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For example, if equilibrium is specified by a single chemical equation:, [24] ∑ j = 0 m ν j R j = 0 {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0} where ν j is the stoichiometric coefficient for the j th molecule (negative for reactants, positive for products) and R j is the symbol for the j th molecule, a properly balanced equation will obey:
The equation of chemical equilibrium can be expressed symbolically as reactant(s) ⇌ product(s) The sign ⇌ means "are in equilibrium with". This definition refers to macroscopic properties. Changes do occur at the microscopic level of atoms and molecules, but to such a minute extent that they are not measurable and in a balanced way so that ...
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
a thermodynamic equilibrium constant, denoted by , is defined to be the value of the reaction quotient Q t when forward and reverse reactions occur at the same rate. At chemical equilibrium , the chemical composition of the mixture does not change with time, and the Gibbs free energy change Δ G {\displaystyle \Delta G} for the reaction is zero.
Then the two systems are said to be in thermal equilibrium when the long-range forces are unchanging in time and the transfer of energy as heat between them has slowed and eventually stopped permanently; this is an example of a contact equilibrium. Other kinds of contact equilibrium are defined by other kinds of specific permeability. [3]
Raoult's law defines the equilibrium vapor pressure of an ideal solution. Dynamic equilibrium can also exist in a single-phase system. A simple example occurs with acid-base equilibrium such as the dissociation of acetic acid, in an aqueous solution. + +
A central aim in equilibrium thermodynamics is: given a system in a well-defined initial state of thermodynamic equilibrium, subject to accurately specified constraints, to calculate, when the constraints are changed by an externally imposed intervention, what the state of the system will be once it has reached a new equilibrium. An equilibrium ...
Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where = = = = Then the only non-trivial equation is the -equation, which now reads + = Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.