# Critical point (thermodynamics)

Phase diagram of the solid (s), liquid (l), gaseous (g) and supercritical (sc) phase of carbon dioxide (not to scale)

In thermodynamics , the critical point is a thermodynamic state of a substance , which is characterized by the equalization of the densities of the liquid and gaseous phases . The differences between the two states of matter cease to exist at this point. In the phase diagram , the point represents the upper end of the vapor pressure curve.

## characterization

The critical point P c is characterized by three state variables :

In multi-component systems in particular , gases in systems above their critical temperature, but in the presence of non-critical substances, are referred to as non- condensable components. These can e.g. B. be important in the thermodynamic description of absorption .

Temperature dependence of the enthalpy of vaporization of water, methanol , benzene and acetone

Since liquid and gas can no longer be distinguished from one another above the critical point, one speaks instead of a supercritical fluid , which is in a supercritical state . Another term that comes from the English-speaking world is supercritical .

When approaching the critical point, the density of the gaseous and liquid state approach each other, the heat of evaporation decreases as the critical point is approached and disappears completely when it is reached. The phenomenon of critical opalescence can be observed just below the critical point : Due to the extremely low heat of vaporization, parts of the substance constantly switch back and forth between the liquid and gaseous state, which leads to visible streaking .

The behavior above the critical point can be clearly described at the molecular level: If a gas is exposed to ever higher pressure, the distances between the gas molecules decrease continuously. When the critical pressure is reached, the distances are then just as large as between the molecules in the liquid phase; there is no longer any discernible difference.

### Critical temperature and pressure liquefaction

Critical data of some substances
material temperature pressure density
Surname Molecular formula K ° C bar kg / m 3
water H 2 O 647.10 373.95 220.64 322
hydrogen H 2 33.19 −239.96 13.15 30th
oxygen O 2 154.60 −118.55 50.46 427
nitrogen N 2 126.19 −146.96 33.96 313
Carbon dioxide CO 2 304.13 30.98 73.77 468
ammonia NH 3 405.40 132.25 113.59 225
methane CH 4 190.56 −82.59 45.99 163
propane C 3 H 8 369.82 96.67 42.48 221
butane C 4 H 10 425.13 151.98 37.96 228
helium Hey 5.20 −267.95 2.27 70
xenon Xe 289.73 16.58 58.42 1103
Ethanol C 2 H 6 O 513.90 240.75 61.48 276
Methanol CH 4 O 513.38 240.23 82.16 282

The critical temperature is of particular technical importance . This is the temperature below which a gas can be liquefied by pressure, while this is no longer possible above the critical temperature. The isotherm of the critical temperature divides the Hs diagram of a substance into an area in which pressure liquefaction is possible and an area in which pressure liquefaction is no longer possible.

This property can be checked in the Hs diagram of a substance for a certain temperature if one follows the isotherm at a certain temperature at which the gas is to be stored:

• If the isotherm reaches into the wet steam area with increasing pressure ( exceeds the dew line ), liquefaction is possible at this temperature and increased pressure.
• If, on the other hand, the isotherm runs above the wet steam area via the critical point into the supercritical area, only compression is possible at this temperature, but no liquefaction.

In order to store the gas in liquefied form, it must also be cooled down to such an extent that the isotherm of the lower temperature re-enters the wet steam area (i.e. below the critical point). If the temperature falls just below the critical temperature, the pressure must also exceed the critical pressure in order to initiate liquefaction. However, if the critical pressure is too high for the application or storage, then a lower temperature must be selected in order to achieve liquefaction with a correspondingly lower pressure.

The liquid phase only remains stable as long as the temperature remains below the critical temperature. In a cold-insulating tank ( cryotank ) without active cooling , part of the liquid is therefore allowed to evaporate and the heat extracted in the process to leave the tank with the gas.

In the case of technical gases that are transported and stored in normal gas cylinders at ambient temperature, only gases with a high critical temperature, such as propane or butane , can be liquefied . The critical temperature of the gas must be so high that it is never exceeded during storage, transport and use.

Liquid nitrogen (LN 2 ), for example, is transported to the consumer in a cooled state (colder than −146.96 ° C), whereby the cooling is usually obtained - as described above - by evaporation of the nitrogen (and thus loss). The same applies to liquid hydrogen (LH 2 ): In test vehicles such as the BMW Hydrogen 7 , the hydrogen used as fuel is permanently drained from the cryotank and discharged into the environment when the engine is not running.

In gas cylinders for industrial use , on the other hand, there is gaseous hydrogen or nitrogen that is under high pressure. The gas bottles are designed for high pressures (up to 200 bar). The same applies to CNG tanks in vehicles.

## Experimental observation

1: Subcritical ethane, coexistent liquid and vapor phase
2: Critical point, opalescence
3: Supercritical ethane, fluid

The transition from the subcritical to the supercritical state can be easily observed, since a clearly visible change in the phases takes place at the critical point .

The substances are enclosed under pressure in thick-walled tubes made of quartz glass . Below the critical temperature (for example about 304.2  K for carbon dioxide or 305.41 K for ethane ) the tube is partly filled with the liquid substance and partly with the substance's vapor . Both phases are colorless, clear and transparent and separated by the clearly visible liquid surface ( phase boundary ). When it is heated below the critical temperature, the volume of the liquid initially increases due to thermal expansion , while the volume of the vapor decreases due to compression . If the substance has reached the critical temperature, a dense fog ( critical opalescence ) forms for a short time , which dissolves again after a few seconds of further heating. This mist can also have distinct colors; CO 2 and ethane are not colored, the fog is white. The tube is then filled with a single homogeneous , clear, transparent phase, the supercritical fluid. When it cools down, fog briefly appears again before the substance divides into a liquid and a gaseous phase.

## Estimation and calculation

In addition to a comparatively complex empirical measurement, the critical state variables can also be estimated from the Van der Waals equation , whereby they are also used here to define the reduced variables .

In addition to these equations of state , group contribution methods such as the Lydersen method and the Joback method are often used, with which the critical quantities are determined from the molecular structure .

## discovery

With the increasing spread of steam engines in the 18th century, the investigation of the boiling behavior of various substances also became a focus of scientific interest. It turned out that as the pressure rises, so does the boiling point temperature. It was assumed that the coexistence of liquid and gas was possible up to any high pressure.

First attempts to refute this assumption were made in 1822 by the French physicist Charles Cagniard de la Tour . The critical point was therefore sometimes referred to as the Cagniard de la Tour point . In 1869, the Irish physicist and chemist Thomas Andrews was able to show on the basis of investigations with CO 2 that there is a point at which the difference between gas and liquid no longer exists, and which is defined by a certain temperature, a certain pressure and a certain density excels. He called this point the "critical point". Four years later, the Dutch physicist Johannes Diderik van der Waals gave a plausible explanation (see above) for the behavior of substances in the supercritical range and also provided a mathematical description.

Subsequently, the scientific question arose whether there was a critical point not only in the transition from liquid to gas, but also in the transition from solid to liquid, above which a liquid can no longer be distinguished from a solid . In the 1940s, however, Percy Williams Bridgman found in experiments with over 10,000  bar pressure, for which he was awarded the Nobel Prize in Physics in 1946 , that such a point does not exist.

## Applications

Supercritical fluids combine the high solvency of liquids with the low viscosity similar to gases. They also disappear completely ( evaporate ) when the pressure is reduced . Thus, they are ideal solvents , the only disadvantage of which is the high pressure during the process. Supercritical fluids are also used to generate the finest particles. Extractions with supercritical fluids are called distractions .

In supercritical water can SiO 2 are dissolved. When crystallizing on the seed crystal , single crystals are formed from quartz . These are then sawn into small pieces and used as oscillating crystals in quartz watches .

Supercritical water dissolves fats from meat . Since many different substances were previously deposited in the fat, drugs and other substances are extracted from the meat and detected with this method .

In textile dyeing applications , the good solubility of the dye in the supercritical state can be used to absorb the dye and transfer it into the fiber. After completion of the process, the supercritical fluid is relaxed and the remaining dye precipitates out solid .

One application of supercritical CO 2 is the decaffeination of tea and coffee.

With supercritical CO 2 biological preparations such. B. for scanning electron microscopy , dry very gently ( critical point drying or supercritical drying ). The samples are first wetted , the water is gradually exchanged for a solvent (usually acetone ) and the acetone is discharged with supercritical CO 2 . As a result of this procedure, the structures are largely retained and only a few artifacts occur.

Supercritical fluids, especially alcohols, are used to make airgel .

## Table values

Table values ​​for the critical pressure and critical temperature of gaseous substances can be found in the following article:

## Individual evidence

1. VDI Society for Process Engineering and Chemical Engineering (ed.): VDI-Wärmeatlas . 11th edition. Springer-Verlag, Berlin Heidelberg 2013, ISBN 978-3-642-19980-6 , Part D.3 Thermophysical material properties, D 3.1. Table 1. Critical and other scalar data .
2. Sven Horstmann: Theoretical and experimental investigations on the high pressure phase equilibrium behavior of fluid mixtures for the extension of the PSRK group contribution state equation , doctoral thesis, Carl von Ossietzky University of Oldenburg, 2000.
3. a b c Andreas Pfennig: Thermodynamics of the mixtures . Springer Verlag, Berlin Heidelberg 2004, ISBN 3-540-02776-9 , pp. 7-8.