from combining the integrated form of the Clausius-Clapeyron equation with Trouton's Rule for latent heat of vaporisation.)

It is sometimes convenient to define an equilibrium constant k_ifor each species:

k_i = P^*_i(T) / P

Here P is the total or system pressure and so k_i is a function of both temperature and pressure.

Liquid and vapour phases in general have different compositions. The mole fraction of each species is denoted by x_i in the liquid phase and y_i in the vapour phase.

For an ideal mixture the equilibrium relationship between liquid and vapour phase mol fractions is given through Raoult's law and and partial pressures as:

P y_i = x_i P^*_i (T)

Or:

y_i = k_i(T,P) x_i

We also note that all the mole fractions in a each phase will sum to one, i.e.

$\begin{displaymath}\Sigma x_i = 1 \end{displaymath}$

$\begin{displaymath}\Sigma y_i = 1 \end{displaymath}$

All the above equations are relevant. (But note that there occasions when we must exercise care in using the summation equations in connection with material balances since they will not always be independent. For simple VLE calculations this is not a problem.)

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