Molar quantities

One of the most common units in chemistry is the mole (mol), used to measure amount of substance (i.e. how much of something we have). This can be quite a difficult concept to grasp, but it may help if you keep in mind that a mole is simply a large, fixed number of things.

When first confronted with the concept of amount of substance, you may think that it’s a little redundant. After all, we can measure how much of something we have by weighing it, right? Well, this is true – but not in the way that you might be thinking. In chemistry, we always have to convert physical weights into molar quantities – units that tell us how many moles we have.

Elemental entities

The rationale behind using molar quantities is that chemical reactions take place on the atomic level. Consider the following example:

If we burn methane (CH4) in oxygen (O2), we will get carbon dioxide (CO2) and water (H2O). We can write this in the form of a chemical equation:

CH4 + O2 → CO2 + H2O

However, this isn’t quite correct yet. Our equations must always balance – that is, we must have the same elements on the left-hand side as we do on the right-hand side. In the equation above, we have three oxygen atoms on the right but only two on the left, and four hydrogen atoms on the left but only two on the right. We cannot just create oxygen atoms out of nothing and remove hydrogen atoms from existence, so we must adjust our quantities:

CH4 + 2O2 → CO2 + 2H2O

Combustion of methane

Combustion of methane

Now the equation balances, and we can see that one molecule of methane reacts with two molecules of oxygen to give one molecule of carbon dioxide and two molecules of water. When we burn a large amount of methane – say, a full 1.5 litre bottle (this much methane will weigh about 1 g) – this reaction is happening millions and millions of times for all the millions and millions of methane molecules we have.

When we study chemical reactions, therefore, we are studying the interaction of elemental entities – a general term for atomic-scale matter such as atoms, molecules, electrons, photons and so on.

The mole

If we burn our 1 g of methane in oxygen, how much carbon dioxide will we get? Looking at our equation, we know that we will get one molecule of CO2 for every molecule of CH4 – but how many molecules are there in 1 g?

This is where we start using molar quantities, which are essential to the understanding of chemistry. Imagine for a second that we can have a chemical reaction between a golf ball and two feathers to give a Golden Snitch:

Golf ball + 2 feather → Golden Snitch

Snitch reaction

Snitch reaction

Just like our methane reaction, we know that one ball will react with two feathers to give one Snitch. Now, let’s say that we have 1 kg of golf balls, and that each ball weighs 100 g. Therefore we will need 20 feathers to make our Snitches with no waste. Will 20 feathers weigh 1 kg? Unlikely, even if they’re made of gold. If we tried to react 1 kg of golf balls with 2 kg of feathers (our 1:2 molar ratio), we would have a lot of feathers left over because there are far more feathers per kg than there are golf balls.

Moles and masses

Moles and masses

Instead of thinking in terms of grams, which represent different amounts of molecules depending on how dense things are, we must think in terms of moles, which tell us directly how many molecules we have. Remember, a mole is just a large, fixed number of atoms (or molecules, golf balls, feathers or anything) – so one mole of golf balls will react with two moles of feathers to give one mole of Golden Snitches.

Strictly, a mole is defined as the number of atoms in 12 g of carbon-12 (which turns out to be 6.02214179 x 1023, known as the Avogadro constant) – but you don’t actually need to know this to use moles in calculations.

Molar mass

Going back to our methane example, we can now say that the number of moles is proportional to the number of molecules – if we burn a mole of CH4 in oxygen, we will get a mole of CO2. We’ve increased our scale a little, and are now talking about billions of molecules instead of individual ones, but how many moles are there in 1 g?

We now come to the concept of molar mass, which relates the number of moles (i.e. number of atoms, molecules etc.) to a measurable physical quantity (mass). The molar mass is defined as the mass of one mole of a substance, which is equal to the sum of the masses of the component entities. For example, a Snitch is composed of one gold golf ball and two feathers, and methane (CH4) is composed of one atom of carbon and four of hydrogen.

Methane molar mass

Methane molar mass

To find the molar mass of methane, we must therefore find the masses of carbon and hydrogen, which we measure as atomic weight. Consulting a periodic table, we find that carbon has an atomic weight of 12 (actually 12.0107, but 12 is good enough for this example), and that hydrogen has an atomic weight of 1 (actually 1.00794). Therefore, a CH4 molecule has a relative molar mass of 16.

Strictly, atomic weight is also measured relative to carbon-12, an atom of which has six protons and six neutrons in its nucleus. Protons and neutrons have about the same mass, and represent almost all of an atom’s atomic weight. If we divide the mass of a carbon-12 atom by 12, therefore, we will get the mass of a single proton/neutron (generally called an atomic mass unit). We can say that the atomic weight is the ratio of the average masses of the atoms of an element to 1/12 of the mass of an atom of carbon-12 – but, again, for practical chemistry we do not need to think about this.

Relative atomic masses

Relative atomic masses

This definition is why our result of 16 is given as the relative molar mass – as the atomic weights are measured relative to carbon-12, the calculated molar mass must also be relative to carbon-12. To convert it into something we can measure, we have to multiply by the molar mass constant, which is conveniently 1 g mol-1. Hence our methane molecule has a molar mass of 16 g mol-1, which means that one mole of methane has a mass of 16 g.

Of course, the relative molar mass is numerically identical to the molar mass. In everyday chemistry, we can just add up the atomic weights from our periodic table and use the result directly.

At long last, let’s go back to our 1 g of CH4. The molar mass of CH4 is 16 g mol-1. Since we have less than 16 g, we know that we have less than 1 mol, and can calculate that we have 1 g / 16 g mol-1 = 0.0625 mol (1/16 mol). This will react with 0.125 mol of O2 (twice as much) to give 0.0625 mol of CO2 (the same number of moles as CH4) and 0.125 mol of H2O.

How much CO2 do we get? As before, we can find the molar mass from the atomic weights – carbon is 12 (12.0107) and oxygen is 16 (15.9994), so CO2 has a molar mass of 44 g mol-1. Since we have less than 1 mol of CO2, we know that we will have less than 44 g, and can calculate that we have 0.625 mol x 44 g mol-1 = 2.75 g. Burning 1 g of methane in oxygen will therefore result in 2.75 g of carbon dioxide.

Combustion of methane (with quantities)

Combustion of methane (with quantities)

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