Environmental Engineering Reference
In-Depth Information
PURE SOLUTE ( A )
Two-phase
envelope
T 1
T 2
T 3
PURE
SOLVENT ( S )
PURE
DILUENT ( B )
Figure 3.13 Effect of temperature on solubility envelope ( T 3 >
T 2 >
T 1 ).
of mass transfer is limited by either the rate of diffusion through the fluid phase or the rate
of sorption onto or into the sorbent. The sorption/desorption steps are normally considered
to be rapid relative to the diffusion steps. So, equations describing the equilibrium between
the fluid and solid phase (at constant temperature) have been developed; these equations
are called isotherms. Isotherms allow one to predict the capacity of a given sorbent for a
particular sorbate as a function of sorbate concentration in the fluid phase. More complete
descriptions and derivations are available elsewhere [5-7].
Single-component isotherms
Isotherms are derived from equilibrium measurements of mass of sorbate adsorbed for a
given mass of sorbent as a function of sorbate concentration in the fluid phase in contact
with the sorbent at constant temperature. Based on the shape of the resulting curve, the
measurements can be fitted to an equation. Figure 3.14 illustrates the various types of
isotherms and their classification by Roman numeral. Types I and II are the most common.
A Type I isotherm is representative of sorbents with very small pore size which lead to
unimolecular adsorption. Types II and III are representative of sorbents with a pore-size
distribution such that multilayer sorption (and even capillary condensation) are possible.
Types IV and V are characterized by a hysterisis loop. The amount adsorbed at equilibrium
is different at a given solute concentration in the fluid phase depending on whether the
fluid phase concentration is increasing or decreasing. This effect implies that it is difficult
to desorb the solute once it is adsorbed within the concentration range of the hysterisis
loop (can you explain why?). Note that Types IV and V isotherms have similar shape to
Types II and III respectively during sorption.
Once the measurements have been obtained, the data can be fitted to an isotherm as stated
above. The model equations can be derived based on various assumptions concerning the
accessibility of adsorption sites, the number of molecules that can be adsorbed per site
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