Solid Surfaces—Adsorption - Surface and Colloid Chemistry: Principles and Applications - page 121

5.6.1.1 adsorption of acetic acid onto activated charcoal
Adsorption at liquid surfaces can be monitored using the Gibbs adsorption isotherm
since the surface energy, γ, of a solution can be readily measured. However, for solid
substrates, this is not the case, and the adsorption density has to be measured in some
other manner. In the present case, the concentration of adsorbate in solution will be
monitored. In place of the Gibbs equation, we can use a simple adsorption model
based on the mass action approach.
On any solid surface, there are a certain number of possible adsorption sites per
gram (N m ), where any adsorbate can freely adsorb. There will be a fraction θ of
sites which are filled by one adsorbing solute. There will also exist an adsorption-
desorption process at the surface. The rate of adsorption will be given as

[concentration of solute][1− θ] N m (5.19)

and the rate of desorption will be given as

[concentration of solute][θ] N m (5.20)

It is known that at equilibrium these rates must be equal:

k ads C bulk (1 − θ) N m = k des θ N m (5.21)

where k ads , k des are the respective proportionality constants, and C bulk is the bulk solu-
tion concentration of the solute. The equilibrium constant, K eq = k ads /k des , gives

C bulk /θ = C bulk + 1/K eq (5.22)

and since θ = N/N m , where N is the number of solute molecules adsorbed per gram
of solid, one can write

C bulk /N =C bulk /N m + 1/(K eq N m ) (5.23)

Thus, measurement of N for a range of concentrations (C) should give a linear plot of
C bulk /N against C bulk , where the slope gives the value of Nm, and the intercept gives
the value of the equilibrium constant K eq . This model of adsorption was suggested
by Irving Langmuir and is referred to as the Langmuir adsorption isotherm . The aim
of this experiment is to test the validity of this isotherm equation and to measure the
surface area per gram of charcoal, which can easily be obtained from the measured
N m value if the area per solute molecule is known.
Adsorption experiments are carried out as follows. The solid sample (for example,
activated charcoal) is shaken in contact with a solution with a known concentration
of acetic acid. After equilibrium is reached (after 24 h), the amount of acetic acid
adsorbed is determined.
The concentration of acetic acid can be determined by titration with NaOH
solution. Solutions of dyes (such as methylene blue) may also be used, and after