The success of kinetic theories directed toward the measurements of surface areas depends upon their ability to predict the number of adsorbate molecules required to cover the solid with a single molecular layer. Equally important is the cross-sectional area of each molecule or the effective area covered by each adsorbed molecule on the surface. The surface area then, is the product of the number of molecules in a completed monolayer and the effective cross-sectional area of an adsorbate molecule.

The asymptotic approach of the quantity adsorbed toward a limiting value indicates that type I isotherms are limited to, at most, a few molecular layers. In the case of chemisorption, only one layer can be bonded to the surface and, therefore, true chemisorption always exhibits a type I isotherm. Although it is possible to calculate the number of molecules in the monolayer from the type I chemisorption isotherm, some serious difficulty is encountered when attempts are made to apply the cross-sectional adsorbate area. This difficulty arises because chemisorption tightly binds and localizes the adsorbate to a specific surface site so that the spacing between adsorbed molecules will depend upon the adsorbent surface structures as well as the size of the adsorbed molecules or atoms. In those cases where the surface sites are widely separated, the calculated surface area will be smaller than the actual values because the number of molecules in the monolayer will be less than the maximum number which the surface can accommodate. Nevertheless, it will be instructive to consider the type I isotherm in preparation for the more rigorous requirements of the other five types.

Using a kinetic approach, Langmuir was able to describe the type I isotherm with the assumption that adsorption was limited to a monolayer. According to the kinetic theory of gases, the number of molecules N striking unit area of surface per second is given by

... 1

where  is Avogadro's number, P is the adsorbate pressure, M is the adsorbate molecular weight, R is the gas constant and T is the absolute temperature. If  is the fraction of the surface unoccupied (i.e., with no adsorbed molecules) then the number of collisions with bare or uncovered surface per unit area of surface each second is

... 2

where k is . The number of molecules striking and adhering to each unit area of surface is

... 3

where A1 is the condensation coefficient and represents the probability of a molecule's being adsorbed upon collision with the surface.

The rate at which adsorbed molecules leave each unit area of surface is given by

... 4

where N m is the number of adsorbate molecules in a completed monolayer of unit area,  is the fraction of the surface occupied by the adsorbed molecules, E is the energy of adsorption and V1 is the vibrational frequency of the adsorbate normal to the surface when adsorbed. The product  is the number of molecules adsorbed per unit area. Multiplication by V1

converts this number of molecules to the maximum rate at which they can leave the surface. The term e ^-E/RT represents the probability that an adsorbed molecule possesses adequate energy to overcome the net attractive potential of the surface. Thus, equation (4) contains all the parameters required to describe the rate at which molecules leave each unit area of surface.

At equilibrium the rates of adsorption and desorption are equal. Thus equating (3) and (4):

... 5

Recognizing that  one obtains

 ... 6

then

 ... 7

Allowing

 ... 8

Substitution of equation (8) into (7) gives

 ... 9

The assumption implicit in equation (8) is that the adsorption energy E is constant, which implies an energetically uniform surface. Up to and including one layer of coverage one can write

 ... 10

where N and N m are the number of molecules in the incomplete and complete monolayer, respectively, and W/W m is the weight adsorbed relative to the weight adsorbed in a completed monolayer. Substituting W/W m for , in equation (9) yields

 ... 11

Equation (11) is the Langmuir equation for Type I isotherms. Rearrangement of equation (11) gives

 ... 12

A plot of P/W versus P will give a straight line of slope 1/W m and intercept 1/KW m from which both K and Wm can be calculated. Having established W m, the sample surface area S t can then be calculated from equation (13):

 ... 13

where Ax and  are the cross-sectional area and the molecular weight of the adsorbate, respectively, and  is Avogadro's number.

Although the Langmuir equation describes type I and sometimes chemisorption isotherms, it fails to be adequately general to treat physical adsorption and the type II-type V isotherms. In addition, surface area measurements obtained from type I isotherms are subject to uncertainties, regardless of whether chemisorption or physical adsorption is occurring. In chemisorption, localization of the adsorbate molecules leaves the value of A x seriously in question, since the adsorbate will adsorb only at active surface sites, leaving an unspecified area around each chemisorbed molecule. When applied to physical adsorption, the type I isotherm is associated with the pore filling of micropores with no clearly defined region of monolayer coverage.