Page 112 - Gas Adsorption Equilibria

98 Chapter 2

On principle calorimetric data of adsorbed phases can be calculated from
adsorption equilibria data, i. e. adsorption isotherms, if these are available for
different temperatures. From the Clausius-Clapeyron equation applied to the
phase equilibrium in the ideal sorptive gas (f) – adsorbate (a) system, one can
derive an equation for the isosteric differential adsorption enthalpy or isosteric
differential heat of adsorption [2.2, p. 43], [2.26, p. 38]

which here has been assumed to be independent of temperature, cp. Chap. 7,
Fig. 7.1. This quantity is related to the enthalpy of the adsorbate by

i. e. we have

In practical applications of Eq. (2.37) the r.h.s. differential quotient has to be
approximated by a difference quotient, i. e.

This may cause considerable deviations of numerical values for
calculated in this way via (2.37) from measured data of or which
may add up to a 100 % or even more [2.23]. Hence it always is recommended
to measure integral adsorption enthalpies or integral heats of adsorption
(2.36) and to determine the differential heats of adsorption by
differentiating analytic expressions for to the mass
adsorbed, cp. (2.38).

In order to measure simultaneously the mass and the enthalpy of an
adsorbed phase, the adsorption vessel in the volumetric instrument, Fig. 2.1,
has to be replaced by a calorimeter vessel. Traditionally this vessel is