The Andrews’s Critical Point

Thomas Andrews was born in Belfast, Northern Ireland, on December 19th, 1813. He was a chemist; physicist and physician who studied phase transitions in the 1860's.

Andrews studied chemistry and physics in Great Britain and Paris. In 1835 he received his medical degree at the University of Edinburgh. After developing his career in medicine in Belfast and teaching in chemistry at Belfast Royal Academy for ten years, in 1845 he was Vice President of Northern College in that city, contributing to its reorganization and creating the Queens College in 1849, where he was professor of chemistry until the end of his career in 1879 at age 66 (¹).

In 1869, he discovered the necessary conditions for the liquefaction of gases by studying the relationship between the pressure, temperature and volume of carbon dioxide, by measuring the pressures at different volumes at constant temperature. When repeating these measurements at different temperatures he plotted the isotherms for carbon dioxide (²) and established the critical constants, which then enabled the development of liquefaction techniques for gasses which until that moment could not be taken to the liquid state. Oxygen, hydrogen, nitrogen and helium were in this group, the so called “stable gases”, during mid-nineteenth century.

The critical constants are the critical temperature, the critical pressure and the critical volume (some authors as D. Fernandez and Fernandez Prini (³) prefer to refer to the critical density, which is inversely proportional to the critical volume). Considering the isotherm corresponding to the critical temperature, critical pressure and critical volume converge at the critical point.

By increasing the pressure (and decreasing the volume) in a system containing carbon dioxide at a constant temperature which is lower than the critical temperature, Andrews noted that to a certain volume, the gas phase abruptly starts to coexist with a liquid phase. This occurs during a range of volumes, with constant pressure throughout the transition phase. This pressure is the vapor pressure of the liquid.

At the critical point, the properties of liquid and gas phases are indistinguishable. It cannot be stated that there is a liquid phase and a gaseous phase.

At temperatures above the critical temperature, Andrews observed a behavior consistent with Boyle's law, which is valid for ideal gases: P1V1 = P2V2, temperature and number of moles of gas constant. He found that at temperatures higher than the critical temperature it is impossible to liquefy a gas.

Why at lower temperatures the behavior of the gas deviates from Boyle's law? Because when the temperature drops, interactions between gas molecules, especially the attraction, starts to be more important, depending on the distance between them, and showing a real gas behavior.

By increasing the system pressure (T always constant and less than the critical T), the molecules come to be at a distance in which the intermolecular attraction force is maximum, joining each otherand forming the liquid phase. If the pressure increases further, then the repulsive intermolecular forces start to prevail.

These studies have been the background to Johannes van der Waals in 1873, who proposed the equation of state for real gases in his doctoral thesis ("Over the Continuïteit van den Gas - in Vloeistoftoestand" or "On the Continuity of liquid-gas state")

Considering the isotherms obtained empirically by Andrews, van der Waals tried to find an explanation for the experiments that revealed the existence of "critical temperatures" of the gases. He could finally establish a relationship between pressure, volume and temperature of gases and liquids taking into account the molecular volume and intermolecular attractive forces, the "Van der Waals forces" (⁴).

Indeed, the "new" equation of state, which took into account the repulsive and attractive forces between molecules, were consistent with the isotherms observed by Andrews.

P=RT/(Vm-b) – aVm2

Where P is pressure, R is the constant of gases (8.3144 J/Kmol), T is the temperature in Kelvin, Vm is the molar volume of gas. a and b are the Van der Waals constants: a, related to the attractive forces, and b related to the molecular volume, and hence the repulsive forces imposed at high pressures. At very high temperatures, the components of the equation for these constants (or rather the corresponding intermolecular forces) become negligible compared to the component dominated by T, leaving as a result the old equation of state for ideal gases, and assuming that also are negligible interactions between molecules.

PVm=RT

Without going into detail on the limitations of the equation of state for real gases formulated by van der Waals, we can say that his studies made it possible to calculate the conditions for the liquefaction of gases, which opened the door to modern techniques of cooling (⁵).

The critical point and the hazardous substances

Almost one hundred and forty years after the experiments of Andrews, the critical point remains.

At a first sight, the critical constants don’t seem to have much importance in the world of hazardous substances. Is it important for safety to know at what temperature a gas can be liquefied if it is compressed?

I have never seen a product safety sheet (MSDS) containing the critical constants of a liquid or gas. These parameters are not even mentioned in any regulation relating to MSDS authoring. Taking this into account we can assume that in fact the critical point is not so important after all.

Wrong. The Globally Harmonized System of Classification and Labelling of Chemicals (GHS) establishes the criteria for classification of gases under pressure according to the critical temperature. It identifies four groups of gases:

• Compressed gases: those with critical temperature less than or equal to -50 °C.
• Liquefied gases: at high pressure, those with critical temperature between -50 °C to 65 °C, and low pressure, those having a critical temperature higher than 65 °C.
• Refrigerated liquefied gases: partially liquefied gases when they are at low temperatures.

·      Dissolved gases in a liquid phase.

The critical temperature defines the type of gas, if it is compressed or liquefied, at high or low pressure. In the definition of this temperature, the GHS only refers to pure gases (⁶).

However, it is necessary to note that GHS states these groups are only valid for gases under pressure, with risks of explosion by heating or cryogenic burns or injuries. GHS consider these gases in Chapter 2.5, separately from gases presenting other hazards, such as oxidizing gases (GHS Chapter 2.4), gases which are flammable and chemically unstable (GHS Chapter 2.2), and toxic gases (GHS Chapter 3.1) thus the concept of critical temperature is limited only to the pressurized gases.

At the end of Chapter 2.5, the GHS contains an informative paragraph regarding the classification of gases under pressure (GHS Chapter 2.5, paragraph 2.5.4.2). According to this paragraph, It is necessary to know three characteristics of the substance in order to classify it as a gas:

• The vapor pressure at 50 °C.

• The physical state at 20 ° C at standard pressure.

• The critical temperature.

The GHS does not indicate further details on these parameters, or why they should be considered, or what vapor pressure is at 50 °C, or what does it mean with “physical state at 20 ° C and standard pressure”. Regarding the latter, I suppose I would have to be completely gaseous. But perhaps it could include both gaseous and liquid phases present in the system in equilibrium, so as to consider the substance as a gas for the purposes of classification risk according to the GHS.

GHS only indicates that the information can be found in the literature, calculated or determined by tests. For pure gases, it indicates that the majority are classified on the Recommendations on the Transport of Dangerous Goods of the United Nations. This is true. Almost all pure gases are identified in the list of dangerous goods of Chapter 3 of the Recommendations, with a UN number assigned along with a proper shipping name and the risk class.
What happens with gas mixtures? The GHS is not conclusive on this issue, and it indicates that "most of mixtures require additional calculations that can be very complex." This statement is special for the determination of the critical temperature.

To take one example, which may not have much to do with "gases under pressure" referred to the GHS, but can illustrate the complexity of the issue, F. Escobar suggests a procedure for determining the critical properties of hydrocarbon mixtures (⁷). The critical temperature of each component is taken and then they are multiplied by the corresponding volume fraction. The sum of all is the critical temperature of the mixture. This procedure would only be valid when the components are hydrocarbons lighter than heptanes.

Trying to find an answer for the other two aspects mentioned in the GHS (vapor pressure at 50 °C, and physical state at 20 °C and standard pressure), this can be found in the UN Recommendations, or Orange Book.
The Orange Book of the United Nations provides the same four categories of gases according to their physical state, but unlike the GHS, this classification is valid for all gases, regardless of the risk involved. On the other hand, although there is no definition of the critical temperature, there is a definition of "gas".

For the Orange Book, gases are substances with a vapor pressure exceeding 300 kPa at 50 °C, or gases which are completely gaseous at standard pressure of 101.3 kPa. Even though these concepts are applicable to all gases according the UN Recommendations for the Transport of Dangerous Goods, they are consistent with the GHS indications valid only for the "gases under pressure".

Once we know whether a substance can be defined as a gas or liquid (a typical case where the situation is not so obvious could be a mixture of light hydrocarbons), if it is a gas, then the critical temperature may help making the classification according to their physical state.

If we consider the Orange Book, the categories will define the conditions of transport, for instance, Packing Instruction P200.

The first impression when I studied the critical parameters when I began my studies was that these concepts are of little practical application. Then I realized that the legacy of Andrews was much more important than I imagined. His contribution to the history of science, which enabled the subsequent liquefaction of stable gases, which led to the studies of Van der Waals and his equation of state and deserved Nobel Prize, and which enabled the development of applications such as refrigeration or exploitation of hydrocarbons, also left consequences in the world of chemical safety.


(1) "Thomas Andrews." Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc., 2012. Web. 18 Feb. 2012.

http://www.britannica.com/EBchecked/topic/24010/Thomas-Andrews.

(2) Elements of Physical Chemistry, Samuel Glasstone, Surgical Medical Publishing, New York, 1946.

(3) "Fluídos supercríticos", Diego Fernandez and Roberto Fernandez Prini, Science Today, Volume 8, No. 43, November-December 1997.

(4) "J. D. van der Waals - Biography". Nobelprize.org.17 February 2012

http://www.nobelprize.org/nobel_prizes/physics/laureates/1910/waals.html.

(5) "Nobel Prize in Physics 1910 - Presentation Speech". Nobelprize.org. 20 Jan 2012

http://www.nobelprize.org/nobel_prizes/physics/laureates/1910/press.html

(6) "Critical temperature is the temperature above which a pure gas can be liquefied, regardless of the degree of compression," according Chapter 2.5 "Gas Pressure", GHS United Nations, Edition 4th, 2011.

(7) " Fundamentos de Ingeniería de Yacimientos ", Freddy Humberto Escobar Macualo, PhD, Surcolombiana University Editorial, First Edition.

(8) Recommendations on the Transport of Dangerous Goods, United Nations, Edition 17th.