Title: differential molar energy of adsorption
Long Title: IUPAC Gold Book - differential molar energy of adsorption
DOI: 10.1351/goldbook.D01705
Status: current

Definition
When the addition of a differential amount \(\mathrm{d}n_{i}^{\sigma }\) or \(\mathrm{d}n_{i}^{\rm{s}}\) is effected at constant gas volume, the differential molar energy of adsorption of component \(i\), \(\Delta _{a}U_{i}^{\sigma }\) or \(\Delta _{a}U_{i}^{\rm{s}}\), is defined as: \[\Delta _{a}U_{i}^{\sigma }=U_{i}^{\sigma }- U_{i}^{\rm{g}}\] or \[\Delta _{a}U_{i}^{\rm{s}} = U_{i}^{\rm{s}}- U_{i}^{\rm{g}}\] where the differential molar surface excess energy, \(U_{i}^{\sigma }\), is given by \[U_{i}^{\sigma }=(\frac{\partial U^{\sigma }}{\partial n_{i}^{\rm{s}}})_{T,m,n_{j}^{\sigma }}=(\frac{\partial U}{\partial n_{i}^{\sigma }})_{T,m,V^{\rm{g}},p_{i},n_{j}^{\sigma }}\] and the differential molar interfacial energy, \(U_{i}^{s}\), by \[U_{i}^{\rm{s}}=(\frac{\partial U}{\partial n_{i}^{\rm{s}}})_{T,m,V^{\rm{g}},p_{i},n_{j}^{\sigma }}=(\frac{\partial U}{\partial n_{i}^{\rm{s}}})_{T,m,V^{\rm{g}},V^{\rm{s}},p_{i},n_{j}^{\rm{s}}}\] \(U_{i}^{\rm{g}}\) is the differential molar energy of component \(i\) in the gas phase, i.e. \[(\frac{\partial U}{\partial n_{i}^{\rm{g}}})_{T,V,n_{i}^{\rm{g}}}\]

Source
- PAC, 1972, 31, 577. 'Manual of Symbols and Terminology for Physicochemical Quantities and Units, Appendix II: Definitions, Terminology and Symbols in Colloid and Surface Chemistry' on page 603 (https://doi.org/10.1351/pac197231040577)

Other Outputs
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- json: https://goldbook.iupac.org/terms/view/D01705/json
- xml: https://goldbook.iupac.org/terms/view/D01705/xml

Citation: Citation: 'differential molar energy of adsorption' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.D01705
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Accessed: 2026-05-31T03:41:27+00:00