# What is fugacity?

When one attachs a manometer to car tires or carbon dioxide fire extinguishers, what is being measured: the pressure or the fugacity?

For ideal gases both are the same, but not for real gases. As fugacity is used on thermodynamics calculations, I see it as the correct value and would expect it to be the property being measured on the situation above. However, the Wikipedia page says that the vapour pressure of a liquid is not equal to the fugacity of the vapour. Therefore, it cannot be the property being measured on the situation described.

What is it then? Is it just a value used for making the thermodynamic equations work? Therefore being a correction factor to thermodynamics.

• Fugacity is a terrible invention. It causes more confusion than anything. It is the effective pressure, useful when modeling stuff, but not useful in the real world – B. Kelly Jun 9 '20 at 7:59

The original paper of Lewis [1, p. 54], who invented the concept of fugacity explains it in a clearer way than Wikipedia's convoluted explanation:

### II. FUGACITY.

If any phase containing a given molecular species is brought in contact with any other phase not containing that species, a certain quantity will pass from the first phase to the second. Every molecular species may be considered, therefore, to have a tendency to escape from the phase in which it is. In order to express this tendency quantitatively for any particular state, an infinite number of quantities could be used, such, for example, as the thermodynamic potential of the species, its vapor pressure, its solubility in water, etc. The quantity which we shall choose is one which seems at first sight more abstruse than any of these, but is in fact simpler, more general, and easier to manipulate. It will be called the fugacity,† represented by the symbol ψ and defined by the following conditions:—

1. The fugacity of a molecular species is the same in two phases when these phases are in equilibrium as regards the distribution of that species.
2. The fugacity of a gas approaches the gas pressure as a limiting value if the gas is indefinitely rarefied. In other words, the escaping tendency of a perfect gas is equal to its gas pressure.

That these two conditions are sufficient to define a property of every substance which is not a mathematical, fictitious quantity, but a real physical quantity, capable of experimental determination in every case, must now be shown. It is obvious from the above conditions that in any case where our present methods of measurement are unable to show a deviation of the vapor of a substance from the gas law then the vapor pressure is the nearest approximation to the fugacity. In all cases the vapor pressure is an approximation to the fugacity, the approximation being nearer the nearer the vapor is to a perfect gas. […]

†In the earlier paper this quantity was called the escaping tendency and represented by the same symbol. For the sake of brevity I have chosen to substitute the word “fugacity” for “escaping tendency” without the slightest change in the meaning of the function.

More in Lewis's original words [2, p. 262]:

The fugacity of a substance is therefore equal to its vapor pressure if the vapor behaves like a perfect gas. Speaking in terms not very precise, we may say that the fugacity of a substance is equal to the vapor pressure that the substance x could have if its vapor were a perfect gas. It has been shown in the preceding paper that for a given substance in a given state the fugacity is a definite property of which the numerical value can in most cases be readily determined, and which is well suited to serve as an exact measure of the escaping tendency.

### References

1. Lewis, G. N. The Law of Physico-Chemical Change. Proceedings of the American Academy of Arts and Sciences 1901, 37 (3), 49. DOI: 10.2307/20021635. (Free Access)
2. Lewis, G. N. Outlines of a New System of Thermodynamic Chemistry. Proceedings of the American Academy of Arts and Sciences 1907, 43 (7), 259. DOI: 10.2307/20022322. (Free Access)
• Very clear indeed. The manometer measures the pressure then. I thought fugacity could be something like a "real pressure". Once I read on Reddit that the papers that introduce concepts often offer clearer explanations, as no reader has any idea of the concept whatsoever (it was about quantum physics, specifically). – NecaNe Jun 9 '20 at 6:53
• Straight to the source, splendid answer! It's also good to know what time does the usage of em dash after colon stems from:) – andselisk Jun 9 '20 at 7:45
• I still have trouble understanding fugacity. Lewis's article speaks of "any phase" in contact with "any other phase". So these phases may be two liquids, like water and cyclohexane. And here the fugacity is not related to the gas pressure. It is related to the concentration or to the activity. So what is fugacity ? – Maurice Jun 9 '20 at 9:33
• @andselisk, Your perfectionism in formatting is unbeatable :-) I didn't even notice that. Your grammar teacher must have been very good. – M. Farooq Jun 9 '20 at 14:38
• @M.Farooq I also found this intersting: hsm.stackexchange.com/questions/1926/… – Nilay Ghosh Jun 9 '20 at 15:47