The Langmuir theory of adsorption only applies to forming a monomolecular layer of gas molecules on a solid surface. The theory of adsorption proposed in 1938 by Brunauer, Emmett and Teller is known as the BET theory. They assume that physical adsorption resulting in the formation of multilayers is the accurate picture of adsorption.
The BET theory assumes that the solid surface possesses uniform, localized sites and that adsorption at one site does not affect adsorption at neighbouring sites, as was in the Langmuir theory. It is further assumed that molecules can be adsorbed in the second, third,….. and nth layers, the surface area available for the nth layer being equal to coverage of the (n-1)th layer.
The energy of adsorption in the first layer, E1, is assumed to be constant, and the energy of adsorption in succeeding layers is supposed to be the same as EL, the energy of liquefaction of the gas. Based on the above assumptions, Brunauer, Emmett, and Teller derived the following equation, known after them as the BET equation;
Here, vtotal = volume of the gas adsorbed at the pressure p
Vmono = volume adsorbed when the surface of the solid is entirely covered with a monolayer of the adsorbed molecules of the gas
C = constant depending upon the nature of the gas
Here, E1 = the heat of adsorption in the first layer
EL = the heat of liquefaction of the gas
C = constant for a given gas
Vmono = constant for a gas-solid system
Plot a graph of p/vtotal (p0-p) against p/p0 should give a straight line. It is checked in the case of the adsorption of many gases on various solid adsorbents. As shown in the graph, the result obtained in the case of adsorption of nitrogen on silica gel at -183˚C.
BET plot for the adsorption of N2 on silica get at 183c
The plot obtained is a straight line in most cases as long as pressure p does not exceed one-third of the saturation pressure p0, i.e. the pressure required to condense the gas into the liquid state at the prevailing temperature.
The slope of the linear plot gives the value of (c-1)/(vmono c), while the intercept yields the value of 1/(vmonoc). So, both vmono and c can be evaluated from the slope and the intercept.
