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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.
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.
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .
The relative activity of a species i, denoted a i, is defined [4] [5] as: = where μ i is the (molar) chemical potential of the species i under the conditions of interest, μ o i is the (molar) chemical potential of that species under some defined set of standard conditions, R is the gas constant, T is the thermodynamic temperature and e is the exponential constant.
The value of the equilibrium constant for the formation of a 1:1 complex, such as a host-guest species, may be calculated with a dedicated spreadsheet application, Bindfit: [4] In this case step 2 can be performed with a non-iterative procedure and the pre-programmed routine Solver can be used for step 3.
An example of this is quasi-static expansion of a mixture of hydrogen and oxygen gas, where the volume of the system changes so slowly that the pressure remains uniform throughout the system at each instant of time during the process. [2] Such an idealized process is a succession of physical equilibrium states, characterized by infinite ...
relating the equilibrium constant, , for a given equilibrium reaction with substituent R and the reference constant when R is a hydrogen atom to the substituent constant σ which depends only on the specific substituent R and the reaction rate constant ρ which depends only on the type of reaction but not on the substituent used.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...