Physical Equilibria. It deals with balance between phases. A phase is my homogeneous and physically distinct part of a system which can be separated from other parts by definite boundary surface e.g. miscible liquids have one phase, immiscible liquids have 2 phases while water can exist in 3 phases. The word phase can replace the word state.

Liquid-Liquid Mixtures.

One Phase System (Miscible Liquids)

Miscible liquids are liquids which dissolve in one another in all proportions to form a uniform solution.

The solubility of a liquid in a liquid is governed by the same principle as a solid in a liquid but when a liquid dissolves in another liquid, we use the word miscible instead of soluble.

Examples of mixtures of miscible liquids;

• Water and ethanol
• Methyl benzene and benzene
• Heptane and hexane
• Propanol and oil

The solution consists of at least two components the one present in greater quantity is called a solvent and the one present in smaller quantities is a solute. Therefore a solvent is a substance that dissolves a solute to form a uniform solution. A solute is a substance that dissolves in a solvent to form a uniform solution. A solution is a uniform mixture of a solute and a solvent. There are three types of solutions;

• Saturated solution; one at a particular temperature which can no longer dissolve any more solute in the presence of undissolved solute.
• Unsaturated solution; one at a particular temperature that can dissolve more solute in the presence of undissolved solute.
• Aqueous solution; one in which water is a solvent.

Liquid-Liquid Mixtures That Form Ideal/Perfect Solutions.

There are hardly any liquids which when mixed form an ideal or perfect solution but some do form nearly an ideal solution.

An ideal solution is one that obeys Raoult’s law exactly and possesses the following properties.

• Intermolecular forces of attraction between light molecules (molecules of the same component) or between unlight molecules (molecules of the two components) are exactly equal and therefore the escaping tendency of the molecules of each component in a mixture does not change compared to that in the pure state at the same temperature. Therefore boiling point of the solution is between the boiling points of the two components.
• When the two liquids are mixed to form an ideal solution, there is no enthalpy change.
• When two components are put together to form an ideal solution, the total volume of the solution is exactly equal to the sum of the volumes of the individual components.

Raoult’s Law.

The partial vapour pressure of a component in a solution is equal to the vapour pressure of the pure component multiplied by the mole fraction of the component in the solution.

Or.

The partial vapour pressure of a component in solution is directly proportional to its mole fraction in the solution.

Equations.

Partial vapour pressure of a component is defined as the pressure that component will exert on the walls of the container which was originally occupied by their components. For two components A & B that form an ideal solution, their total vapour pressure of the mixture at a particular temperature

Equations.

Examples.

Vapour Pressure Composition Diagram of an Ideal Mixture.

The vapour pressure of a pure liquid increases when temperature is increased until it reaches atmospheric pressure when it begins to boil at constant temperature.

For an ideal solution, the force of attraction between the molecules of the individual components is the same as that between the molecular different components. Therefore the escaping tendency of each molecule into the vapour form is uniform.

Graph.

Temperature Boiling Point Composition Curve.

Graph.

Example.

Consider the following boiling point composition diagram for pentane-hexane mixture.

Graph.

Explain what happens when a liquid of composition X is fractionally distilled.

At any composition of the liquid, the vapour above the liquid mixture is always richer in the more volatile constituent than the liquid within which it is in equilibrium.

For the liquid of composition X above, when it is distilled, its vapour rises and constitutes a vapour pressure which when it becomes equal to atmospheric pressure allows the mixture to boil. The vapour is always richer in pentane. When the vapour is cooled, it then gives a liquid mixture the same as that of the vapour but this liquid is richer in pentane than the original liquid X is distilled.

When the distillate is redistilled it gives off a vapour which is richer in pentane than the previous and on cooling it forms a liquid with the same composition as the vapour but also richer in pentane than the previous liquid.

Repeated evaporation and condensation of the distillate will eventually give pure pentane as the distillate and pure hexane as the residue. The process is called fractional distillation and the description above illustrates the principle of fractional distillation.

Distilling a mixture containing pentane and hexane gives a vapour richer in pentane. When this vapour is condensed, a liquid with the same composition as the vapour is obtained thus a liquid richer in pentane is obtained. When the resultant is re-distilled, a vapour which is even richer in pentane is got and when condensed, a liquid with the same composition is obtained as the vapour. Continuous boiling and condensing results in a pure distillate of pentane and a pure residue of hexane.

Fractional Distillation.

This is a technique of separating completely volatile miscible liquids by taking into account the difference in their boiling points.

Effective separation can be achieved by using a fractionating column/long vertical column attached to a distilling flask and filled with glass beads. Vapour from the liquid that is heated rises up the column until it condenses in the cooler parts and runs back into the vessel.

The rising vapour in the column flows over the descending liquid and eventually a steady state is reached in which there is a decreasing temperature gradient up the column. The vapour in the column has a more volatile component towards the top and the less volatile components at the bottom. Various fractions of the mixture can be drawn off at points in the column.

Diagram.

Uses.

• Manufacture of O₂, N₂ and inert gases from liquid air in industries.
• Refining petroleum.
• Separation of some organic compounds in the lab.

Non-Ideal Solutions.

One that does obey Raoult’s law.

The intermolecular forces of attraction between the like molecules are completely different from intermolecular forces of attraction between the non-like molecules.

Such a solution is said to have deviated from Raoult’s law. There are two types of deviations from Raoult’s law;

• Positive deviation.
• Negative deviation.

Positive Deviation.

It arises when intermolecular forces of attraction between like molecules are greater/stronger then intermolecular forces of attraction between the un-like molecules. As a result there is increased repulsion between the molecules and this increases the escaping tendency of each type of molecules from solution into the vapour phase, giving a maximum vapour composition curve and a corresponding minimum boiling point composition curve.

Formation of a solution which deviates positively from Raoult’s law is accompanied by absorption of heat and increase in total volume of the mixture. Most of the liquids which deviate positively from Raoult’s law, one of two must be able to form hydrogen bonds.eg. Water and ethanol, benzene and ethanoic acid, pentan-1-ol and water.

Vapour Pressure Composition Diagram for a Mixture of Components That Deviated Positively from Raoult’s Law at Constant Temperature.

Graph.

Boiling Point Composition Curve Corresponding To the Above Vapour Pressure Composition Curve.

Graph.

The liquid of composition Z is called an azeotrope/azeotropic mixture/constant boiling point mixture and in this case it is called the minimum constant boiling point mixture. When this mixture is boiled, the temperature remains constant until all the liquid has turned into vapour and when the vapour is cooled, it forms a liquid of the same composition as the one originally distilled. In this way, the azeotropic mixture behaves as if it is a pure liquid yet it is not. Because when the external pressure is changed, the composition of the azeotrope changes.

Distillation of a Mixture That Deviates Positively from Raoult’s Law.

Fractional distillation of this mixture cannot separate the components completely because they form an azeotropic mixture. However from the above diagram, if the mixture distilled has a composition to the left of Z, the distillate will be the azeotrope and the residue X and if the mixture distilled has a composition to the right of Z, the distillate is still the azeotrope and the residue maybe mainly Y.

An azeotropic mixture is one whose composition and boiling point remain constant at a given confining pressure with continued distillation of the mixture.

Separation of azeotropic mixtures.

• Distillation with a third component (physical).

To separate an azeotropic mixture of components X & Y, a third component is introduced in which Y must be readily soluble to form an ideal solution and X must be immiscible with the third component, such that a separating funnel can be used to separate the two and Y in the third component is obtained by fractional distillation.eg. An azeotrope consisting of 95% water and ethanol, benzene can be introduced as a third component.

• Chemical method.

An azeotropic mixture of ethanol and water can be separated by addition of calcium oxide which absorbs the water.

• Absorption.

It is done by addition of charcoal which absorbs one of the components.

Negative Deviation.

It arises when the intermolecular forces of attraction between unlike molecules are stronger than the intermolecular forces of attraction between like molecules. As a result, there is a reduction in escaping tendency of each molecule from solution to vapour phase. This results into a minimum vapour pressure composition curve and the corresponding maximum temperature composition curve.ie. The mixture has a total vapour pressure which is lower than that predicted by Raoult’s law.

When the two liquids that form a mixture that shows negative deviation from Raoult’s law are mixed;

• There is a reduction in total volume.
• Heat is evolved.

Vapour Pressure Composition Diagram at Constant Temperature for Negative Deviation.

Graph.

Boiling Point Composition Diagram at Constant Pressure.

Graph.

Distillation of Mixtures That Deviate Negatively from Raoult’s Law.

Liquid mixtures which have a minimum in their vapour pressure curves cannot be completely separated into their pure components by fractional distillation. This is explained below;

The boiling point composition curve for the binary liquid mixture that deviates negatively from Raoult’s law is shown above. A minimum in the vapour pressure composition curve corresponds with a maximum in the boiling point composition diagram. This occurs at composition corresponding to point X. at this point, both the vapour and the liquid have the same composition and such a mixture known as an azeotropic mixture (an azeotrope/ a maximum constant boiling point mixture) will distil without change in its composition.

It behaves to all intents and purposes as a pure compound would but it is clearly a mixture since its composition is dependent upon the pressure under which the distillation is carried out. Consider a mixture of composition to the left of the composition.

If this mixture is subjected to fractional distillation, virtually pure A will be obtained. Removal of A will result in the mixture remaining in the flask becoming richer in B; once the composition of the mixture in the flask corresponds to that of the azeotropic mixture, it will distil unchanged.ie. It will be impossible to distil over anymore A.

Similarly if a mixture of composition to the right of the azeotrope is fractionally distilled, it is virtually possible to obtain pure B. the removal of B will gradually increase the mole fraction of A in the mixture in the flask.

Once the composition of the azeotropic mixture is attained, it will distil over unchanged. It is therefore possible to obtain pure A or pure B from a mixture of these two liquids. In either case however, a mixture is eventually left corresponding to the composition of the azeotrope. This then distils over unchanged.