Batch Study

1. Title of the Experiment:- Batch adsorption study of a synthetic dye
Aim of the Experiment:- Batch adsorption removal of malachite green (MG) dye by using
reduced graphene oxide based composite as an adsorbent

2. Theory:-
The batch adsorption study is used to optimize the adsorption parameters like solution pH, adsorbent dosage, adsorption
time, initial dye concentration, and temperature. Also it is used to analyze the isotherm, kinetic and thermodynamic study
of the adsorption process. The adsorption capacity of MG dye at equilibrium (qe), time t (qt), and the removal (%R) were
calculated using the formula:
% 𝑅 =
(𝐶𝑜−𝐶𝑡)
𝐶𝑜
× 100 (1)
𝑞𝑒 =
𝐶𝑜− 𝐶𝑒 ×𝑉
𝑚𝑠
(2)
𝑞𝑡 =
𝐶𝑜−𝐶𝑡 ×𝑉
𝑚𝑠
(3)
Where Co is the initial concentration of dye, Ct is the concentration of dye at time t, Ce is the concentration of dye at
equilibrium, ms is the amount of adsorbent (mg), and V is the volume of the solution (mL).

3. Isotherm study:
The isotherm study is used to calculate the maximum monolayer adsorption capacity, also it is critical in optimizing the use of
adsorbent. Here, the batch adsorption process were fitted with three typical isotherm models: Langmuir, Freundlich, and
Temkin to fit the experimental data.
The linear form of Langmuir, Freundlich, and Temkin isotherm model can be written as:
𝐶𝑒
𝑞𝑒
=
𝐶𝑒
𝑞𝑚
+
1
𝑞𝑚𝐾𝐿
(4)
𝑙𝑛𝑞𝑒 = ln 𝐾𝑓 +
1
𝑛
ln 𝐶𝑒 (5)
𝑞𝑒 =
𝑅𝑇
𝑏𝑇
ln 𝐴𝑇 +
𝑅𝑇
𝑏𝑇
ln 𝐶𝑒 (6)
Where, KL (L/mg) is the Langmuir isotherm constant, qm is the maximum adsorption capacity (mg/g), kF ((mg/g)(mg.L−1)–1/nF)
is the Freundlich constant, 1/nF is the heterogeneity factor, bT (J/mol) is the Temkin constant, T is the absolute temperature
(K), R is the universal gas constant (8.314 J/mol.K), and AT (L/mg) is the binding energy.

4. Kinetic study:
Adsorption kinetic study help to know the dynamics and mechanism of the sorption process. The kinetic study of MG dye is
also essential for designing and modelling the adsorption process by selecting optimal parameter conditions. Well-established
kinetic models pseudo-first-order (PFO), and pseudo-second-order (PSO) model are used to analyze data obtained from the
batch experimental study to determine the parameters. The linear form of PFO and PSO can be expressed as:
ln(𝑞𝑒 − 𝑞𝑡) = ln𝑞𝑒 − 𝑘1𝑡 (7)
𝑡
𝑞𝑡
=
𝑡
𝑞𝑒
+
1
𝑘2𝑞𝑒
2 (8)
Where qe is the adsorption capacity at equilibrium (mg/g), k1 is the pseudo-first-order rate constant (min-1), and k2 is the
pseudo-second-order rate constant (g.mg-1.min-1).

5. Thermodynamic study:
Thermodynamics analysis of the adsorption process is done to evaluate the parameters such as entropy change (∆So), enthalpy
change (∆Ho), and Gibbs free energy (∆Go) by using the following equations:
𝐾𝑑=
𝑞𝑒
𝐶𝑒
× ρ (9)
ln 𝐾𝑑 =
∆𝑆𝑜
𝑅
−
∆𝐻𝑜
𝑅𝑇
(10)
∆𝐺𝑜 = ∆𝐻𝑜 − 𝑇∆𝑆𝑜 (11)
Where, Kd is the adsorption coefficient, ρ is the solution density (g/L), and R is the universal gas constant (8.314 J/mol.K).
From the plot of ln Kd vs. 1/T, the parameters like ∆So and ∆Ho are determined from the linearization of the plot.

6. Apparatus Required
1. Thermostatic shaker
2. Conical flask
3. Micropipette
4. 1 mL centrifuge tube
4. UV-vis spectroscopy
Chemicals Required
1. MG dye
2. Distilled water
3. Adsorbent
4. NaOH solution
5. HCl solution

7. Procedure:-
1. Stock solution of is prepared by dissolving 1 g of MG dye in 1000 mL of distilled water.
2. The standard solution of MG dye having concentration 100, 200, 300, 400, and 500 mg/L are prepared by diluting the
stock solution.
3. The MG dye solution is put in conical flask with fixed amount of adsorbent and then the conical flask is put in shaker for
adsorption.
4. Effluents is collected in 15 min time interval to measure the kinetic study.
5. The UV-Vis spectroscopy is used to measure the effluent concentration.

8. Tabulation
Calibration data
Concentration Absorbance
0 0
2 0.0682
4 0.136
6 0.204
8 0.266
10 0.345
12 0.415
14 0.497
16 0.571
18 0.63
20 0.679
Effect of pH
pH %Removal
5 85.185
6 92.458
7 95.897
8 99.146
9 98.132
10 97.321
Adsorbent dosage %Removal
10 55.452
15 79.218
20 97.145
25 97.856
30 98.652
35 99.215
Effect of adsorbent dosage

9. Adsorption time % Removal
0 0
15 45.214
30 63.542
45 78.634
60 88.754
75 94.568
90 98.892
120 98.984
150 99.214
Effect of time
Temperature % Removal
20 78.245
25 89.921
30 98.124
35 98.857
40 99.256
Effect of temperature

10. Calculation:-
The concentration of the MG dye can be calculated from the calibration plot of MG dye
by using the below equation.
y = 0.067 x + 0.0021

11. Batch adsorption study
Effect of
a. pH
b. Dosage
c. Time
d. Temperature
(a) (b)
(c) (d)
0 15 30 45 60
75 90 120 150

12. Isotherm study
a. Langmuir model
b. Freundlich model
c. Temkin model
Isotherm model Isotherm Parameters
Langmuir
qm
(mg/g)
KL
(L/mg)
R2
1168.224 0.453 0.996
Freundlich
1/n KF
(mg/g)(L/mg)1/n
R2
0.342 392.313 0.892
Temkin
bT
(J/mol)
AT
(L/mg)
R2
6.183 1.34 0.991

13. Kinetic study
Concentrations, (mg/L)
Parameters 100 200 300 400 500
qexp (mg/g) 248.803 496.691 741.027 969.14 1158.74
Pseudo first order
k1 (min−1) 0.081 0.062 0.081 0.076 0.048
qcal (mg/g) 42.822 72.552 80.652 1164.49 58.256
R2 0.879 0.886 0.9 0.868 0.799
Pseudo second order
k2 × 103 (g/mg.min) 9.1 4.2 0.42 0.5 0.3
qcal (mg/g) 249.376 497.512 740.74 970.5 1160.91
R2 0.997 0.998 0.993 0.999 0.995
a. Pseudo-first-order
b. Pseudo-second-order

14. Thermodynamic study
Temperature (K) ΔGo (kJ/mol) ΔHo (kJ/mol) ΔSo (J/mol.K)
293 -17.79
102.047 409.306
298 -19.84
303 -21.88
308 -23.92
313 -25.97

15. Conclusions
 The standard solution of MG dye is successfully prepared from stock solution.
 Calibration plot is used to find out the concentration of the effluent dye solution.
 The maximum monolayer capacity is 1164.224 mg/g.
 Pseudo-second-order is the best fitted model.
 Thermodynamics study confirmed that the adsorption process is spontaneous, and endothermic
in nature.
 Positive value of ΔSo confirmed that randomness increased in the solid/solution interfaces.