 Now we're going to look at the maths of equilibrium. The relationship between the concentrations of reactants and products in an equilibrium can be expressed mathematically, which is interesting and useful, and can be used, for instance, to predict whether a system is at equilibrium, what it will look like when it does come to equilibrium, or how it will change if we alter something about it. So take a hypothetical reaction involving chemicals A and B turning into C and D. The small A, B, C and D in this equation are the stoichiometric coefficients, the numbers that we have to put in there to balance the chemical equation. So, for instance, in the reaction between hydrogen and oxygen, the stoichiometric coefficients are two for the hydrogen and one for the oxygen, which we don't bother putting in, and two for water. So the small A, B, C and D are those coefficients. So for our hypothetical reaction, when it comes to equilibrium, we can say that the concentrations of the reactants and products will always obey this relationship. When a chemical formula is put inside a square bracket, so this, for instance, the square brackets mean the concentration of that chemical. So this is the expression. You take the concentration of the products at equilibrium, that's C and D, and you put them over the concentrations of the reactants at equilibrium, that's A and B, and you raise each concentration to a power equal to its stoichiometric coefficient. So in the original equation, the stoichiometric coefficient of chemical C was little C. So we raise the concentration of chemical C to the power of little C and also for D, A and B. This expression will then always equal a particular constant, which is called the equilibrium constant or KEQ. A given chemical reaction will have a particular KEQ and nothing can change this constant except for temperature. So as long as you're performing a reaction at a constant temperature, you can say that at equilibrium, the concentrations of products and reactants will always obey this relationship. So in very rough terms, KEQ is like a ratio, products over reactants. And you can use this in a number of ways. Because KEQ is fixed, because it's a constant, if you know the concentrations of three of your species in this situation where we've got four altogether, you can work out what the fourth should be. You could also determine experimentally the concentrations of all of the species involved and then use those to work out KEQ for a reaction. We're going to practice a few of these types of problems. Before we do, I need to point out some variations on KEQ. The constant in the expression above is written KEQ with a subscript EQ for equilibrium. But it's sometimes referred to as KC where the C refers to concentration and that's to indicate that that expression is written in terms of the concentrations of the species involved. But if you're dealing with a reaction involving gases, it's also possible to write the expression in terms of the pressures of the gases like this. So P means pressure. The subscript C means the pressure of gas C. And then just as in the other form of the expression, we raise that number to the power of the stoichiometric coefficient. However, we will usually be using KC in this course rather than KP.