What is a Mole? The Basics of Stoichiometry

Imagine a chemist in a laboratory is attempting to perform the combustion reaction below $$CH_{4 (g)} +2O_{2 (g)} \to CO_{2 (g)} + 2H_{2}O_{(l)}$$ and is absolutely sure that he has exactly 100g of methane gas ($CH_4$). Contrary to popular believe, methane gas does not smell like anything, but assume, regardless, that this chemist wants to be absolutely sure that all of the gas reacts. How would he be certain that the right amount of oxygen gas is present for the reactants to be used up entirely?

He could try using 100g of oxygen gas, however after all the oxygen is used up, he'd have roughly $\frac{3}{4}$ of the methane he began with. It turns out that methane gas is around twice as light as oxygen gas is, and in addition, the reaction above shows us that each molecules of methane gas needs two of oxygen to react.

So how would the chemist know exactly how much oxygen to use? This brings us to the concept of a mole, the SI unit for the amount of a substance.

The Definition of a Mole

A mole is standardized unit which measures the amount of a chemical element or compound. We define one mole as exactly $6.022 \times 10^{23}$ atoms (or molecules, ions, etc.) of a substance, a quantity known as Avogadro's number. Whenever we talk about $1$ mol of a substance, this is really to say six hundred and two sextillions atoms.

Of course, an element like helium is much lighter than something like water, since an atom of helium has far fewer protons and neutrons than a molecule of water does. As such, were we to count out 602 sextillion atoms of both hydrogen and water, the latter would be about four times heavier. What we are observing here is the concept of a molar mass, the exact mass of one mole of a chemical substance. For instance, if each molecule of water weighed one gram, this value would be 602 sextillion grams per mole, though thankfully atoms are far lighter than that, and the molar mass of water ends up being around $18$ g/mol instead.

A Mathematical Description

Using the concepts we've explain above, we can begin to imagine that every substance, atoms and compounds alike, has a distinctive molar mass, usually denoted as $M$. Furthermore, it shouldn't be surprising that if we take this molar mass, and multiply it by the number of moles of our substance, which we'll denote as $n$, that we would get the exact mass, $m$, of our substance. This is true, and the formula is usually written in the form shown below, $$n=\frac{m}{M}$$ which we use to compute the number of moles of a substance of known mass. This is one of the most-used and fundamental formulae in the whole of chemistry.

Moles in Chemical Reactions

Going back to the reaction we mentioned at the start, the chemical equation below indicates that one molecule of methane gas reacts in the presence of two molecules of oxygen gas, and produces two molecules of water and one molecule of carbon dioxide. $$CH_{4 (g)} +2O_{2 (g)} \to CO_{2 (g)} + 2H_{2}O_{(l)}$$ Naturally, this would also mean that 10 molecules of methane gas would react with 20 molecules of oxygen, to produce 20 and 10 molecules of water and $CO_2$. By identical logic, 602 sextillion molecules of methane gas would combust in the presence of 1.2 septillion molecules of oxygen gas, or in other words, one mole of methane gas reacts with two moles of oxygen, to produce one mole of carbon dioxide and two moles of water.

In fact, thinking of chemical reactions in terms of moles rather than the molecules themselves is often far more useful to chemists, since they represent realistic quantities of the substances reacting.

Going back to our question at the beginning, we can use the formula and theory above to calculte that the chemist would need about 400g of oxygen gas to fully rid the lab of methane. With this amount, there's about twice as many moles of oxygen gas as there are of methane, so we can be sure that each molecule of methane has two oxygen molecules to combust with, so a perfectly efficient reaction will take place, blowing up the lab.