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Equilibrium is the condition at which a system is not changing. State variables such as temperature and pressure are constant, the number of phases is not changing, and the concentrations of the components of the system are not changing. Reactions are still occurring on the microscopic scale, but the macroscopic concentrations are not changing.
When we say a system is at equilibrium we always mean that it is in a thermodynamic equilibrium. A system might be kinetically stable or metastable, but not at equilibrium. A balloon containing a mixture of H2 and O2 at room temperature is not in equilibrium. However, it does not explode without a spark. Similarly, equilibrium and a "steady state" are not necessarily the same thing. An open system in which reactants are entering and products are leaving a reactor can be in a steady state but not at equilibrium.
Equilibrium is described quantitatively by the equilibrium constant. The related reaction quotient provides a quantitative measure of how far a system is from equilibrium.
A chemical specie will always exist in equilibrium with other forms of itself. The other forms may exist in undetectable amounts but they are always present. These other forms arise due to the natural disorder of nature that we call entropy (it's impossible to be perfect). As an example, pure water consists of the molecular compound and dissociated ions that exist together in equilibrium:
H2O(l) H+(aq) + OH-(aq)
The (l) subscript refers to the liquid state, and the (aq) subscript refers to ions in aqueous solution.
More details are available for the following classifications of chemical equilibria:
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