Today, to mix things up a bit, I'm gonna be talking about chemistry, with regards to the mole. It's a very important concept in chemistry, and one I think some students struggle to understand.
Essentially- a mole is a number. Saying "three moles" is no different from saying "three dozen", or "three hundred", apart from the fact that rather than meaning 12, or 100, it means approximately 6.02x10^23. Now, that's not a very nice looking number, so I'll break it down quickly.
6.02x10^23 is in scientific notation, which basically means it's such a big number that scientists can't be bothered to write it out in its entirety. Powers of 10 are easy, though- 10^1 is a 1 followed by one 0. 10^2 is followed by two 0s. So 10^23 is a 1 followed by 23 0s. Multiplying that by 6 gives you a 6 followed by 23 0s, and multiplying it by 6.02 makes it 602 followed by 21 more (two less, since it has two decimal places.)
A mole, written out properly, looks like this: 602000000000000000000000
(technically that isn't right, but we're rounding it, kinda like how we call pi 3.14)
Why is this number so useful? Well for that, let's take a look at carbon.
Carbon, in the most stable form, has 6 protons, 6 neutrons, and 6 electrons. Electrons are very light compared to protons and neutron (which are almost the same), so we can ignore them for now. If we add the protons and neutrons, and assume each one weighs one "atomic mass unit", we end up with a mass of 12 atomic mass units (or amu).
Unfortunately, atomic mass units are very small, and hard to use in calculations. It's a lot easier to use grams. This raises a question- if one carbon atom weighs 12amu, and we have 12 grams of carbon, how many atoms do we have? The answer is one mole. No, this isn't a coincidence- in fact, this is how a mole is defined. A mole is the number of atoms needed to have a mass of an element, in grams, equal the atomic mass number you would find for it on a periodic table.
This is very useful for calculations, for a couple of reasons.
Firstly- if you ever need to know the amount of atoms in a sample (not that I can think of a case where you would, but I'm sure they exist), you can divide the mass of the sample by the atomic mass, then multiply it by 6.02x10^23. For instance- 32g of oxygen, divided by 16, multiplied by 6.02x10^23 gives you 1.20x10^24 atoms of oxygen.
Secondly, and more significantly- you can use moles for stoichiometry. If you don't know what that means, it's basically the real-world version of balancing an equation. Let's do a quick example.
CH4 + 2O2 -> CO2 + 2H2O
Those numbers are the number of moles of each compound used or produced. One mole of methane plus two moles of oxygen makes one mole of carbon dioxide plus two moles of water. The cool thing about this is that it allows you to find mass- simply multiply the number of moles by the mass of the compound.
CH4 = 1 carbon and 4 hydrogens = 1x12 + 4x1 = 16 amu. 16 amu x 1 mole = 16g
This is really useful for doing chemistry problems. An example might be "if you have 48 grams of methane to burn, how much oxygen do you need to completely react?" You can use the process I showed above, in reverse, to get the moles of methane, stick that in the balanced equation, get the moles of O2, then multiply that by the mass of O2 to get the answer.
It can seem a bit confusing at first, but it's pretty simple once you get the hang of it. I might do a post in the future explaining stoichiometry problems in greater depth.
Anyways, hopefully you enjoyed today's blog, and if you're learning chemistry, hopefully it helped to reinforce your understanding of moles and stoichiometry! If you have any questions, I'll be happy to answer them.
NOTE: a lot of what I say here is simplified, especially when I explained how a mole is defined. Protons actually weigh slightly less than neutrons, even if you take the electrons into account, and in any sample of carbon there will be other isotopes (namely carbon-13 and carbon-14). I've also rounded a lot of numbers for the sake of convenience. That said, carbon-12 is actually used to define a lot of things- the mass of a neutron is defined as 1/12th the mass of an atom of it, for instance.
