Introductory note: Anyone who has really thought about their chemistry or physics classes, rather than just endure them, has realized (perhaps in other words) that the seemingly endless equations that define our physicochemical universe (which includes the biological universe 😉 ) are a bit like those Russian matryoshka nesting dolls. If you define one phenomenon with an equation, you are probably well on your way to “nesting” that equation within several other equations that all define some aspect of what you were defining. This article is going to be like that and it is pretty inescaple. Have patience and enjoy.
When we say we are “under pressure,” we should intend that to be a positive thing. If we weren’t, we would be more diaphanous than outer space. Short of that meaning we have become a hive-mind of neutrinos, we should celebrate being under pressure! You could say that being pressured is the opposite of being vacuous but that might be unkind.
I’ve written two of three posts on The Mess (Part 1 and Part 2 so far). In Part 2, I spent a good bit of time using the word “vacuum” but I didn’t end up talking about what that means, except that a complete vacuum has never been achieved and it is difficult to achieve high vacuum (aka low pressure) without leaks occurring. The more I thought about it, the more I wanted to rectify that issue.
Our earthly pressure is due to the force that the weight of atmospheric gases (dry air is a mixture comprised mostly of nitrogen (78.09%) and oxygen (20.95%); “wet” air includes varying amounts of water and is lighter due to the lower atomic mass of water (18 amu) vs. nitrogen (28 amu) or oxygen (32 amu)) place on us. Since we experience the weight of the atmosphere, we also feel a force that is inextricably linked to our experience of pressure; that force is gravity and is related to the masses of objects interacting with each other over a distance and to the gravity constant, defined by Sir Isaac Newton.
Mass and weight are different. Mass is a physical constant related to the number of protons and neutrons in atoms of various elements and their isotopes (electrons, although very important, add negligible mass and are ignored here). Weight is the mass of an item (the sum of all of its constituent atoms) multiplied by the force exerted upon it by gravitational acceleration (gn), or:
W = m * gn
Mass, then, is weight divided by gravitational acceleration. By the way, because stuff like gravity is usually complicated it is worth stating that it is not constant but changes with latitude and altitude on earth (and between planets, stars, galaxies, etc., but that folds the theory of relativity and we are not going there). As r2 is larger for a person standing on top of Mt. Everest, even though the mass of the earth is larger at that point, the acceleration due to gravity is less, although the mass of the person remains constant (ignoring any hypothermic dehydration that is going on).
The mass of earth’s atmosphere – all those speedy, invisible molecules of nitrogen, oxygen, argon, and water racing about and colliding with each other – is estimated at about 5.15×1018 kg. That’s a mass-ive amount of air! And all of that air is multiplied by the force of gravity pulling it towards the nickel-iron alloy center of our planet. To reprise, that is atmospheric pressure. Imagine a square inch on top of your skull, roughly postage stamp-sized (stamp size may vary with special editions and countries and may be larger than they appear in your rear view mirror). The atmosphere extends about 12 kilometers above your head (this varies with your location, etc.). There are, therefore, 1,200,000 cubic centimeters of air above your head and that contains a hole bunch of molecules of “air,” which is a mixture of gases. Every day at sea level, with variations due to latitude, that square inch of skull experiences 14.7 pounds (6.7 kg) of pressure from the weight of all that column of air pressing down upon you. The square inch is sort of misleading as it is really a COLUMN of air reaching all the way to where the atmosphere on this planet fades off into space. All of those molecules in a miles-high column with an area of a square inch – 14.7 lbs (14.7 pounds per square inch (psi) or about half to a third of the pressure in your car tires). And each square inch of your body that points skyward, whether you are standing, prone, supine, or lying on your side, gets this same treatment. If there were no gravity, the air would way 1/6th as much and the pressure would be reduced (if there were no gravity, the atmosphere would have dissipated into space so I wouldn’t have to explain this).
That’s atmospheric pressure. In a volume of air enclosed in a metal vessel within a scientific instrument, that same pressure is present if the instrument has not been hooked up to vacuum pumps and the air evacuated, in other words, if the instrument has just been assembled but not initiated for use. Scientists don’t use psi as a useful measurement. Instead, they use 1 atmosphere as the pressure at sea level; it is one of two measurement standards folded into virtually all chemical and physical measurements. The measurements are “standard temperature and pressure (STP)” and are 1 atmosphere (or 760 torr or 760 mmHG or 101,325 Pascals (101 kPa) or 1.01325 bar (1,013 millibar) and 273.15 Kelvin (K) or 32°F or 0°C (the Kelvin scale, based on absolute zero, does not use the “°” sign). The different units make use in some physics and chemistry a little easier, hence the large number of pressure and temperature scales. There is also a “standard ambient temperature and pressure,” which uses 298.15 K as the standard temperature; that is often more useful as it is a comfortable laboratory temperature. Standardization and calibration of scientific instruments to consensus measurements allow experiments to be compared conveniently between laboratories. Even if SATP (or STP) is not used in every laboratory, it can be used to understand how conditions might need adjustment to replicate results lab-to-lab.
As Parmenides said in about 485 B.C.E. “Nature abhors a vacuum,” although I’m pretty sure he said it ancient Greek. Again, we find that so long ago the Greeks were constructing rules of the universe that would not be proven for a few millennia but they were correct. This idea, of the implausibility of a complete vacuum in the universe, got many people thinking, among them Empedocles, Plato, Aristotle, and so forth into the present era where attempt at achieving a complete vacuum will continue until attained. It’s in our nature.
How is this done? Using various kinds of pumps. How does that work? If you pump water, you know quite well how it works. The water goes up a tube, through the pump, which has an object in it of various designs intended to exert a change in pressure on the material to be moved. The devices are sort of like tight-fitting fan blade in a water- (or gas-) proof housing. As it turns, it exerts a force on the water and the “pumpate” (to coin a word) is moved from point A to point B. If the water source was finite and can be inspected after pumping, you will see some volume of water left in the source. Move the tube around and try to “vacuum” it up and it will run up the tube a little bit and trickle back down. The same kind of thing happens with gases.
There are a bunch of different pump mechanisms, all of which are fascinating in their own right but the same principle applies to all of them: move something from one place to another by exerting a superior force against an inertial force (e.g. gravity, magnetic, electric, normal, air resistance, friction (viscosity), tension, spring). Vacuum pumps move gases.
For ease of calculations, let’s pretend the volume with our exotic scientific instrument (a x-ray photoelectron spectrometer (XPS)) is 22.4 liters (L). To make this relatable for people still using the U.S. “customary unit” system rather than metrics, 22.4 L. is about a gallon more than the typical upside down water jug found in various offices. Imagine such a space at the center of the following instrument (the actual analytical volume in which samples are analyzed is much smaller than 22.4 L.):
In this version of an XPS with the 22.4 L. volume of air at SATP (standard ambient temperature and pressure), there are Avogadro’s number of individual gas molecules in the vessel at 1 atm pressure. Avogadro (1776-1856) was an Italian scientist who worked out that there would be 6×1023 molecules of any gas in 22.4 L. if the temperature and pressure were kept constant. This is a HUGE number of molecules but if they are molecules of gas they will always occupy 22.4 L. at SATP. This number of molecules is called a mole and correlates the number of molecules, by way of its atomic mass, in a mole of molecules. It is a constant number, just like there are always 12 of an item in a dozen or 144 of an item in a gross.
Let’s compare some other, more visible molecules. Because (in part) a molecule of water has a mass of 18 atomic mass units (amu) a mole of water molecules weighs 18 grams and occupies a volume of about 18 milliliters (0.018 L.). You could put 55 moles of water in a 1 L. container (55moles x 18 milliliters) – and 1,244.4 moles of water in a 22.4 L. container. Why? One of the reasons that water is a liquid between 0C and 100C is because all of them hydrogen bond to each other.
Gases at SATP do not make friendly clusters of molecules; instead, they bounce against each other and against the walls of any container with maddening speed, like bumper cars at the fair driven at blinding speed.
A property called the root mean square velocity of gases can be calculated, a measurement which is temperature and mass-dependent; gases with low masses move at higher speeds than those with higher masses. A molecule of hydrogen (it occurs in nature as a molecule with two covalently bonded atoms of hydrogen, or H2) has a velocity (speed) of 1,920 meters per second (m/s) or 4,295 miles/hour. A molecule of oxygen has a velocity of 485 m/s or 1,085 miles/hour, right around one-fourth the velocity. This makes sense as one molecule of hydrogen is one-fourth the mass of a molecule of oxygen. If we were to look at fluorine, also diatomic, with an atomic mass of about 19 amu we would see a velocity somewhat slower than oxygen at about 424 m/s. Why do I tell you all of this? Because the pressure (1 atm) in that vessel is related to the mass of all of those molecules but it also related to all of those invisible particles smashing into each other and into the walls of the container at those mind-imploding speeds.
We have our 22.4 L. vessel in the middle of the XPS instrument and it has 6×1023 molecules of air in it. To do our surface analysis experiments we are going to have to reduce the pressure in that vessel from 1 atm to as low as we can go, which will probably be between 9.87×10−13 and 9.87×10−16 atm. We will have two pumps connected in series (one after the other): (1) roughing pump and (2) turbomolecular pump. The purpose of the roughing pump is to reduce the air pressure in the xps instrument and in the turbomolecular pump to around 1×10−5 atm. After this is achieved, the turbomolecular pump is activated and it can reduce the pressure due to remaining gases to somewhere in the range of 9.87×10−13 to 9.87×10−16. The following video does a reasonable job of showing how a turbomolecular pump functions, although there are other videos available that examine the moving parts of these pumps.
In these ultra-high vacuum conditions it is important to remove as many of the gas molecules as possible. This is done with various types of ion pumps. The remaining gases are bombarded with energy sufficiently high to create positively charged ionic versions of the gases that then collide with the walls of the pump and react. The gases are no longer gases and no longer add to the pressure inside the apparatus being evacuated.
I watched a duck herder with his collies at a state fair some decades ago. The dogs had been trained remarkably by the herder and I assume that the ducks had also worked with these non-duck lifeforms previously. As the herder and the collies positioned themselves in ways to coerce the ducks into a cage, three ducks would enter but as the fourth duck approached, one duck would pop out, then another, then two ducks would go in and another would exit. This went on for a while and, perhaps because I had never seen it before, I found it to be extremely entertaining and funny. I also thought of the problem of trying to eat the remaining green peas in a metal bowl using only a knife (no pea-stabbing please!). The difference between these analogies and teasing the last gas molecules out of an evacuated volume is that the ducks eventually enter the cage and the peas will be eaten.
The reason I bring this up is that “herding” gas molecules out of a volume is a lot like this. Some exit, but others sort of bump around at the exit port and return to the cylinder to play a few more games of hyper-bumper cars with the walls of the vessel. As I read for this article, I saw some ultra-high vacuum wizards talk about how it is invevitably the hydrogen molecules that will not leave. These have the highest gas velocity and the lowest mass. They are also the most present element in the universe; about 74% of mass fraction of the universe composed of mass (only about 5% of the universe, the rest being composed of dark matter and dark energy) is made up of hydrogen.
To sum up:
- Atmospheric pressure is the force created by all of those gas molecules above your body being pulled towards the earth’s center of gravity (F=m*g);
- There are a whole bunch (6×1023) of gas molecules in a 22.4 L. container at SATP;
- Getting most of those gas molecules out of the container involves some spectacular types of pumps;
- Getting absolutely ALL of those gas molecules out of the container has never been achieved to date.
I have glossed over a huge and beautiful realm of gas laws in the above. These roll up into the enormous topic of thermodynamics and kinetic theory. I will leave it to you (and future posts) to explore these further. They are a wonderful set of nesting dolls!