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What is the liquid-vapor equilibrium?

The vapor-liquid equilibrium is a dynamic state that establishes a liquid, either a pure substance or a mixture, with steam surrounds and interacts with its surface. For it to take place, the container must be closed, otherwise the air currents would cause the liquid to evaporate slowly.

When the system is closed, the pressure exerted by the molecules in the vapor phase against the liquid will increase as time passes. There will come a point where the pressure will stop; This is the vapor pressure of the liquid, which is a physical property of matter , being independent of the size of the container, or the volume of the liquid.

When a carbonated drink is uncovered, its liquid-vapor balance is disturbed, causing an imbalance of the pressures outside and inside the bottle, and with it the bubbling of the dissolved CO₂ towards the surface. Source: OpenStax, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons

All liquid, pure or mixed, will have an associated vapor pressure that will depend on the volatility of its components; and consequently, of the intermolecular forces that hold them together within the liquid and on its surface.

This pressure can be described assuming the ideality of the solutions, or the miscibility of the components of a mixture. For this, the use of binary diagrams is very useful, in which it is possible to contemplate the feasibility of a separation process.

Pure substances

The molecules of a pure substance A are not still, but instead move from one place to another thanks to an intrinsic kinetic energy. This energy can sometimes be large enough to overcome the intermolecular forces that “pull” a particular A molecule into the liquid. Then molecule A will escape from the surface of the liquid into the vapor phase.

In the vapor phase, the molecules will collide against the internal walls of the container, gaining or losing speed until they meet again with the surface of the liquid, where once they become part of the conglomerate of molecules of the liquid phase.

Thus, time goes by until, at a certain temperature (to say 25 ºC), the number of molecules that escape from the surface equals those that enter from the steam. It is therefore said that a liquid-vapor equilibrium has been established in a pure substance A.

The vapor pressure of A experienced by the internal walls of the container, as well as the surface of the liquid, will be equal to P A º, which is constant and reproducible; no matter how big or small the container is, nor the volume of liquid A considered.

In liquid mixtures there will also be a component that exerts pressure on the surface of the liquid and the contours of the container. Its vapor pressure, as can be expected, will be composed of contributions from each of the components of the mixture, that is, two substances A and B. These mixtures can be miscible, partially miscible, or immiscible.

Miscible

In a miscible mixture between A and B, both substances make up a single phase, which at first glance looks like a pure substance. Thus, according to Dalton’s law, the pressure of the mixture or solution will be equal to:

sol = P A + P B + ··· P i

Being P i any other component that is also present in the mixture. Note that P A ≠ P A º, that is, the pressures of the substances in the mixture are not the same as in their high purity states.

By assuming that the solution is ideal, the differences between the AA, BB, and AB interactions are obviated. This can be applied, for example, in a mixture of ethanol and methanol.

Therefore, the vapor pressures of the components in the mixture will depend on their relative amounts in the liquid phase, expressed as mole fractions X i . And this is where Raoult’s law intervenes, which seeks to relate the pressure P A and P A º:

A = X A P A º

Now being the total pressure equal to:

sol = X A P A º + X B P B º + ···

The vapor phase, on the other hand, will have its own compositions, expressed as Yi mole fractions:

Yi = P i / P sol

= X i P i º / P sol

Binary diagram

Diagram of the boiling points and molar compositions for a binary mixture. Source: Binary_Boiling_Point_Diagram.PNG: H Padleckasderivative work: Michbich, CC BY-SA 2.5 <https://creativecommons.org/licenses/by-sa/2.5>, via Wikimedia Commons

When the mole fractions of the components of a binary mixture (A + B) are plotted, as a function of temperature or pressure, binary diagrams are obtained (see above). This particular form, the simplest, corresponds to that of the ideal solutions.

The area above the “oval” corresponds to the vapor phase, while the area below corresponds to the liquid phase of the mixture. Note that when the mole fraction of component 1 or A is 0 (X 1 = 0), the mole fraction of component 2 or B will be equal to 1 (X 2 = 1), and then the vapor pressure will be due only to B This temperature comes to be that of the boiling point of B.

Meanwhile, at the other end (right), when X 2 = 0 but X 1 = 1, the vapor pressure will only be due to A. This temperature is the boiling point.

The bottom line of the oval corresponds to the bubble point, which is when the first bubble appears as the liquid mixture heats up (going up in the diagram). And the top line corresponds to the dew point, which is when the vapor phase cools and the first drop appears (going down in the diagram).

Azeotropes

In many non-ideal solutions we will have azeotropes, which are mixtures that evaporate, keeping their composition constant; that is, they evaporate as if they were a pure compound.

It is impossible to “break” an azeotropic composition by further distillation steps. Instead, other methods are used to increase the purity of the desired component.

For example, the ethanol-water mixture forms an azeotrope with a composition of 95.4 ethanol. This means that it is impossible, by distillation, to obtain ethanol with a concentration higher than 95.4%; there will always be 4.6% water remaining. If one wanted to prepare absolute ethanol (100%), it would require the use of dehydrating materials, or other synthetic routes.

In a binary diagram we can see the presence of an azeotrope, which has the following form:

Binary diagram of a positive azeotrope mixture. Source: Karlhahn at English Wikipedia, Public domain, via Wikimedia Commons

On the left of the diagram it can be seen that within the “oval”, the region where we have the liquid-vapor balance, we can distill in consecutive steps (A, B, C, D and E) to obtain a mixture that is increasingly rich in the most volatile component (X for this diagram).

At the azeotropic point, however, the X and Y mixture will boil as if it were a single substance, so no matter how many distillations are done, both the liquid and the vapor will have the same composition.

Partially miscible

In partially miscible mixtures, two recognizable phases will form, depending on the temperature: one rich in component A, and the other rich in component B. The binary diagrams for these cases are much more rigorous and extensive, since they involve regions where it coexists. steam along with the two phases.

Immiscible

When it comes to immiscible mixtures, each component will behave as if it were in a state of high purity, since it hardly interacts with the other molecules. Therefore, the vapor pressure for these mixtures will be equal to:

sol = P A º + P B º + ··· P i º

The mixture will boil at a lower temperature than that of the pure components, because the pressure of the immiscible mixture will be higher, since it is equal to the sum of the pressures of each component in its pure state. More vapor pressure implies that it is more volatile, and therefore it will boil at a lower temperature.

Applications

Distillations

In distillations, especially at the industrial level, knowledge of the liquid-vapor equilibrium is essential. From the components of the mixture, and their phase diagrams, it can be calculated how many plates are needed in the construction of a fractionation tower for the correct separation of said components.

Steam distillation

Water vapor can be pumped into a mixture undergoing distillation. By bubbling the water vapor into the liquid, the vapor pressure of the mixture will increase, so it will boil at a lower temperature and help to extract the more volatile components (such as essences).

Drinking bird

Drinking bird, one of the most ingenious toys of all time. Source: Tiia Monto, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons

Although it is not precisely a liquid-vapor equilibrium, the truth is that several thermodynamic phenomena are hidden behind the operation of the drinking bird.

When the bird’s head gets wet, it begins to cool as the water evaporates. This drop in temperature causes a decrease in pressure inside the bird’s head. The methylene chloride, located at the base of the bird, will seek to balance the pressures, flowing upward through a glass tube that connects the head to the head.

The liquid will rise towards the bird’s head, making it heavier and leaning its body forward. The bird will then “drink water” and the vapor pressures will balance out. Once the pressures are balanced, the bird’s body will return to the vertical position and the cycle will repeat while the water in the head evaporates again.

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