The Langmuir Adsorption Isotherm

Abstract
The Langmuir Adsorption Isotherm
Patrick Leahy
November 17, 2010
Six acetic acid solutions were prepared, standardized, and allowed to adsorb onto samples of activated
charcoal. The concentration of each solution was measured before and after adsorption. The adsorption
constant Kads was measured to be 12.61 ± 0.911.
Introduction
Owing to its mostly hollow structure, even a small mass of activated charcoal presents a large surface area to
adsorbants. The purpose of this experiment was to measure the adsorption of acetic acid onto that surface
by allowing six solutions of varying concentration to adsorb onto samples of activated carbon of known mass.
The reaction between the adsorbant A and the substrate S is
and the adsorption constant Kads is
Noting that [AS] = 1 − [S],
Relabeling [AS] as θ and [A] as C,
and hence
Kads =
A + S ⇀↽ AS (1)
Kads = [AS]
[A][S]
Kads =
[AS]
[S] (1 − [AS])
θ
C (1 − θ)
θ = KadsC
C (1 − θ)
which is the form of the Langmuir adsorption isotherm. This is equal to Y
Ymax , where Ymax is the maximal
adsorption. Dividing C by this yields
C
Y =
1
KadsYmax
+ C
Ymax
A low-concentration approximation of this is the Freundlich isotherm:
where k and n are empirical parameters.
Y = kC 1
n (5)
1
(2)
(3)
(4)

Experiment
Six masses of activated charcoal were measured out, each being approximately 1.5g, and added to acetic
acid solutions containing between five and one hundred percent 0.4M stock solution. The stock solution
itself was titrated against potassium hydrogen phthalate (KHP) and its concentration was determined to
be 0.390 ± 0.007M, and the six solutions were likewise standardized. The mass of each sample of activated
charcoal and the standardized molarity of each acetic acid solution is given in the following table.
Solution m(g) % 0.4M AcOH / 100mL Standardized molarity
1 1.5049 100 0.0390
2 1.5016 75 0.02925
3 1.5062 50 0.0195
4 1.5028 25 0.00975
5 1.5017 10 0.00390
6 1.5011 5 0.00195
The six flasks were stoppered, placed in a heated shaking bath, and allowed to remain there for one week,
whereafter the concentrations of the solutions in the flasks were measured again and compared to their
original values. A difference was thereby obtained:
Results and Discussion
Solution mol AcOH (initial) mol AcOH (final) Difference (mol)
1 0.0390 0.0339 0.00510
2 0.02925 0.0248 0.0445
3 0.0195 0.0159 0.00360
4 0.00975 0.00716 0.00259
5 0.00390 0.00244 0.00146
6 0.00195 0.00101 0.000940
From the differences in the number of moles in solution before and after absorption, the number of moles
adsorbed onto the charcoal in each of the six flasks was determined; from this, the parameters necessary to
describe the Freundlich and Langmuir isotherms were computed:
Solution Y (mol) C (molL −1 ) C
Y (L−1 ) lnC
1 3.39 E-3 ± 1.63 E-5 0.339 ± 0.001 100 ± 0.564 -1.082 ± 2.95 E-3
2 2.96 E-3 ± 1.32 E-5 0.248 ± 4.81 E-4 83.8 ± 0.408 -1.394 ± 1.94 E-3
3 2.39 E-3 ± 1.52 E-5 0.159 ± 1.22 E-4 66.5 ± 0.426 -1.839 ± 7.67 E-4
4 1.74 E-3 ± 3.30 E-5 0.0716 ± 1.87 E-3 41.6 ± 1.35 -2.637 ± 2.61 E-4
5 9.72 E-4 ± 1.32 E-5 0.0244 ± 5.20 E-4 25.1 ± 0.634 -3.713 ± 0.0213
6 6.26 E-4 ± 9.95 E-6 0.0101 ± 2.93 E-4 16.1 ± 0.533 -4.595 ± 0.0290
as a function of C to a linear least-squares regression, by
which Ymax was determined to be 0.003986 ± 2.88 E-4 mol and Kads was determined to be 12.61 ± 0.911.
Similarly, by fitting Y as a function of ln(C) to a linear least-squares regression, the Freundlich parameters
k and n were determined to be 0.005815 ± 3.698 E-5 and 2.079 ± 0.01552, respectively.
Ymax and Kads were determined by fitting C
Y
2

Figure 1: The Langmuir and Freundlich isotherms plotted against the data.
In general, the Langmuir isotherm is further from the data than the Freundlich isotherm.
If an acetic acid molecule can be assumed to require an area A on the charcoal, then the area the charcoal
offers for adsorption is AYmaxNA; hence, if A is 21 ˚A, this evaluates to 504 ± 36 m 2 g −1 .
Conclusions
Although the Kads derived for the Langmuir isotherm does not provide as good a fit to the data as the
Freundlich isotherm (which is peculiar, since the Freundlich isotherm is an approximation), the measurment
of Ymax yields a value close to the 708 m 2 g −1 of Brunauer, Emmett, and Teller [1].
References
[1] Brunauer, S., Emmett, P. H., and Teller, Edward. Adsorption of Gases in Multimolecular Layers. Journal
of the American Chemical Society, 60, page 309 (1938).
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