Evaporation of molecules

The BET approach is essentially an extension of the Langmuir approach. Van der Waals forces are regarded as the dominant forces, and the adsorption of all layers is regarded as physical, not chemical. One sets the rates of adsorption and desorption equal to one another, as in the Langmuir case in addition, one requires that the rates of adsorption and desorption be identical for each and every molecular layer. That is, the rate of condensation on the bare surface is equal to the rate of evaporation of molecules in the first layer. The rate of evaporation from the second layer is equal to the rate of condensation on top of the first layer, etc. One then sums over the layers to determine the total amount of adsorbed material. The derivation also assumes that the heat of adsorption of each layer other than the first is equal to the heat of condensation of the bulk adsorbate material (i.e., van der Waals forces of the adsorbent are transmitted only to the first layer). If it is assumed that a very large or effectively infinite number of layers can be adsorbed, the following result is arrived at after a number of relatively elementary mathematical operations... 

If the chemical reaction proceed by the combination and evaporation of molecules from m adjacent spaces the velocity of chemical change will be given by... 

Vapor pressure is caused by the evaporation of molecules at the surface of a liquid. These escaping molecules exert an upward pressure as they leave the liquid (Figure 7.2). For example, gasoline has a greater vapor pressure than syrup because molecules of gasoline evaporate more readily than molecules of syrup. Perfume and alcohol have vapor pressures that are greater than the vapor pressure of water. 

Evaporation (outgassing) is the release of adsorbed molecules at room temperature and pressure, while desorption (degassing) is the forced evaporation of molecules by either applying greater heat or decreasing the ambient pressure. 

Any valid chemical model of adsorption should predict an equation that accurately describes the experimental adsorption isotherm. In 1918, Langmuir developed a kinetic model of adsorption that described vapor adsorption on a homogeneous surface. The surface is assumed to possess a certain number of identical sites, S. Of these sites, Sa are occupied by adsorbate molecules and So = S — Sa are vacant. The rate of evaporation of molecules from the surface is reasoned to be proportional to S because all molecules are adsorbed with the same bond strength on identical sites (adsorbate molecules on adjacent sorption sites are assumed not to interact). Thus, each molecule has an equal chance of desorbing from the surface in any particular time period. Mathematically, this means that... 

From a kinetic point of view, a cluster is formed and changes its size by the condensation and evaporation of molecules. At a given temperature, the evaporation rate of molecules (per unit time and unit area) is independent of S, but determined primarily by i, while... 

For diatomic molecules and polyatomic molecules generally, the moment of inertia appears in the integration constant of the vapour-pressure equation, because the existence of rotations in the gas, while there are usually none in the solid, favours the evaporation of molecules by offering more possibilities of distribution in the gas phase. The greater the moment of inertia, the smaller the rotational quantum and the more numerous the levels. Hence the increase of i with I revealed in the formula. 

A crystal of iodine in an evacuated vessel will gradually change into iodine gas by the evaporation of molecules from its surface. Occasionally one of these free gas molecules will again strike the surface of the crystal, and it may stick to the surface, held by the van der Waals attraction of the other crystal molecules. This is called condensation of the gas molecules. 

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