1.a. Determination of adsorption isotherm parameters in methylene blue –
water - activated charcoal system
A model example of the physical adsorption of a substance dissolved in liquid on
a solid phase surface is the adsorption of dyes on activated charcoal due to Van
der Waals's attractive forces. In this case, the adsorption isotherm is the dependence
of the amount of the adsorbed dye na on its equilibrium concentration c in the solution.
When methylene blue dye adsorbs on activated charcoal, the equilibrium between the
charcoal surface and the solution is established after 24 hours. We can obtain isotherm
values that are practically identical to the true equilibrium after 30 minutes of shaking
if we choose constant adsorbent weights.
The theoretical description of adsorption uses different adsorption models that lead to
mathematically different descriptions. The most well-known are:
Langmuir isotherm:
𝑛𝑛𝑎𝑎 = 𝑛𝑛𝑎𝑎,𝑚𝑚𝑚𝑚𝑚𝑚
ω 𝑐𝑐
1+ω 𝑐𝑐
(1.)
where 𝑛𝑛a,max is the maximum amount of the adsorbed substance (θ = 1), ω is the socalled
adsorption parameter equal to the reciprocal value of concentration at which the
half degree of coverage (θ = 0.5) is reached, i.e., 𝑛𝑛a =
1
2
𝑛𝑛a,max .
Freundlich isotherm:
𝑛𝑛𝑎𝑎 = 𝑘𝑘 𝑐𝑐
�
1
𝑛𝑛
�
(2.)
where k and n are empirical parameters specific for different adsorption systems.
Temkin isotherm:
𝑛𝑛𝑎𝑎 = 𝑘𝑘1 𝑙𝑙𝑙𝑙(𝑘𝑘2 𝑐𝑐) (3.)
where k1 a k2 are empirical parameters of the Temkin isotherm for the adsorption
system.
TASK: Measure the amount of methylene blue adsorbed on activated charcoal at
different dye concentrations in solution at constant temperature (i.e., the
experimental adsorption isotherm). Determine the parameters of the Langmuir,
Freundlich and Temkin isotherms for this adsorption system. Obtain the best fit of the
experimental results using theoretical isotherms in one common graph. Decide what
theoretical isotherm best describes the adsorption of methylene blue on activated
charcoal. Use the sum of quadrates of deviation between experimental and fitted
values as the criterion to determine which isotherm best fits the experiment.
LABORATORY AIDS AND CHEMICALS: Spectrophotometer, laboratory scales,
laboratory shaker, 6 flat bottom flasks (250 cm3), 6 funnels and funnel stand, 6
Erlenmeyer flasks, 1 volumetric flask (50 cm3), 7 graduated flasks (25 cm3), scale
pipettes (1, 5, 10 and 25 cm3), weighing boat, spoon, filter paper, activated charcoal,
stock solution 2 mg/cm3 methylene blue (CAS 122965-43-9).
INSTRUCTIONS: Fill 6 flat bottom flasks (250 cm3) with 7.5; 8; 9; 10.5; 12; 14 cm3 of
methylene blue stock solution. Fill each flask with water to the final volume of
50 cm3. Add 90 mg of the activated charcoal into each flask (discuss the weight with the
laboratory assistant). Close flasks with stoppers and shake for 30 min on the laboratory
shaker to obtain the adsorption equilibrium.
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?

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For each equilibrium system. Put a dry filter in the funnel. Start filtration. Discard the
first portion of the filtrate (about 20 cm3) to be sure that the filter paper is saturated with
dye. Subsequently collect the remaining part of the dye filtrate. Use the final part of the
dye filtrate to determine the dye concentration by spectrophotometer.
Determination of the calibration curve. Take volumetric flask (50 cm3), fill with
1.25 cm3 of the stock dye solution, and dilute with water up to the mark.
Take 7 volumetric flasks (25 cm3) and add 0.5; 1; 1.5; 2; 3; 4, and 5 cm3 of dilute dye
solution of methylene blue. Fill flasks with water up to the mark.
Set up the spectrophotometer in absorbance mode at a wavelength of 660nm. If the
absorbance measurement is outside the calibration curve, dilute the dye solution
appropriately and record the dilution factor, which will be used to calculate the
equilibrium dye concentration.
When finished, clean the cuvettes and laboratory aids with ethanol.
DATA ANALYSIS: Each theoretical isotherm (70.), (71.) and (72.) has the form y =
f (x) where the independent variable 𝑥𝑥 is the equilibrium concentration 𝑐𝑐 and the
dependent variable 𝑦𝑦 is the weight of the dye sorbent per unit weight of the adsorbent.
There are two experimental adsorption parameters in each of the relations. Adsorption
parameters can be determined for an individual isotherm using one of the following
procedures.
Procedure A (Use of the non-linear regression): Make the best fit of the
experimentally measured adsorption isotherm by an assumed non-linear theoretical
adsorption function. Use the appropriate numerical method, which can be found in the
"Solver" function in the MS-EXCEL software.
Procedure B (Use of the linear regression): Transform the dependencies (70.), (71.)
and (72.) into linearized forms, as follows:
1
𝑛𝑛𝑎𝑎
=
1
𝑛𝑛𝑎𝑎,𝑚𝑚𝑚𝑚𝑚𝑚
+
1
ω 𝑛𝑛𝑎𝑎,𝑚𝑚𝑚𝑚𝑚𝑚
1
𝑐𝑐
(4.)
ln 𝑛𝑛𝑎𝑎 = ln 𝑘𝑘 +
1
𝑛𝑛
ln 𝑐𝑐 (5.)
𝑛𝑛𝑎𝑎 = 𝑘𝑘1 𝑙𝑙𝑙𝑙(𝑘𝑘2) + 𝑘𝑘1 ln 𝑐𝑐 (6.)
where you can find the new variable pairs:
1
𝑛𝑛𝑎𝑎
and
1
𝑐𝑐
, ln 𝑛𝑛𝑎𝑎 and ln 𝑐𝑐, 𝑛𝑛𝑎𝑎 and ln 𝑐𝑐. Plot the
graphs using the new variables. For each isotherm dependence, make a linear
regression and find the intercept and slope. Calculate the isotherm parameters from
the intercept and slope for each linear dependence.
REPORT: Calibration table 1: concentration of dye standard [mg/cm
3
] and its
absorbance. Calibration graph 1: Dependence of dye standard absorbance on
its concentration. Table 2: for each adsorption experiment: the number of the dye
solution, weight of activated charcoal in [mg], the amount of dye [mg] in the solution
before and after adsorption, solution dye loss in [mg], equilibrium concentration c
[mg/cm3] evaluated from Calibration graph 1, amount of dye adsorbed per 1 gram of
activated charcoal [mg dye / g act. charcoal]; values:
1
𝑛𝑛𝑎𝑎
,
1
𝑐𝑐
, ln 𝑛𝑛𝑎𝑎, ln 𝑐𝑐, and 𝑛𝑛𝑎𝑎 . Graphs
2-4: linear dependences (73.), (74.), and (75.). Table 3: adsorption parameters of
Langmuir, Freundlich and Temkin isotherms. Table 4: about 10 chosen dye
concentrations and their calculated values 𝑛𝑛𝑎𝑎 for all isotherms (apply parameters given
in Table 3). Common graph 5: Experimental dependence (plotted using symbols) of
adsorbed amount [mg dye / g act. charcoal] on the equilibrium concentration c [mg/cm3]
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
together with the theoretical adsorption isotherms (Table 4) obtained by best fit (plotted
using lines).