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Vapor - liquid equilibrium (VLE)

 There is so much information about vapor-liquid equilibrium (VLE) that entire books are devoted to parts of this subject. Then, so many details shall be avoided and special attention to binary mixtures shall be paid.

Diagrams

Phase diagrams depend, traditionally, on temperature and pressure but since in distillation the vapor and liquid phase change in composition with time, then, concentration is considered as a third variable to be taken into account. In this way, a true phase diagram would be three-dimensional but also being hard to read so that some sort of shortcut needs to be introduced.

Some of these diagrams are,

  • boiling diagrams,
  • vapor pressure diagrams and
  • equilibrium diagrams.

A typical representation of a phase diagram, or better said equilibrium diagram, is as plot of the boiling temperature versus the composition of the liquid mixture, being all this, at constant pressure.

Fig. 01 Boling diagram at constant pressure for a binary mixture of components $A$ and $B$. Recall that $A$ is the most volatile component.


Several comments need to be made on the diagram presented in Fig. 01. Despite its simplicity the physics may become intricate. First, let us identify the components of this diagram:

  • $t_A$ is the boiling temperature of the pure component $A$,
  • $t_B$ is the boiling temperature of the pure component $B$ and
  • $x$ and $y$ represent the mole fraction of the component $A$ in the liquid and in the vapor phases, respectively.

Now, some comments about the physics conveyed in the diagram of Fig. 01:

  • below the bottom curve or that corresponding to the liquid mixture, the mixture remains liquid as in point $C$,
  • above the top curve corresponding to the vapor phase the mixture is vapor always, as for point $D$ and
  • any point among these two curves is a combination of liquid and vapor such as those on the line $EF$.

The way of using diagrams such as that in Fig. 01 is through the straight, vertical and horizontal, lines. In this manner, you can always think of boiling and condensing something.

For example, if you heat the liquid mixture to an intermidiate temperature, say $t_1$, it will boil and right before any part of it becomes vapor, say at point $E$, the component $A$ will have a concentration $x_E$. Later, vapor is formed and once all liquid has become vapor, say at point $F$, the content of $A$ in the mixture shall be $y_F$. This is what actually happen in the distillation column.

Also, as you heat the liquid mixture, as close as possible, to the boiling temperature of the most volatile component $A$, the concentration of $A$ in the vapor increases so that the concentration of the concentration of the component $B$ which is of no interest is reduced. In this way, it should be logical to start heating the liquid mixture using temperatures below $t_A$.

Finally, a diagram such as that in Fig. 01 is in fact a map to perform the distillation process since using initial conditions, the final results can be estimated.

Azeotropes and the law of Raoult

The idea of azeotropes can not be fully understood with without the law of Raoult. From the point of view of the physycho-chemical principle leading to azeotropic mixtures a reasonable understanding of the ideal behavior stated by Raoult is required.

However, for a quick start we will say first that an azeotropic mixture can be formed during the distillation process. Once the critical conditions of temperature and concentration are reached the mixture can not be separated at that pressure. At the azeotropic critical condition the concentration of the vapor and that of the liquid are the same.

From the point of view of the law of Raoult, an azeotropic mixture represents a deviation. The azeotropic mixture would then correspond to a maximum or minimum in the curve of vapor pressure versus composition.

Recall that Raoult's law states that for a liquid ideal solution the partial pressure of a component equals the product of its mole fraction and its vapor pressure. This is,

$p_A=x_AP_A$    Eq. (01)

Also, Eq. (01) may not always be satisfied. If the total pressure of the mixture, estimated with the law of Raoult, is greater than that predicted by Raoult's law the deviations is called positive. The deviation is called negative for the other case.

For the case of an ideal gas mixture, the analogous of Eq. (01) is,

$p_A=y_AP_t$        Eq. (02)

where $y_A$ is the mole fraction in the vapor phase and $P_t$ is the total pressure. This is the end of the post. I hope you find it useful.

Any question? Write in the comments and I shall try to help.

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Ildebrando.

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