Page 178 - Separation process principles 2

4.7 Solid-Liquid Systems 143

q~ =concentration of adsorbate, mollunit mass of
adsorbent
Q = volume of liquid (assumed to remain constant
during adsorption)
S = mass of adsorbent (solute-free basis)
A material balance on the solute, assuming that the entering
adsorbent is free of solute and that adsorption equilibrium is
achieved, as designated by the asterisk superscript on q,
i mmole
! Equilibrium concentration, c, - gives
liter
Figure 4.25 Adsorption isotherm for phenol from an aqueous
solution in the presence of activated carbon at 20°C.
This equation can be rearranged to the form of a straight line
that can be plotted on the graph of an adsorption isotherm of
I
the type in Figure 4.25, to obtain a graphical solution at equi-
be performed at a fixed temperature for each liquid mixture
librium for c~ and qi. Thus, solving (4-28) for q;,
and adsorbent to provide data for plotting curves, called
adsorption isotherms. Figure 4.25, taken from the data of
Fritz and Schuluender [13], is an isotherm for the adsorption
of phenol from an aqueous solution onto activated carbon at
20°C. Activated, powdered, or granular carbon is a micro- The intercept on the c~ axis is cr)Q/S, and slope is
crystalline, nongraphitic form of carbon that has a microp- -(Q/S). The intersection of (4-29) with the adsorption
orous structure to give it a very high internal surface area isotherm is the equilibrium condition, c~ and q; .
per unit mass of carbon, and therefore a high capacity for Alternatively, an algebraic solution can be obtained.
adsorption. Activated carbon preferentially adsorbs or- Adsorption isotherms for equilibrium-liquid adsorption of a
ganic compounds rather than water when contacted with an species i can frequently be fitted with the empirical I
aqueous phase containing dissolved organics. As shown in Freundlich equation, discussed in Chapter 15:
Figure 4.25, as the concentration of phenol in the aqueous
phase is increased, the extent of adsorption increases very
rapidly at first, followed by a much-slower increase. When I
where A and n depend on the solute, carrier, and particular I
the concentration of phenol is 1.0 rnmoVL (0.001 mol/L of
adsorbent. The constant, n, is greater than 1, and A is a func-
aqueous solution or 0.000001 moVg of aqueous solution),
tion of temperat~~re. Freundlich developed his equation from
the concentration of phenol on the activated carbon is some-
experimental data on the adsorption on charcoal of organic
what more than 2.16 mmoVg (0.00216 mollg of carbon or
solutes from aqueous solutions. Substitution of (4-30) into
0.203 g phenoVg of carbon). Thus, the affinity of this adsor-
(4-29) gives
bent for phenol is extremely high. The extent of adsorption
depends markedly on the nature of the process used to
produce the activated carbon. Adsorption isotherms like Fig-
ure 4.25 can be used to determine the amount of adsorbent
which is a nonlinear equation in c~ that can be solved
required to selectively remove a given amount of solute from
numerically by an iterative method, as illustrated in the
a liquid.
following example.
Consider the ideal, single-stage adsorption process of
Figure 4.26, where A is the carrier liquid, B is the solute, and
C is the solid adsorbent. Let
EXAMPLE 4.12
CB z concentration of solute in the carrier liquid,
One liter of an aqueous solution containing 0.010 rnol of phenol is
moVunit volume
brought to equilibrium at 20°C with 5 g of activated carbon having
the adsorption isotherm shown in Figure 4.25. Determine the per-
Solid adsorbent, C,
of mass amount S cent adsorption of the phenol and the equilibrium concentrations of
phenol on carbon by:
Liquid, Q
(a) A graphical method
Equilibrium
Liquid mixture Solid, S (b) A numerical algebraic method
Carrier, A For the latter case, the curve of Figure 4.25 is fitted quite well with
Solute, B, of concentration cs, the Freundlich equation (4-30), giving
of total volume amount Q
Figure 4.26 Equilibrium stage for liquid adsorption.