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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.
For example, adding more S (to the chemical reaction above) from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward (though the equilibrium constant will stay the same).
Some multistep reactions can also have apparent negative activation energies. For example, the overall rate constant k for a two-step reaction A ⇌ B, B → C is given by k = k 2 K 1, where k 2 is the rate constant of the rate-limiting slow second step and K 1 is the equilibrium constant of the rapid
An example is a hydrogen atom abstraction reaction R' + H–R ⇌ R'–H + R with equilibrium constant K H, where R' and R are organic radicals such that R' forms a stronger bond to hydrogen than does R.
For example, carbonic acid: H 2 CO 3 (l) + H 2 O (l) ⇌ HCO 3 − (aq) + H 3 O + (aq) . The concentrations of reactants and products in an equilibrium mixture are determined by the analytical concentrations of the reagents (A and B or C and D) and the equilibrium constant , K .
Le Chatelier–Braun principle analyzes the qualitative behaviour of a thermodynamic system when a particular one of its externally controlled state variables, say , changes by an amount , the 'driving change', causing a change , the 'response of prime interest', in its conjugate state variable , all other externally controlled state variables remaining constant.
For example, if a macromolecule M has three binding sites, K′ 1 describes a ligand being bound to any of the three binding sites. In this example, K′ 2 describes two molecules being bound and K′ 3 three molecules being bound to the macromolecule. The microscopic or individual dissociation constant describes the equilibrium of ligands ...
For example, a poly-cationic receptor containing copper (the host) is coordinated with molecules such as tetracarboxylates, tricarballate, aspartate, and acetate (the guests). This study illustrates that entropy rather than enthalpy determines the binding energy of the system leading to negative cooperativity.