How is the mass of atoms in a gas measured, assuming it has not been measured before?

That is a very interesting question, one that involves a lot.

One hypothesis of early chemists that eventually made it to the way we understand the universe today is the atomic theory. That hypothesis implied that there are a number of fundamental building blocks (elements) whose smallest particles (atoms) have certain properties, including a mass. This also means that these properties of atoms do not change when you change the state of matter – in other words, whether your oxygen atom is solid, liquid, or gaseous, or in a compound with one of those states of matter, doesn’t matter.

On the other hand, from the early 18th century there was already an impetus towards the kinetic gas theory – a theory that aims/was to calculate the properties of gases (and then it concerns volume, temperature, pressure, viscosity, … ) based on the assumption that gases consist of volumeless particles that move according to Newton’s laws of motion. Somewhat to the surprise of physicists and chemists of the time, this theory succeeded in predicting the properties of many gases on the basis of calculations.

The kinetic gas theory provides a formula that directly relates the volume V of the gas to the number of moles n present. (pV = nRT, the so-called “ideal gas law”, with p the pressure, T the temperature and R the ideal gas constant, which turns out to be the same for every gas)

In the mid-19th century, Victor Meyer devised a device in which you could drop an ampoule containing a liquid into a hot environment, causing the liquid to evaporate. The total volume of this device can be read via a gas burette, in which the water level drops as the volume of the device increases. Since you can weigh the empty ampoule, and the liquid-filled ampoule can also weigh, you know exactly how much substance you have introduced into the device, and you can therefore also determine exactly what the extra gas volume is when this liquid is evaporated. This was useful for determining the density of gases, but as we will see below, also for determining the molar mass.

Now there is still one puzzle piece that is missing – chemists have long known that certain chemicals react with each other in certain fixed proportions, and that is how they arrived at the term “mole” – a mole is a fixed number of particles of a substance, which depend on of the mass of the involved atoms also together have a certain mass. The proportionality constant between the two is Avogadro’s number – more on that later. Once you have defined how heavy it is for one mole of a certain substance (the current definition is that one mole of carbon atoms weighs 12 g) you can determine through chemical reactions how heavy a mole of any other compound is.

That amount of one mole also comes back in Victor Meyer’s experiment – and if you read the formula carefully you will see that one mole of gas at a certain temperature and pressure always has the same volume – regardless of molecular mass.

So you can calculate exactly how many moles were in your ampoule on the basis of the volume increase – and you have also weighed the ampoule, so you also know exactly how many grams that number of moles weighs. Then it is also easy to calculate how many grams one mole weighs.

Do that for enough compounds and by listing the combinations in the compounds you only have one mass for each type of atom for which all measured molar masses are correct. (eg CH₄ MM=16g.mol^-1CO₂=44g.mol^-1huh₂Oh, 18 g.mol^-1 – the only possible outcome is C=12g.mol^-1O=16g.mol^-1H=1g.mol^-1)

So far the history of the story – meanwhile we have much better methods for measuring the mass of an atom, the fastest and most convenient of which is mass spectrometry – if you manage to give your atom a charge, you can put it in an electric field. accelerate to high speed in vacuum, then send it through a magnetic field, causing it to deflect. That deflection is greater the smaller the atomic mass is, and based on the deflection you can also calculate back to the mass – and that is now very accurate. So now you can also see at the microscopic level how the masses of atoms are related – you divide 12g/mol carbon by Avogadro’s number, and measure the real mass of a single atom with a mass spectrometer – also in your mass spectrometer you can now comparing atoms.

In short – the mass of a mole is in fact defined as exactly 12g for one mole of carbon (the isotope with 6protons and 6 neutrons), and all the other molar masses follow from this via the ratios in which substances react.

Avogadro’s number links this molar mass to the mass of a single atom, which we can determine by mass spectrometry.

The difference in mass between, for example, water and ice is due to the space left open or left between the atoms when the state of aggregation changes, and is not due to the mass of the atoms themselves, which is absolutely unchangeable.

If that wasn’t very clear, and you still have questions, I’ll hear it, won’t I?

Kind regards,

Christophe Vande Velde