The effect of temperature and pressure on the adsorption of gases on solid surfaces can be described using adsorption isotherms, which are mathematical equations that relate the amount of gas adsorbed on a solid surface to the pressure or concentration of the gas at a constant temperature. Two widely used isotherms are the Langmuir isotherm and the Freundlich isotherm.1. Langmuir Isotherm:The Langmuir isotherm is based on the assumption that adsorption occurs on a homogeneous surface with a finite number of adsorption sites, and that there is no interaction between adsorbed molecules. The Langmuir isotherm equation is given by: = KP / 1 + KP where is the fractional coverage of the surface the ratio of occupied sites to the total number of sites , P is the pressure of the gas, and K is the Langmuir constant, which is related to the enthalpy of adsorption and temperature.According to the Langmuir isotherm, at low pressures, the adsorption is directly proportional to the pressure P , while at high pressures, the adsorption reaches a saturation limit 1 . The effect of temperature on the Langmuir constant K can be described by the Arrhenius equation:K = K0 * exp -H_ads / RT where K0 is the pre-exponential factor, H_ads is the enthalpy of adsorption, R is the gas constant, and T is the temperature. As the temperature increases, the value of K decreases, which means that the adsorption capacity of the solid surface decreases.2. Freundlich Isotherm:The Freundlich isotherm is an empirical equation that assumes a heterogeneous surface with a non-uniform distribution of adsorption sites and energies. The Freundlich isotherm equation is given by:x/m = KF * P^1/n where x/m is the amount of gas adsorbed per unit mass of the solid, P is the pressure of the gas, KF is the Freundlich constant, and n is the heterogeneity factor.The Freundlich isotherm does not predict saturation of the surface, and the effect of temperature on the adsorption can be described by the van't Hoff equation:ln KF = -H_ads / RT + ln KF0 where KF0 is the pre-exponential factor, H_ads is the enthalpy of adsorption, R is the gas constant, and T is the temperature. Similar to the Langmuir isotherm, as the temperature increases, the adsorption capacity of the solid surface decreases.Real-life examples:1. Activated carbon is widely used for the adsorption of pollutants from air and water. The adsorption of volatile organic compounds VOCs on activated carbon can be described by the Langmuir or Freundlich isotherms, depending on the specific compound and the surface properties of the activated carbon.2. Silica gel is commonly used as a desiccant to remove moisture from air and gases. The adsorption of water vapor on silica gel can be described by the Langmuir isotherm, with the adsorption capacity decreasing as the temperature increases.3. Metal-organic frameworks MOFs are a class of porous materials with potential applications in gas storage and separation. The adsorption of gases such as hydrogen, methane, and carbon dioxide on MOFs can be described by the Langmuir or Freundlich isotherms, depending on the specific MOF and the gas being adsorbed.