# Moles, Avogadro’s Number, and Atomic Mass Units

I quite enjoyed Chemistry in Secondary School: I think I even did a CSYS course in it. However, I remember always having problems with the concept of a Mole and the calculations surrounding it. I’m not sure if I was being particularly dim, or just didn’t have enough context be able to relate to it at the time.

Anyway, I thought I’d figure it out this evening: to me now, I grokked it pretty fast. I’m gonna doc it here to fix it in my head properly:

• Each element in the periodic table has its average weight given in Atomic Mass Units (aka “Unified Atomic Mass Units” aka “Daltons”).
• Why an average weight? ‘cos elements in the periodic table can have multiple different isotopes which have different weights. For simplicity, the periodic table weight is the average of all the isotope AMUs weighted by the abundance of that isotope. An approximation, but good enough!
• An Atomic Mass Unit is (today) defined as 1/12th of the weight of a Carbon-12 Isotope atom. (Previously, different definitions such as an 1/16th of an Oxygen atom were used, but Carbon-12 is the current definition).
• Although I personally needed to know this fact in order to “fix” it into reality, I’d imagine this fact is not really relevant for most chemistry.
• You can calculate the approximate molecular weight in AMU of any given molecule simply by adding the atomic mass units of its constituent atoms together. But how is that useful outside of the very small?
• Well, chemists define a Mole of any given “thing” as the Atomic Mass Unit weight in grams. A molecule of water weighs approximately 18.01528 AMU (2xHydrogen atoms + 1xOxygen atom), so a Mole of water is therefore simply 18.01528 grams.
• Avogadro’s number is a constant defining the number of – ah – things (eg atoms, molecules, fish) in a Mole of that thing. You can use it as a magic conversion factor between the individual thingweight in AMU and the unit moleweight in grams.
• We just happen to have carefully chosen this constant so the weights at the very small and in the real world have the same number to make things easier for us.
• Avogrado’s number is currently defined as 6.02214076×1023. (Note this constant has changed over time as the ability to measure it has improved).
• So, with this information, you – for example – can now calculate how many instances of a given thing are in a real world weight of that thing. If I have 1000g of water:
• 1000g is ~55.5 moles of water (1000g / 18.01528g).
• Therefore we know there are ~3.3422881218×1025 molecules of water present (55.5 * 6.02214076×1023).