# Bonded Phases - The Derivation of the Langmuir Adsorption Isotherm for Reverse Phases

The number of molecules will strike and adhere to
the exposed surface (N_{2}) will be proportional to the concentration of solvent in mobile
phase, the unexposed area of surface and another constant
(a),

Thus, _{}

Now, under equilibrium conditions,

N_{1} = N_{2}

Thu _{}

and _{}

or, _{}.......................(3)

where (K) is the distribution
coefficient of the solvent between the stationary phase and a solution
of the solvent in water at a concentration (C_{m}).

Actually, this means that if a
neat sample of solvent is injected on to a column as a solute, when the
mobile phase consists of an aqueous solution of the solvent at
concentration (C_{m}), then the magnitude of its retention
volume will be determined by the magnitude of the distribution
coefficient (K).

Thus, _{}............... ...... (4).

where g = b/a = the desorption-adsorption coefficient of the adsorbing solvent

Now, if the reverse phase is
packed into a column and used with a mobile phase having a solvent
concentration of (C_{m}) in water, the corrected retention
volume (V') is given by the equation derived from the Plate Theory
(30),

V' = Kj where (j) is the total chromatographically available surface area of the reverse phase in the column.

Substituting for (K) from equation (3),

_{}

or, _{} ............................(5)

It is seen that equation (5)
shows that there will be a linear relationship between the reciprocal
of the corrected retention volume and the concentration of solvent in
the mobile phase. It follows, that if retention data is measured over a
range of solvent concentrations, using the solvent itself as a solute,
a linear relationship should be obtained by plotting (1/V') against
(C_{m}). It also follows, that from the intercept and slope of
the graph, numerical values for the (j), (g) and (K) can be
calculated.