1

2

3

4

And in the pink one below we have the consequences (equations in the yellow

box are the complete differentials).

5

The last term of the expression is a key to understanding the essence of this

issue. It means infinitisemally small change in concentration (contents) of ith

component at constant T, P and concentrations (contents) of all other (different

then i) components.

6

7

8

9

10

11

12

First partial derivative is a result of transformation shown in slide „Basic

equations (3)”.

P0 = 1 Bar = 1,00000·105Pa.

G0 we call standard free energy.

13

There are good reasons to define the

standard state this way.

1. If one assumes that in the standard state

f = P0, then standard states of different

gases would differ.

2. If one assumes that standard state

corresponds to P = 0, then we are in

trouble as G -, when P 0.

Correlation of Z with the virial equation –

see slide „Compressibility of gases (1)”.

One can calculate fugacity also from the

Van der Waals equation.

Dimension of fugacity is the same as of

14

15

The states are denoted as ’ and ” because

digital symbols are reserved for the

components here.

16

Other basic concepts are: vaporization (esp. boiling), condensation, melting

and freezing, sublimation and resublimation.

Also: vapor pressure, saturated vapor pressure.

Phase boundary – a surface separating two phases, a surface where two phases

contact each other.

17

The straight lines on the graph are actually curves (G at constant P doesn’t

change linearly with T). Melting and boiling temperatures depend on pressure.

Metastable phases are the ones where the transition has been kinetically

blocked. For example, diamond, which is a metastable phase (allotropic form)

of carbon, should spontaneously turn into graphite. In certain rocks in

Morocco in 1950s, graphite inclusions were found, which had been diamonds

ca. 150 mln years ago (in midth of the Earth, at high pressure). The rock was

found to be kimberlite (like in the RSA). In South African kimberlites, which

reached Earth surface after ca. 5 mln years, the diamond to graphite transition

was not completed.

Yellow arrows on the graph indicate that a metastable to stable phase transition

is spontaneous, as it occurs with negative ΔG.

Examples of metastable phases: molten sodium tiosulphate (pentahydrate) –

sipercooled liquid (melting point ca. 50oC) – a chemical heater; superheated

liquids – what is the goal of placing some broken porcelain in distillation

flasks?

18

In the graph Tm > T3. This relation is true for majority of substances

(excluding water and bismuth).

At P=P0 we have the standard melting point, while at P=1 atm we have the

normal melting point.

19

If in a closed and tight container there is no other gas, then vaporization is

always boiling (a liquid boils when its vapour pressure is equal to the external

pressure).

20

At temperature T3 the state of superheated vapour (steam) is reached.

Temperature T4 is critical temperature, there are no more two phases (one new

appears – supercritical fluid), above this temperature no gas (vapour) can be

liquefied (see also slidesvan der Waals Isotherms ).

21

Change in sign of the dP/dT derivative !!! Tt<T3 !!!

Triple point of water as the second point of the thermodynamic sale of

temperature units !

22

Ice IV („red ice” – „Cat’s craddle”). Many triple points. Cat's Cradle is the

fourth novel by American writer Kurt Vonnegut, first published in 1963. It

explores issues of science, technology, and religion, satirizing the arms race

and many other targets along the way. After turning down his original thesis in

1947, the University of Chicago awarded Vonnegut his master's degree in

anthropology in 1971 for Cat's Cradle.

23

Why the „dry ice” exist, while the liquid CO2 cannot be seen in the open,

though it exists in closed containers?

What is temperature of „dry ice” thrown „into the air”?

One can see here a „standard temperature of sublimation” !!!

24

(lambda) curve separates the areas of liquid and superliquid phases,

indicating an equilibrium between them.

3He diagram is even more complex (quantum effect play some role as 4He has

zero nuclear spin, while 3He nonzero one).

In this specific case the entropy of superliquid phase is smaller than that of the

solid, and melting is an exothermic process !!!

25

By reducing volume we forced dn of the substance to go from phase β to α, as

pressure (vapour pressure) is maintained, as long as there is an equilibrium

(quasistatic process).

So far this is a criterion for one-component systems.

26

27

One can notice that melting curve has negative slope when liquid (beta) has

lower molar volume (higher density) than the solid (alfa).

This is true for melting water and bismuth (solid remains on surface of its own

liquid).

28

29

30

31

32

Transitions for carbon and sulphur are possible in both directions

(enantiotropy), for phosphorus only as written (monotropy).

White phosphorus may be obtaind from molten red by its supercooling.