Relative method, Harkins and Jura

Harkins and Jura [87] derived ati equation, by analogy with condensed liquid layers, independent of Vm hence avoiding any explicit assumption of the value of molecular area of the adsorbate in the calculation of surface area. 

Condensed monolayers on water are characterized by the fact that they exhibit a linear pressure-area relationship  

The relationship persists up to high pressures where the film is several molecules thick. They transformed this relationship into an equivalent equation  

0 is a constant, S is the surface area of the solid, M is the molar gas volume, R is the molar gas constant, T the absolute temperature and N is the Avogadro s constant. 

Equation (2.65) involves only the quantities P and V which are measured directly in the experimental determination of adsorption. Harkins and Jura reported that this simple equation was valid over more than twice the pressure range of any other two-constant adsorption isotherm equation. 

When a thin film of fatty acid is spread on the surface of water the surface tension of the water is reduced from yo to 7- A barrier placed between pure water and water with a surface film will experience a pressure difference resulting from the tendency of the film to spread. This surface pressure , n, is given by 

Langmuir, in 1917, constructed the film balance for the measurement of the surface or spreading pressure. Thus, it became possible to experimentally observe that adsorbed films pass through several states of molecular arrangement. The various states resemble that of a two-dimensional gas, a low-density liquid, and finally a higher density or condensed-liquid state. In the latter case the spreading pressure can be described by the linear relationship, 

A fundamental equation derived by Gibbs is used to calculate the spreading pressure of films on solids where, unlike films on liquids, it cannot be experimentally determined. Guggenheim and Adam reduced Gibbs general adsorption equation to equation (7.3) for the special case of gas adsorption 

The terms in equation (7.3) have previously been defined asW = weight of adsorbate, M = adsorbate molecular weight, S, = solid surface area and P = equilibrium pressure. 

The implicit assumption made in deriving equation (7.4) is that an adsorbed gas on a solid surface behaves similarly to a thin film of fatty acid on the surface of water. 

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