Equilibrium constant
For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture.
However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
A knowledge of equilibrium constants is essential for the understanding of many chemical systems, as well as the biochemical processes such as oxygen transport by hemoglobin in blood and acid–base homeostasis in the human body.
For a system undergoing a reversible reaction described by the general chemical equation a thermodynamic equilibrium constant, denoted by
An equilibrium constant is related to the standard Gibbs free energy change of reaction
by where R is the universal gas constant, T is the absolute temperature (in kelvins), and ln is the natural logarithm.
On the other hand, the reaction quotient at equilibrium does have the dimension of concentration raised to some power (see § Dimensionality, below).
There is no agreed notation for stepwise constants, though a symbol such as KLML is sometimes found in the literature.
In organic chemistry and biochemistry it is customary to use pKa values for acid dissociation equilibria.
For example, if NTA, nitrilotriacetic acid, N(CH2CO2H)3 is designated as H3L and forms complexes ML and MHL with a metal ion M, the following expressions would apply for the dissociation constants.
The cumulative association constants can be expressed as Note how the subscripts define the stoichiometry of the equilibrium product.
Micro-constant values can, in principle, be determined using a spectroscopic technique, such as infrared spectroscopy, where each micro-species gives a different signal.
If the electrode is calibrated in terms of known hydrogen ion concentrations it would be better to write p[H] rather than pH, but this suggestion is not generally adopted.
In biochemistry equilibrium constants are often measured at a pH fixed by means of a buffer solution.
Thermodynamic equilibrium is characterized by the free energy for the whole (closed) system being a minimum.
For systems at constant temperature and pressure the Gibbs free energy is minimum.
At equilibrium The chemical potential, μi, of the ith species can be calculated in terms of its activity, ai.
Setting the sum for the reactants j to be equal to the sum for the products, k, so that δGr(Eq) = 0 Rearranging the terms, This relates the standard Gibbs free energy change, ΔGo to an equilibrium constant, K, the reaction quotient of activity values at equilibrium.
An equilibrium constant is related to the standard Gibbs free energy of reaction change,
This can be avoided by dividing each concentration by its standard-state value (usually mol/L or bar), which is standard practice in chemistry.
These conditions are usually achieved by keeping the reaction temperature constant and by using a medium of relatively high ionic strength as the solvent.
It is not unusual, particularly in texts relating to biochemical equilibria, to see an equilibrium constant value quoted with a dimension.
In general equilibria between two reagents can be expressed as in which case the equilibrium constant is defined, in terms of numerical concentration values, as The apparent dimension of this K value is concentration1−p−q; this may be written as M(1−p−q) or mM(1−p−q), where the symbol M signifies a molar concentration (1M = 1 mol dm−3).
The first is more useful for practical purposes; in fact, the unit of the concentration quotient is often attached to a published stability constant value in the biochemical literature.
[15] The standard Gibbs energy (for each species or for the entire reaction) can be represented (from the basic definitions) as: In the above equation, the effect of temperature on Gibbs energy (and thus on the equilibrium constant) is ascribed entirely to heat capacity.
For a gaseous-reaction example, one may consider the well-studied reaction of hydrogen with nitrogen to produce ammonia: If the pressure is increased by the addition of an inert gas, then neither the composition at equilibrium nor the equilibrium constant are appreciably affected (because the partial pressures remain constant, assuming an ideal-gas behaviour of all gases involved).
[17] In a condensed phase, the pressure dependence of the equilibrium constant is associated with the reaction volume.
For the above reaction, one can expect the change of the reaction equilibrium constant (based either on mole-fraction or molal-concentration scale) with pressure at constant temperature to be: The matter is complicated as partial molar volume is itself dependent on pressure.
Isotopic substitution can lead to changes in the values of equilibrium constants, especially if hydrogen is replaced by deuterium (or tritium).
An example is a hydrogen atom abstraction reaction R' + H–R ⇌ R'–H + R with equilibrium constant KH, where R' and R are organic radicals such that R' forms a stronger bond to hydrogen than does R. The decrease in zero-point energy due to deuterium substitution will then be more important for R'–H than for R–H, and R'–D will be stabilized more than R–D, so that the equilibrium constant KD for R' + D–R ⇌ R'–D + R is greater than KH.
