Editing Equilibrium constant (section)

== Pressure dependence ==
The pressure dependence of the equilibrium constant is usually weak in the range of pressures normally encountered in industry, and therefore, it is usually neglected in practice. This is true for [[Condensed matter physics|condensed]] reactant/products (i.e., when reactants and products are solids or liquid) as well as gaseous ones.

For a gaseous-reaction example, one may consider the well-studied reaction of hydrogen with nitrogen to produce ammonia:
:N<sub>2</sub> + 3&nbsp;H<sub>2</sub> {{eqm}} 2&nbsp;NH<sub>3</sub>
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). However, the composition at equilibrium will depend appreciably on pressure when:
* the pressure is changed by compression or expansion of the gaseous reacting system, and
* the reaction results in the change of the number of moles of gas in the system.

In the example reaction above, the number of moles changes from 4 to 2, and an increase of pressure by system compression will result in appreciably more ammonia in the equilibrium mixture. In the general case of a gaseous reaction:

:''α''&nbsp;A + ''β''&nbsp;B {{eqm}} ''σ''&nbsp;S + ''τ''&nbsp;T

the change of mixture composition with pressure can be quantified using:

:<math>K_p = \frac{{p_\mathrm{S}}^\sigma {p_\mathrm{T}}^\tau} {{p_\mathrm{A}}^\alpha {p_\mathrm{B}}^\beta} = \frac{{X_\mathrm{S}}^\sigma {X_\mathrm{T}}^\tau} {{X_\mathrm{A}}^\alpha {X_\mathrm{B}}^\beta} P^{\sigma+\tau-\alpha-\beta} = K_X P^{\sigma+\tau-\alpha-\beta}</math>

where ''p'' denote the partial pressures and ''X'' the mole fractions of the components, ''P'' is the total system pressure, ''K<sub>p</sub>'' is the equilibrium constant expressed in terms of partial pressures and ''K<sub>X</sub>'' is the equilibrium constant expressed in terms of mole fractions.

The above change in composition is in accordance with [[Le Chatelier's principle]] and does not involve any change of the equilibrium constant with the total system pressure. Indeed, for ideal-gas reactions ''K<sub>p</sub>'' is independent of pressure.<ref>{{cite book|first=P. W. |last=Atkins |title=Physical Chemistry |publisher=Oxford University Press |date=1978 |edition=6th |page=210}}</ref>

[[Image:Pressure dependence water ionization pKw on P.svg|right|400px|thumb|Pressure dependence of the water ionization constant at 25&nbsp;°C. In general, ionization in aqueous solutions tends to increase with increasing pressure.]]

In a condensed phase, the pressure dependence of the equilibrium constant is associated with the reaction volume.<ref>{{cite journal |pages=549–688 |doi=10.1021/cr00093a005 |title=Activation and reaction volumes in solution. 2 |year=1989 |last1=Van Eldik |first1=R. |last2=Asano |first2=T. |last3=Le Noble |first3=W. J. |journal=Chem. Rev. |volume=89 |issue=3}}</ref> For reaction:

:''α''&nbsp;A + ''β''&nbsp;B {{eqm}} ''σ''&nbsp;S + ''τ''&nbsp;T

the reaction volume is:

:<math>\Delta \bar{V} = \sigma \bar{V}_\mathrm{S} + \tau \bar{V}_\mathrm{T} - \alpha \bar{V}_\mathrm{A} - \beta \bar{V}_\mathrm{B} </math>

where ''V̄'' denotes a [[partial molar volume]] of a reactant or a product.

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:

:<math> \left(\frac{\partial \ln K_X}{\partial P} \right)_T = \frac{-\Delta \bar{V}} {RT}. </math>

The matter is complicated as partial molar volume is itself dependent on pressure.