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- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Analytical_Sciences_Digital_Library/In_Class_Activities/Separation_Science/2%3A_Chromatography__Background/02_Distribution_IsothermsNote that these equations take the form of equilibrium expressions, and that K C is a constant for the distribution of a solute compound between two particular phases. (K X depends on the relative vol...Note that these equations take the form of equilibrium expressions, and that K C is a constant for the distribution of a solute compound between two particular phases. (K X depends on the relative volumes of the two phases.) Coordinate system with the concentration of analyte in the stationary phase (C S ) shown on the y-axis and the concentration of analyte in the mobile phase (C M ) shown on the x-axis.
- https://chem.libretexts.org/Courses/Lebanon_Valley_College/CHM_312%3A_Physical_Chemistry_II_(Lebanon_Valley_College)/10%3A_Complex_Reaction_Mechanisms/10.07%3A_Using_Langmuir_Isotherms_to_Derive_Rate_Laws_for_Surface-Catalyzed_Gas-Phase_ReactionsIt is possible to predict how the kinetics of certain heterogeneously-catalysed reactions might vary with the partial pressures of the reactant gases above the catalyst surface by using the Langmuir i...It is possible to predict how the kinetics of certain heterogeneously-catalysed reactions might vary with the partial pressures of the reactant gases above the catalyst surface by using the Langmuir isotherm expression for equilibrium surface coverages.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/31%3A_Solids_and_Surface_Chemistry/31.07%3A_Isotherms_are_Plots_of_Surface_Coverage_as_a_Function_of_Gas_Pressure_at_Constant_TemperatureThis page examines the equilibrium between gas molecules and adsorbed species on solid surfaces, introducing the Langmuir isotherm, which connects surface coverage to gas pressure at constant temperat...This page examines the equilibrium between gas molecules and adsorbed species on solid surfaces, introducing the Langmuir isotherm, which connects surface coverage to gas pressure at constant temperature. The isotherm predicts increased surface coverage with rising pressure until a monolayer is achieved. The derivation involves temperature-dependent constants and assumptions about surface site energies, emphasizing the importance of constant enthalpy of adsorption for the model's validity.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Surface_Science_(Nix)/03%3A_The_Langmuir_Isotherm/3.02%3A_Langmuir_Isotherm_-_derivation_from_equilibrium_considerationsWe may derive the Langmuir isotherm by treating the adsorption process as we would any other equilibrium process - except in this case the equilibrium is between the gas phase molecules, together with...We may derive the Langmuir isotherm by treating the adsorption process as we would any other equilibrium process - except in this case the equilibrium is between the gas phase molecules, together with vacant surface sites, and the species adsorbed on the surface.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Surface_Science_(Nix)/03%3A_The_Langmuir_IsothermA continuous monolayer of adsorbate molecules surrounding a homogeneous solid surface is the conceptual basis for this adsorption model. The Langmuir isotherm is formally equivalent to the Hill equati...A continuous monolayer of adsorbate molecules surrounding a homogeneous solid surface is the conceptual basis for this adsorption model. The Langmuir isotherm is formally equivalent to the Hill equation in biochemistry.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Topics_in_Thermodynamics_of_Solutions_and_Liquid_Mixtures/01%3A_Modules/1.24%3A_Misc/1.14.02%3A_Adsorption-_Langmuir_Adsorption_Isotherm-_One_AdsorbateThus xj is the mole fraction of solute j in the aqueous phase; xad1 is the mole fraction of water in a thin solution adjacent to the surface of the adso...Thus xj is the mole fraction of solute j in the aqueous phase; xad1 is the mole fraction of water in a thin solution adjacent to the surface of the adsorbate; x1 is the mole fraction of water in the aqueous solution.; xadj is the mole fraction of the substance j in the adsorbed layer.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Surface_Science_(Nix)/03%3A_The_Langmuir_Isotherm/3.03%3A_Langmuir_Isotherm_from_a_Kinetics_ConsiderationThe equilibrium that may exist between gas adsorbed on a surface and molecules in the gas phase is a dynamic state, i.e. the equilibrium represents a state in which the rate of adsorption of molecules...The equilibrium that may exist between gas adsorbed on a surface and molecules in the gas phase is a dynamic state, i.e. the equilibrium represents a state in which the rate of adsorption of molecules onto the surface is exactly counterbalanced by the rate of desorption of molecules back into the gas phase. It should therefore be possible to derive an isotherm for the adsorption process simply by considering and equating the rates for these two processes.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/31%3A_Solids_and_Surface_ChemistryThis page explains the unit cell as the essential component of crystalline solids, detailing concepts such as Miller indices for lattice orientation and X-ray diffraction for lattice measurement. It a...This page explains the unit cell as the essential component of crystalline solids, detailing concepts such as Miller indices for lattice orientation and X-ray diffraction for lattice measurement. It addresses the connection between structure factors and electron density via Fourier transforms, surface adsorption with the Langmuir isotherm, and the influence of surface structure on chemical reactions.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Surface_Science_(Nix)/03%3A_The_Langmuir_Isotherm/3.04%3A_Variation_of_Surface_Coverage_with_Temperature_and_PressureApplication of the assumptions of the Langmuir Isotherm leads to readily derivable expressions for the pressure dependence of the surface coverage.
