PHASE EQUILIBRIA The system is simply the matter that we are studying, collected in one place and with definite boundaries. Our systems will generally not exchange matter with the surroundings, and so will be called closed. They may be isolated and not exchange energy with the environment, or sometimes in contact with a thermal reservoir of temperature T.

Gibbs' Phase Rule The Phase Rule describes the possible number of degrees of freedom in a (closed) system at equilibrium, in terms of the number of separate phases and the number of chemical constituents in the system. It was deduced from thermodynamic principles by J. W. Gibbs in the 1870s.

The Degrees of Freedom [F] is the number of independent intensive variables (i.e. those that are independent of the quantity of material present) that need to be specified in value to fully determine the state of the system. Typical such variables might be temperature, pressure, or concentration

A Phase is a component part of the system that is immiscible with the other parts (e.g. solid, liquid, or gas); a phase may of course contain several chemical constituents, which may or may not be shared with other phases. The number of phases is represented in the relation by P.

The Chemical Constituents are simply the distinct compounds (or elements) involved in the equations of the system. (If some of the system constituents remain in equilibrium with each other whatever the state of the system, they should be counted as a single constituent.) The number of these is represented as C.

The rule is: F = C - P + 2. For example: A system with one component and one phase (a balloon full of carbon dioxide, perhaps) has two degrees of freedom: temperature and pressure, say, can be varied independently. If you have two phases -- liquid and vapour for instance -- you lose a degree of freedom, and there is only one possible pressure for each temperature

Add yet one more phase -- ice, water and water vapour in a sealed flask -- and you have a "triple point" with fixed temperature and pressure. There can be several separate solid phases in a system, and the same is true for (immiscible) liquids. On the other hand there can be no more than one gas phase, because all gases freely intermingle.

PHASE DIAGRAMS OF PURE SUBSTANCES The basic phase diagram A phase diagram lets you work out exactly what phases are present at any given temperature and pressure. In the cases we'll be looking at on this page, the phases will simply be the solid, liquid or vapour (gas) states of a pure substance.

This is the phase diagram for a typical pure substance.

If you look at the diagram, you will see that there are three lines, three areas marked "solid", "liquid" and "vapour", and two special points marked "C" and "T".

The three areas These are easy! Suppose you have a pure substance at three different sets of conditions of temperature and pressure corresponding to 1, 2 and 3 in the next diagram

Moving from solid to liquid by changing the temperature:

Raising the pressure raises the melting point of most solids.

Moving from solid to liquid by changing the pressure:

The critical point You will have noticed that this liquid-vapour equilibrium curve has a top limit that I have labelled as C in the phase diagram. This is known as the critical point. The temperature and pressure corresponding to this are known as the critical temperature and critical pressure.

The stronger the intermolecular attractions, the higher the critical temperature.

Moving from solid to vapour:

The triple point Point T on the diagram is called the triple point. If you think about the three lines which meet at that point, they represent conditions of: solid-liquid equilibrium liquid-vapour equilibrium solid-vapour equilibrium

Normal melting and boiling points

The phase diagram for water

In the case of water, the melting point gets lower at higher pressures In the case of water, the melting point gets lower at higher pressures. Why? DENSITY OF ICE IS LESS THAN THAT OF WATER.

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Applying the phase rule to the simplified one component H2O system. Phase rule becomes P + F = 3, because we are dealing with a one component system (C = 1). At A P = 1 - water F = 2 - two degrees of freedom, So to maintain equlibrium, i.e. have one phase (water) stable temperature and pressure may vary independantly.

At B Point B lies on the boundary curve separating Ice from steam field, P = 2 - Ice and Steam, F = 1 - one degree of freedom, To maintain equilibrium, i.e., to keep the 2 phases stable, must choose an arbitrary value for pressure or temperature, which will automatically fix either temperature or pressure. At T P = 3 - Water, Ice, Steam F = 0 - No degrees of freedom, All three phases coexist at equilibrium. Can not change pressure or temperature without causing the system to move away from Point T, which will cause one or more of the stable phases to disappear.

Therefore the maximum number of phase which can stably coexist in a one component system is three, and they do so only if there are no degrees of freedom.

PHASE DIAGRAM FOR CARBON DIOXIDE

The only thing special about this phase diagram is the position of the triple point which is well above atmospheric pressure. It is impossible to get any liquid carbon dioxide at pressures less than 5.11 atmospheres. That means that at 1 atmosphere pressure, carbon dioxide will sublime at a temperature of -78°C. This is the reason that solid carbon dioxide is often known as "dry ice". You can't get liquid carbon dioxide under normal conditions - only the solid or the vapour.

Moving from liquid to vapour:

Phase diagram of sulphur

The Clausius-Clapeyron Equation The relationship between the temperature of a liquid and its vapor pressure is not a straight line. The vapor pressure of water, for example, increases significantly more rapidly than the temperature of the system. This behavior can be explained with the Clausius-Clapeyron equation.

Assumptions The enthalpy of vaporization (or sublimation) is assumed to be constant over the temperature range of interest. This is never really true, but changes in these H's are very small at low and moderate pressures. As one approaches the critical point, this assumption will fail completely. The vapor is assumed to be an ideal gas. Again, this is a good assumption at moderate pressures for most substances. The external pressure doesn't affect the vapor pressure. There is a slight dependence on external pressure.

Integrated form of the Clausius-Clapeyron equation.   Integrated form of the Clausius-Clapeyron equation.               

RAOULT'S LAW AND IDEAL MIXTURES OF LIQUIDS An ideal mixture is one which obeys Raoult's Law, but I want to look at the characteristics of an ideal mixture before actually stating Raoult's Law. The page will flow better if I do it this way around.

Examples of ideal mixtures There is actually no such thing as an ideal mixture! However, some liquid mixtures get fairly close to being ideal. These are mixtures of two very closely similar substances. Commonly quoted examples include: hexane and heptane benzene and methylbenzene propan-1-ol and propan-2-ol

Raoult's Law The partial vapour pressure of a component in a mixture is equal to the vapour pressure of the pure component at that temperature multiplied by its mole fraction in the mixture. Raoult's Law only works for ideal mixtures.

Vapour pressure / composition diagrams

Boliling point / composition diagrams

Using the phase diagram

FRACTIONAL DISTILLATION OF IDEAL MIXTURES OF LIQUIDS

Fractional distillation in the lab

NON-IDEAL MIXTURES OF LIQUIDS Vapour pressure / composition diagrams for non-ideal mixtures

Positive deviations from Raoult's Law

The classic example of a mixture of this kind is ethanol and water The classic example of a mixture of this kind is ethanol and water. This produces a highly distorted curve with a maximum vapour pressure for a mixture containing 95.6% of ethanol by mass.

Negative deviations from Raoult's Law

The example of a major negative deviation that we are going to look at is a mixture of nitric acid and water. These two covalent molecules react to give hydroxonium ions and nitrate ions .

Boiling point / composition diagrams for non-ideal mixtures A large positive deviation from Raoult's Law: ethanol and water mixtures

It is known as a constant boiling mixture or an azeotropic mixture or an azeotrope.

A large negative deviation from Raoult's Law: nitric acid and water mixtures

Distilling nitric acid more concentrated than 68% by mass

PARTIALLY MISCIBLE SYSTEMS High critical consolute temperature H2O-C6H5NH2 system can only dissolve with each other partly, it is separated into two layer. Underlayer is the saturated aniline in water,solubility is shown by the left half; supersaturated solubility is shown by the right half.

Systems containing two liquid components.

Two component systems: Phenol Phenol / water water

High conjugate layers Increase T, both of the solubility will increase. At point B, interface disappears, become a single liquid phase. Inside cap, solution is separated into two part. At 373K, the composing of two layers separately are A’ and A’’, they are called conjugate layers. An is the average value.

Low critical consolute temperature water-triethylamine system: Lowest critical consolute temperature TB: 291.2K <TB: single liquid phase >TB : bi-phase area.

Systems Showing a Decrease in Miscibility with Rise in Temperature: A few mixtures, exhibit a lower critical solution temperature (low CST), e.g. triethylamine plus water. The miscibility with in temperature. In the preparation of paraldehyde enemas, (consist of a solution of paraldehyde in normal saline). Cooling the mixture during preparation allows more rapid solution, and storage of enema in a cool place is recommended.

Systems Showing Upper and Lower CSTs The miscibility with temp. in systems having a lower CST is not indefinite. > a certain temperature miscibility starts to again with further in temperature. Closed-phase diagram, i.e. nicotine-water system.

High and low critical consolute temperature Water and nicotinic system: The lowest consolute temperature 334K. The highest consolute temperature 481K.