Page 55 - Adsorption Technology & Design, Elsevier (1998)

52 Fundamentals of adsorption equilibria

sum of coverages of the individual components. The resulting isotherm for
component i is

Oi(-qi )= bipin (3.31)
qmi 1 + ~ bipi
1
where qm~ is the quantity of component i in a monolayer of mixed
adsorbates. It has been shown, by invoking thermodynamic principles, that,
for consistency, the monolayer quantity or volume for each of the adsorbed
components must be identical. This means, for example, that qm~ = qmj
(Kemball et al. 1948, Broughton 1948). For a gas mixture containing
adsorbate molecules which would occupy substantially different areas on
adsorption, such a constraint is unrealistic and so the monolayer capacities
of each adsorbate are then regarded as empirical quantities, qm~ in equation
(3.31) would thus be replaced by an empirical constant ai. However, such
empirical constants may not be applicable over an extended range of partial
pressures and their use should then be restricted to the range of partial
pressures for which they are ostensibly constant.
Indeed, the extended Langmuir equation (3.31) provides a satisfactory
correlation of single component isotherm data for carbon dioxide-carbon
monoxide mixtures adsorbed on a porous activated carbon (Battrum and
Thomas 1991). From the single-component isotherm data for CO2 values of
aco~ and bco~ may be obtained from the intercept and slope of a linear plot
of 1/qco2 against 1/pco~. Similarly values of aco and bco are obtained from
single component isotherm data for CO. The values so obtained are then
substituted into equation (3.31) to obtain the isotherms for each of the
components CO2 and CO in the mixture. On the other hand, for mixtures of
benzene and toluene vapours, the extended Langmuir isotherm for binary
mixture adsorption on an activated charcoal is only correlated by the
constants obtained from the single component toluene isotherm when the
constant bB for benzene was determined empirically by linearizing the
extended Langmuir equation for the component toluene (Thomas and
Lombardi 1971). Data relating to the adsorption of benzene-toluene vapour
mixtures on charcoal do not conform with the condition that aT and aB are
equal. This is demonstrated by defining a separation factor
q2[c2
(3.32)
K12 =
ql/cl
by analogy with the definition for vapour-liquid mixtures in which a
comparison is made of the relative volatilities of each component. If QT and
CT represent total concentrations of adsorbed and gas (or vapour) phases,
respectively, then equation (3.32) may be written in the alternative form