Chemical element more than one way, allowing the pure element to exist in multiple chemical structures (spatial arrangements of atoms), known as allotropes, which differ in their properties. For example, carbon can be found as diamond, which has a tetrahedral structure around each carbon atom; graphite, which has layers of carbon atoms with a hexagonal structure stacked on top of each other; graphene, which is a single layer of graphite that is very strong; fullerenes, which have nearly spherical shapes; and carbon nanotubes, which are tubes with a hexagonal structure (even these may differ from each other in electrical properties). The ability
Chemical equilibrium of the concentrations at the given temperature and pressure. (See Thermodynamic databases for pure substances.) Note that the second equation is just the initial constraints for minimization. This method of calculating equilibrium chemical concentrations is useful for systems with a large number of different molecules. The use of "k" atomic element conservation equations for the mass constraint is straightforward, and replaces the use of the stoichiometric coefficient equations. The results are consistent with those specified by chemical equations. For example, if equilibrium is specified by a single chemical equation: , where ν is the stochiometric coefficient for the "j" th