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If at least one has a positive real part, the point is unstable. If at least one eigenvalue has negative real part and at least one has positive real part, the equilibrium is a saddle point and it is unstable. If all the eigenvalues are real and have the same sign the point is called a node.
where ln denotes the natural logarithm, is the thermodynamic equilibrium constant, and R is the ideal gas constant.This equation is exact at any one temperature and all pressures, derived from the requirement that the Gibbs free energy of reaction be stationary in a state of chemical equilibrium.
Most commonly [OH −] is replaced by K w [H +] −1 in equilibrium constant expressions which would otherwise include hydroxide ion. Solids also do not appear in the equilibrium constant expression, if they are considered to be pure and thus their activities taken to be one. An example is the Boudouard reaction: [14] 2 CO ⇌ CO 2 + C
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is ...
It is the equilibrium constant for a chemical reaction + + known as dissociation in the context of acid–base reactions. The chemical species HA is an acid that dissociates into A −, called the conjugate base of the acid, and a hydrogen ion, H +.
In a new bottle of soda, the concentration of carbon dioxide in the liquid phase has a particular value. If half of the liquid is poured out and the bottle is sealed, carbon dioxide will leave the liquid phase at an ever-decreasing rate, and the partial pressure of carbon dioxide in the gas phase will increase until equilibrium is reached.
However, since water is in vast excess, the concentration of water is usually assumed to be constant and is omitted from equilibrium constant expressions. Often, the metal and the ligand are in competition for protons. [note 4] For the equilibrium p M + q L + r H ⇌ M p L q H r. a stability constant can be defined as follows: [28] [29]
In the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system [1] (e.g. gas, liquid, solid, crystal, or emulsion), not the path which ...