NoBull Gas Laws
We've been exposed to gas laws our whole life, and we have intuition about what will happen to gas under certain conditions. For example, people notice that the pressure in their tires might become low on a very cold day. Or perhaps you've been at very high altitudes and you've been short of breath. And everyone knows that if you shake a carbonated beverage before opening it you'll be cleaning up a mess very shortly. Each of these observations has been classified into the laws, and we'll be splitting them up between this blog and the next. Stating the laws is one thing - anyone with google can copy and paste their definitions. However, we have a special interest in these laws as medical professionals because we deal with them on a different level. Sometimes we're manipulating these gas laws on purpose, and other times we're dealing with their side effects. Or perhaps we're just trying to pass our FP-C, CCP-C, or CFRN exam ;)
Let's dive (pun intended) right in!
The Ideal Gas Law
Ah, the IDEAL gas law... wait, which gas is ideal? Well, all of them. The ideal gas law is a good one to start with because it tells us that everything that affects a gas is connected. Most of the other gas laws essentially tell us what happens to a gas when one of these things is constant, one is manipulated, and the other is affected. For example, IF the temperature is constant, and we manipulate the pressure, the volume would change. See how we locked one variable in place, changed one, and it impacted the other? However, in the real-world application of gas laws, everything is changing. Technically, the Ideal Gas Law is a combination of Boyle's, Charle's, and Gay-Lussacs's Laws (because they deal directly with the variables shown above). It's probably best to leave the Ideal Gas Law at that - everything is connected.
Boyle's Law has a lot of clinical applications. Let's start with identifying our constant. Our constant is temperature, so we're assuming that isn't changing. What is being manipulated? Pressure! What is changing as a result of that pressure manipulation? Volume!
Boyle's law (along with others) is the reason we can breathe. As we inhale, we create a negative pressure in the thorax, which increases the volume (because it's being sucked in from outside). Then, when we breathe out, the pressure increases, resulting in a lower volume (it's being forced outside the body). Boyle's law is also responsible for changes in barometric pressure as we climb to higher altitudes. This is because as altitude increases, pressure decreases. Does this change in barometric pressure change the gas mixture? Here's the tricky question that's often asked:
Question: If oxygen makes up 21% of air at sea level, what is the percent of oxygen at the top of Mount Everest?
Why? Because the lower pressure allowed the volume to expand. This causes oxygen molecules to drift farther away from each other, but they still make up 21% of the gas mixture (we're just inhaling fewer molecules for a given volume of gas).
Quick side note for an honorable mention - all the high altitude issues such as acute mountain sickness, HAPE (high altitude pulmonary edema), and HACE (high altitude cerebral edema). High altitude sicknesses are more complicated than just pressure change issues. The low pressures (resulting in oxygen molecules being farther apart) create something called hypobaric hypoxia, which causes the patient to hyperventilate, experience hypoxic vasoconstriction, and a bunch of other mechanisms that are not fully understood. While Boyle's law is part of the reason they get sick, the edema and increased ICP these patients experience is more so due to attempted compensation by the body. Okay... back to the main points.
Alright, that's cool and all, but is that really the only clinical application? No. Think about any gas that you would not want to expand at altitude. A patient with a pneumothorax - would we really want that gas to expand? No. Or consider a patient with air in their sinuses (barosinusitis / 'sinus squeeze'), or in their teeth (barodontalgia / 'tooth squeeze'), or in their eustachian tubes or behind their eardrum (barotitis / ear squeeze). Taken to altitude, the gas expands in these closed spaces because there is less pressure exerted on it, causing pain and perhaps even rupture. Anyone who has ever flown with a sinus infection can relate to the intense pain that trapped air can cause even in a pressurized cabin. Boyle's law is also the reason you become gassy and bloated at altitude, and it's called HAFE - High-altitude flatus expulsion (this means you're breathing a lot of farts on an airplane). If that gas becomes trapped in the gut it can cause serious pain and problems if it cannot be expelled.
You can use the calculator here to calculate pressures at altitudes. You could do these formulas in atm or PSI, but we usually think about things in terms of mmHg, so I pasted the conversions on these pictures.
From sea level to 1500 feet.
From sea level to 10,000 feet.
To make clinical applications with some of our equipment, think of anything that is gas-filled. Air splints, IV pressure bags (or just bags with air in them in general), and any cuffed device such as a cuffed SGA or ETT. All of these will expand at an increased altitude. If we let some air out of them at altitude, they will then return back to a lower volume when we return closer to sea level. If we're talking about a device that needs air in it such as a cuffed device, splint, or pressure bag, we'll have to put more air back in them. There isn't really anything you can do for the vacuum splints besides adjust them, but you can place saline instead of air in cuffs for airway devices, and eliminate air in IV bags to help with this.
Gas laws will have a graph that represents the changing variables. Here is the graph for Boyle's Law.
Closely related to Boyle's law is Henry's law. Henry's law is known by most of the 'soda can law'. Henry's law is all about the movement of a gas into a liquid or vice versa. If the partial pressure of a gas is high above a liquid, that gas is going to get dissolved into that liquid. On the flip side, if there is a high partial pressure of a gas dissolved in the liquid, it will leave if the partial pressure of that gas above the liquid is low. All of this will occur in an attempt to reach equilibrium.
Why did the equilibrium occur in the illustration above? Because there was not adequate pressure to hold the gas in the solution once the cap was opened. We could also think about this in the opposite way - what if we increased the pressure of a gas above a solution? Then just imagine the arrows in reverse in the picture above. The easiest real-world medical application of this would be oxygen administration. As we increase the pressure of oxygen above the serum in the AC (alveolar/capillary) membrane, we increase how much oxygen will get dissolved into the blood. We can do this simply by administering oxygen even without added CMH2O. If we wanted to make the body a little more like a soda can, adding something like CPAP or PEEP will create an added physical force to the gas.
Henry's Law is essential for respiration to happen. To bring in some normal physiology here, this attempt to reach equilibrium with our atmosphere is why oxygen diffuses into the blood, and why carbon dioxide leaves the blood during normal respiration. Oxygen goes down its concentration gradient into the body, and carbon dioxide goes down its concentration gradient into the atmosphere - it all has to do with Henry's Law. When we increase the pressure of oxygen through artificial means, we increase that concentration gradient and cause more oxygen to diffuse into the blood. What about issues going the other way?
Perhaps the biggest issue in gases going the other way is decompression sickness, otherwise known as The Bends (the name comes from painful joints that cause it to be difficult to bend). So, what happens? Divers who are breathing compressed air (~79% nitrogen) develop high pressures of nitrogen in the lungs which then goes down its pressure gradient into the body. If the diver does not ascend slow enough, the nitrogen will form bubbles and will get stuck at various locations around the body (including joints that cause the pain mentioned above).
Understanding how those bubbles form is actually pretty simple. If you look at a clear bottle of carbonated water, beer, or champagne, when the cap is on you cannot see the carbon dioxide inside of it. However, once you open the cap and rapidly decrease the pressure above the liquid, bubbles form because they collect together during their escape. The same thing happens with nitrogen in a diver - the rapid lowering of the pressure above the liquid (the blood/serum) causes bubbles to form, and unfortunately get stuck. These bubbles might get stuck in a joint, under the skin, or even in the heart or brain. While this isn't a blog on the treatment of decompression sickness, these patients need to get back under pressure in a hyperbaric chamber for a prescribed amount of time under several atmospheres of pressure.
Charle's Law and Gay-Lussacs's Law
These two gas laws are usually talked about in the same context because they're related. For our purposes, as the temperature is changed, so are volume and pressure. We can use an oxygen cylinder as an example. On a cold day, the oxygen may read low - why? As the temperature has decreased, molecules of oxygen are colliding with the sides of the cylinder at decreasing speeds. This causes the gas to shrink down (decreased volume). And, since we're measuring that pressure in a fixed container, it reads a lower pressure. Remember the Ideal Gas Law, and how everything is connected? As far as our oxygen tanks go, this is a good example of how we can't really talk about one of these gas laws without talking about the other.
These laws also help us understand a little about the respiratory system as well. Cold air (cold air is more condensed just like the oxygen in our tanks) expands when it enters our lungs due to our ISB (isothermic saturation boundary). This means that we can take in smaller volumes of air in cold environments - we get more molecules of oxygen for a given volume. Warm or hot air (warm or hot air is less condensed) cools down when it hits our ISB, so we get fewer molecules of oxygen for a given volume.
One more thing, these laws are the reason that helicopters and airplanes have more lift in cold weather. When the temperature of air (which is just mixed gasses) is low, molecules are closer together. This means that as a blade slices through them, it produces more force. This idea that far apart molecules prevent flight can actually be tested very easily in a vacuum chamber. The Action Lab (one of my favorite YouTube channels) did this experiment. While the temperature was not the variable here (I suppose this experiment would be compared more with Boyle's law), the idea is the same - move molecules far apart, and things can no longer fly (even flies).
6.022×10 to the 23rd.... anyone who has ever taken a chemistry class probably has that number engrained in their head as Avogadro's number. Gasses of different types, but at identical volumes, will have the same number of molecules, with temperature/volume/pressure being equal. So, how many molecules of oxygen are in one mole? 6.022×10 to the 23rd. And how many molecules of helium, or argon, or krypton are in one mole? 6.022×10 to the 23rd.
In Avogadro's law, we're assuming that we have a given volume of a gas, and the pressure and temperature are equal. However, equal to what? This law allows us to calculate how gases will behave in situations like increased altitude, in the cold, or under pressure, and translate that information to other gases if we need to. This is because gases will behave the same given the same conditions.
A nerdy side point would be that this graph assumes that the volume is not under a vacuum, since that would increase volume, but not moles. Now let's just leave Avogadro be.