Editing Reaction rate (section)

==Pressure dependence==
The pressure dependence of the rate constant for [[Condensed matter physics|condensed]]-phase reactions (that is, when reactants and products are solids or liquid) is usually sufficiently weak in the range of pressures normally encountered in industry that it is neglected in practice.

The pressure dependence of the rate constant is associated with the activation volume. For the reaction proceeding through an activation-state complex:

<math chem display=block>\ce{A + B <=>} \ |\ce{A} \cdots \ce{B}|^\ddagger \ \ce{-> P}</math>

the activation volume, {{math|Δ''V''<sup> ‡</sup>}}, is:

<math chem display=block>\Delta V^{\ddagger} =  \bar{V}_{\ddagger} - \bar{V}_\mathrm{A} - \bar{V}_\mathrm{B} </math>

where {{mvar|V̄}} denotes the [[partial molar volume]] of a species and {{math|‡}} (a [[double dagger]]) indicates the activation-state complex.

For the above reaction, one can expect the change of the [[reaction rate constant]] (based either on [[mole fraction]] or on [[molar concentration]]) with pressure at constant temperature to be:<ref name=LM/>{{rp|390}}

:<math> \left(\frac{\partial \ln k_x}{\partial P} \right)_T = -\frac{\Delta V^{\ddagger}} {RT}</math>

In practice, the matter can be complicated because the partial molar volumes and the activation volume can themselves be a function of pressure.

Reactions can increase or decrease their rates with pressure, depending on the value of {{math|Δ''V''<sup> ‡</sup>}}. As an example of the possible magnitude of the pressure effect, some organic reactions were shown to double the reaction rate when the pressure was increased from atmospheric (0.1&nbsp;MPa) to 50&nbsp;MPa (which gives {{math|1=Δ''V''<sup> ‡</sup> =}}&nbsp;−0.025&nbsp;L/mol).<ref>{{cite book|last=Isaacs|first=Neil S.|title=Physical Organic Chemistry|edition=2nd|chapter=Section 2.8.3|publisher=Addison Wesley Longman|location=Harlow|date=1995|isbn=9780582218635|chapter-url-access=registration|chapter-url=https://archive.org/details/physicalorganicc00neil}}</ref>