It is, however, only in the case of systems of more than one component that any difficulty will be found; for only in this case will a choice of components be possible. Take, for instance, the dissociation of calcium carbonate into calcium oxide and carbon dioxide. At each temperature, as we have seen, there is a definite state of equilibrium. When equilibrium has been established, there are three different substances present--calcium carbonate, calcium oxide, and carbon dioxide; and these are the constituents of the system between which equilibrium exists. Now, although these constituents take part in the equilibrium, they are not all to be regarded as components, for they are not mutually independent. On the contrary, the different phases are related to one another, and if two of these are taken, the composition of the third is defined by the equation
{ 12} Now, in deciding the number of components in any given system, not only must the constituents chosen be capable of independent variation, but a further restriction is imposed, and we obtain the following rule: _As the components of a system there are to be chosen the_ smallest number _of independently variable constituents by means of which the composition of each phase participating in the state of equilibrium can be expressed in the form of a chemical equation._
Applying this rule to the case under consideration, we see that of the three constituents present when the system is in a state of equilibrium, only two, as already stated, are independently variable. It will further be seen that in order to express the composition of each phase present, two of these constituents are necessary. The system is, therefore, one of _two components_, or a system of the second order.
When, now, we proceed to the actual choice of components, it is evident that any two of the constituents can be selected. Thus, if we choose as components CaCO_{ 3} and CaO, the composition of each phase can be expressed by the following equations:--
CaCO_{ 3} = CaCO_{ 3} + 0CaO CaO = CaO + 0CaCO_{ 3} CO_{ 2} = CaCO_{ 3} - CaO
As we see, then, both zero and negative quantities of the components have been introduced; and similar expressions would be obtained if CaCO_{ 3} and CO_{ 2} were chosen as components. The matter can, however, be simplified and the use of negative quantities avoided if CaO and CO_{ 2} are chosen; and it is, therefore, customary to select these as the components.