# Temperature Composition Diagrams

These are phase diagrams which show the composition of two phases in equilibrium at a given pressure, and how these compositions change with temperature (as opposed to the pressure composition diagrams which showed the pressure dependence of the composition at a fixed temperature). For an ideal mixture, in which A is more volatile than B, the vapour-composition diagram has the following form:

 The interpretation of these diagrams is in many respects entirely analogous to the interpretation of pressure composition diagrams, the only difference being that the liquid phase lies below the vapour phase, not above it: Below the lower curved line, only liquid exists, and above the upper curved line, only vapour exists. At points between the two lines, the two phases coexist, and the composition of each phase is given by the x coordinate of the phase boundary at that temperature (just as in pressure composition diagrams). Again the relative abundance of each phase is given by the lever rule.

Though many mixtures have temperature composition diagrams resembling the idealised version given above, there can be marked deviations:
A maximum in the phase diagram may be observed if favourable interactions between the A and B molecules can stabilise the liquid phase with respect to the vapour phase:

If a liquid of initial composition I is heated to boiling (the blue line), then vapour of composition Φ1′ is produced. From the diagram, it may be seen that this vapour is richer in A than the liquid is. If the vapour is removed and condensed elsewhere, then the composition of the liquid changes to one less rich in A (to take account of the excess of A in the removed vapour), for example Φ2.

As this mixture boils, the vapour that is produced (of composition Φ2′, again richer in A than the liquid from which is produced) may again be removed, causing the composition of the liquid to shift to one still less rich in A. Thus as evaporation of the mixture takes place, the composition of the remaining liquid increases in B as excess A is drawn off in the vapour, and the boiling point rises. When so much A has been evaporated that the composition of the liquid has reached II, the vapour and liquid that are present have the same composition, and evaporation of the liquid causes no further change in composition.If a liquid of initial composition I is heated to boiling (the blue line), then vapour of composition Φ1′ is produced. From the diagram, it may be seen that this vapour is richer in A than the liquid is. If the vapour is removed and condensed elsewhere, then the composition of the liquid changes to one less rich in A (to take account of the excess of A in the removed vapour), for example Φ2.

Note that the overall composition of the system has gone from I to II, i.e. there has been a reduction in the mole fraction of A in the system by the removal of vapour that is rich in A.

Removal of the vapour ensures that the system behaves as a one-phase (liquid phase) system. If the vapour is not removed and condensed elsewhere, then the overall composition of the system does not alter, and hence the state of the system remains on the same vertical line as I, the two phases that are present obeying the lever rule. Liquid of the composition II will not be present under such conditions.

When the mixture is at the composition II, it is called an azeotrope, signifying that it boils without change of composition.

It is not possible to separate the two constituents of the mixture in their azeotropic composition by distillation, as the condensate has the same composition as the original liquid.

As the above discussion implies, temperature composition diagrams find many applications in distillation processes, predicting the composition of condensates obtained at different temperatures.

Deviations from ideality may also be seen where there is a minimum in the phase composition diagram:

This also has important consequences for distillation. Consider the behaviour of a mixture of initial composition II under fractional distillation:

Upon heating, the mixture will come into equilibrium with its vapour, of composition Φ2′. This rises up the fractionating column, where it will condense without change of composition to form liquid (at the point Φ3 on the above diagram). This liquid, as it heats up, will gradually come into equilibrium with its vapour, of composition Φ3′. This will rise up the column, condensing to form liquid at the point Φ4 on the diagram. This process continues until the azeotropic composition, at II, is reached. At this point, the liquid and vapour are of the same composition. Further fractionation will thus not change the composition any further, so the final product of fractional distillation is vapour (or liquid if condensed) of the azeotropic composition.