Fundamental gas laws relevant to critical care medicine

Even though this chapter is most relevant to Section W(i) from the 2017 CICM Primary Syllabus ("Describe the laws governing the behavior of gases"), it acts as an effective portal into the Respiratory section, as logically it should (that system being the main governor of the gases' movements and behaviours throughout the human body). As such, the discussion of gas laws here will be somewhat more detailed and skewed towards respiratory mechanisms, rather than treating them with dry abstraction. Elsewhere, the raw untreated mathematics of these laws are massaged with the appropriate level of reverence.

There being no past paper SAQs on this topic, the CICM Part One candidate is at a loss as to what to study, and how much of it. One can only assume that some rote-learned equations might one day be called upon, or that at some stage during a viva station one will be expected to hold forth on the definitions of these laws. Whether one ought to expect a mindless recitation or some level of analysis, that is not clear. In any case, a short memorable blurb is called for:

In terms of peer-reviewed resources, the best single offering is probably Physics of Gases by Thomas & Stamatakis (2009). It is short, dense and to-the-point. Unfortunately, at the time of writing, Anaesthesia and Intensive Care are asking US$39.95 for the pdf copy. If one is severely affected by class inequality, one may resort to reading Gases and Vapours by  Ben Gupta (at that stage, in 2012 he was an Anaesthetics registrar at the Sir Charles Gairdner Hospital in Perth). This article contains virtually the same information but is free.  The definitive resource, if one has infinite time and money, is Basic physics and measurement in anaesthesia by Parbrook (actually, by the Parbrooks- Geoffrey and Evelyn). At the time of writing the 2003 5th edition is current, though the author of this chapter referred to his 4th edition as if the gas laws hadn't changed since 1995.

Boyle's Law

Boyle's 1660 publication, "New Experiments Physico-Mechanicall, Touching the Spring of the Air, and its Effects" has been covered brilliantly by JB West (yes, John B. West, of West's Physiology).

In brief summary, the law states that at any given temperature, the product of pressure and volume is constant. Conversely, as you change one, the other will change predictably.

Boyle's apparatus

Boyle wrote an extensive essay (in the form of a letter to his nephew) detailing his experiment- to be precise, his 43 experiments - on the behaviour of vacuum and rarified gas. Of the engravings he commissioned for this publication, some are selected for display above - not for the purposes of education, but to recall a time when experimental apparatus was lovingly rendered by artists, rather than by software.

Boyle's experiment is discussed in great detail in the course of West's article. In short, Boyle evacuated a huge glass bulb using a ratcheted piston, and then observed what happens to the stuff he put in there. The bulb was huge - around 28 litres - and he was apparently able to reduce it to a pressure of 22.8mmHg, according to the recently developed Toricellian mercury barometer. Among the objects which enjoyed a brief exposure to such a vacuum were lamb's bladders, burning candles, coals, loaded pistols, insects, as well as several unlucky birds and mice, who "droop and appear sick, and very soon after [were] taken with as violent and irregular Convulsions as are wont to be observ’d in Poultry, when their heads are wrung off" as air was removed from the chamber. Unfortunately, there being no Priestley for another hundred years or so, Boyle was unaware of oxygen, and piles of dead animals were generated in the course of his experiments. The exceptions to the rule were house snails: apparently, they were entirely unaffected by the extremes of pressure, and continued to function normally in the near-vacuum. This was no accident - a little digging has revealed that in fact, molluscs are the kings of anoxia, and many bivalves live their lives at about 1.0ppm of pO₂ (0.00072 mmHg), so at around 5mmHg the snails were probably quite comfortable.

Anyway, the key issue is that for any given constant temperature the pressure of any gas can be predicted from its mass and the volume of the chamber it occupies. West finishes his assessment of Boyle's works by saying that "modern students who are interested in high-altitude physiology should be aware of this classic book".

Charles's Law

The law was published by Joseph Louis Gay-Lussac who credited Jaques Charles with its discovery. Apparently, the unpublished material from which this law was derived dates to 1787. A certain team of chemistry teachers has an excellent entry regarding these two chemists, complete with snide remarks regarding Charles' appearance (looks drunk, they say).

Charles's contribution to gas laws derives much of its success from his excited attempts to replicate Joseph and Etienne Montgolfier's hot air balloon experiences. The first hydrogen balloon, of Charles' design, was a rubberised silk bag filled with the hydrogen which was produced when vast quantities of sulfuric acid were poured over approximately 1000kg of iron filings. The resulting gas was hot - so hot, in fact, that it had to be cooled by passing through lead pipes. Observers then remarked that as the gas cooled, so the balloon deflated. The experiment came to a splendid conclusion after the hydrogen balloon came to rest some ten miles away near the village of Gonesse, whose villagers apparently tore it to shreds with a variety of improvised weapons.

Enraged villagers destroying Charle's hydrogen balloon. Apparently, it made weird noises and had a foul odour. (c 1783)

Fortunately, this early balloon was too small to carry Charles himself. Though he himself did not publish anything of scientific merit, J.L.Gay-Lussac published on his behalf. A specific experiment was the inspiration for what we now (mostly) call Charles's Law. Five balloons of similar volumes were filled with different gases, and then heated to about 80C°. The resulting expansion was measured, and was noted to be the same irrespective of the gas involved.

Gay-Lussac's law

This was the direct extension of Charles's law. It is variably credited to Gay-Lussac and Guillaume Amontons, both of whom had arrived at certain conclusions regarding the behaviour of gases of fixed mass and fixed volume. A translation of Gay-Lussac's original publication can be found online.

Avogadro's law

In other words, for any gas, at any temperature and pressure, there will be the same amount of molecules present in the specified volume.

Avogadro's law is of particular interest because it uncovers a fundamental constant value, which is encountered everywhere: the Universal Gas Constant, R. This constant is also a feature of Boyle's and Charles's laws, the equations of which can be rearranged to demonstrate it. R is the constant of proportionality which relates the energy scale to the temperature scale; it is expressed as work (joules) per degree per mole. Its approximate value is 8.314.

Graphical representation of the ideal gas laws

In the event that one recalls visual information more easily than equations, one might potentially derive some benefit from being able to represent the gas laws as graphical plots:

Boyle's law relationship is hyperbolic. Pressure is inversely proportional to volume. The other two laws are relationships which are directly proportional, and their graphs are straight diagonal lines. One needs to remember to correctly represent temperature in the case of Charles' law; at zero degrees Celsius most volatile gases occupy a nonzero volume. 

The Ideal Gas Law

This is the mutant offspring of Boyle's, Charles's, Gay-Lussac's and Avogadro's principles.

Graham's Law

Graham's law describes the rate of gases mixing together (diffusion) or escaping from their confinement through miniscule pores in the storage medium (effusion).

In most circumstances, the mass of the particles and the density of the gas are sufficiently correlated to one another that an approximation can be made:

Thus, if a gas had particularly large particles, or is particularly dense, it will mix more slowly with other gases, and ooze more slowly out of containers.