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The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
The van 't Hoff equation also shows that, for an exothermic reaction (<), when temperature increases K decreases and when temperature decreases K increases, in accordance with Le Chatelier's principle. The reverse applies when the reaction is endothermic.
The third of seven children, van 't Hoff was born in Rotterdam, Netherlands, 30 August 1852. His father was Jacobus Henricus van 't Hoff Sr., a physician, and his mother was Alida Kolff van 't Hoff. [10] From a young age, he was interested in science and nature, and frequently took part in botanical excursions.
In 1884, Jacobus van 't Hoff proposed the Van 't Hoff equation describing the temperature dependence of the equilibrium constant for a reversible reaction: = where ΔU is the change in internal energy, K is the equilibrium constant of the reaction, R is the universal gas constant, and T is thermodynamic temperature.
To a first approximation, the van 't Hoff equation may be used. ... An example of gas-phase equilibrium is provided by the Haber–Bosch process of ammonia synthesis.
Here is the concentration of a species in the aqueous phase, and is the partial pressure of that species in the gas phase under equilibrium conditions. The SI unit for H s c p {\displaystyle H_{\rm {s}}^{cp}} is mol/(m 3 ·Pa); however, often the unit M/atm is used, since c a {\displaystyle c_{\text{a}}} is usually expressed in M (1 M = 1 mol ...
Despite the limitations of this derivation, the equilibrium constant for a reaction is indeed a constant, independent of the activities of the various species involved, though it does depend on temperature as observed by the van 't Hoff equation.
The enthalpy of reaction is then found from the van 't Hoff equation as = . A closely related technique is the use of an electroanalytical voltaic cell , which can be used to measure the Gibbs energy for certain reactions as a function of temperature, yielding K e q ( T ) {\displaystyle K_{\mathrm {eq} }(T)} and thereby Δ rxn H ⊖ ...