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Athens Journal of Sciences- Volume 2, Issue 3 – Pages 187-202
https://doi.org/10.30958/ajs.2-3-3 doi=10.30958/ajs.2-3-3
A Novel Ionic Liquid for Carbon Capture
By Amita Chaudhary
Ashok N. Bhaskarwar†
Many chemical processes require use of a solvent. Due to the adverse environmental
effects of volatile organic compounds (VOCs), there is a need for replacement of
traditional volatile solvents and hence a rising interest among researchers in the field
of non-volatile solvents. A large number of chemical reactions are carried out in the
presence of a solvent. Recently, a new class of non-volatile solvents has emerged
called ionic liquids. An ionic liquid is an organic salt mainly composed of ions which
are poorly coordinated, resulting in a low melting point often below 100°C. It consists
of an organic or an inorganic bulky cation and a smaller anion. Due to the
unsymmetrical ions, the lattice energy and the melting point of the ionic liquids are
lower than of inorganic salts. Ionic liquids have many unique properties, such as high
thermal stability, large oxidative and reductive range, good solvent for most of the
organic and inorganic solutes, non-corrosive and corrosion-preventing nature, high
ionic conductivity, and negligible vapour pressure. Their properties can be tailored,
and hence ionic liquids have also been termed as the "designer solvents”. Ionic
liquids can broadly be categorized into protic and aprotic ionic liquids. We have
synthesized, and filed a patent on a new low-cost ammonium-based protic ionic liquid
by solvent-free acid-base neutralization method. Its physicochemical properties like
viscosity and density, and their variation with temperature have been measured, as
well as its thermal stability quantified. Its application in carbon capture, considering
its great affinity towards the CO2 molecules, has also been explored. Effect of
interaction of water molecules with the ionic liquid on its absorption capacity for CO2
has also been assessed. It is found that this novel ionic liquid has the highest
absorption capacity to cost ratio compared to all ionic liquids reported to date.
Keywords: Absorption capacity, CO2, Density, Green solvent, Protic ionic liquid
(PIL), Viscosity.
Introduction
Over the last two decades, alarming temperature increase due to
continuous increase in carbon dioxide concentration in the atmosphere has
shown serious repercussions for the environment and mankind. Researchers,
scientists, and environmentalists are all expressing concern over changes in the
overall climate. Researchers are in search of better solvents or better
technologies to capture the carbon dioxide. Large part of the carbon dioxide
emission is from the combustion of fossil fuels like coal in power- generating
plants. The technologies used for capture of carbon dioxide from flue gases
Research Scholar, Indian Institute of Technology, India.
†Professor, Indian Institute of Technology, India.
.
Vol. 2, No. 3
Chaudhary et al.: A Novel Ionic Liquid for Carbon Capture
188
are: absorption, adsorption, membrane separation/permeation, and cryogenic
distillation. Out of these technologies, absorption is widely used at large scale
due to its low cost and energy-efficient merits. Commercially, amines and
alkanol amines are used for scrubbing carbon dioxide in post combustion-based
carbon-capture systems. Over a period, ionic liquids are likely to emerge as the
best green-solvents which have wide range of applications due to their unique
properties. Ionic liquids are salts which have low melting points (<100 oC).
They exhibit high solubility and selectivity for carbon dioxide, especially at a
high pressure and at room temperature. Ionic liquids are non-flammable and
non-volatile (Maginn, 2005). The decomposition temperature is generally
above 300 °C. Ionic liquids have negligible vapour pressures selectively
capturing carbon dioxide from a mixture of gases (Bates, 2002). In the past
decade, conventional ILs, such as those based largely on imidazolium,
pyrrolidinium or ammonium cation coupled with large anions with delocalised
or sterically hindered charge, have been intensively investigated for CO2
capture by a physical absorption mechanism (Yokozeki, 2008). The effect of
the anion on the solubility of carbon dioxide for imidazolium based ionic
liquids has been studied and the results indicate that, in the case of anions
containing fluorinated alkyl groups, a strong interaction with carbon dioxide is
responsible for the higher solubility (Scovazzo, 2004). Yokozeki and Compton
researcher proved that ionic liquid having acetate anion shows better
absorption capacity of carbon dioxide in compare to the purely physical
absorption of CO2 by many RTILs (Room Temperature Ionic Liquids)
(Barrosse-Antle & Compton, 2009). Hence, attention has been more focused on
tailoring the sites of ions with more basic functionalized group having the
capability of chemically binding with carbon dioxide. Davis and co-workers
studied an ionic liquid consisting of an imidazolium cation, tetra fluoro borate
anion with amine functionality was having the absorption capacity of 0.5 mole
of carbon di-oxide per mole of ionic liquid (Aki, 2006). With primary and
secondary amine the theoretical maximum absorption can reach up to 0.5 mole
of carbon di-oxide per mole of amine. Wang and co-workers (2010) got
enhanced equi-molar reversibly absorption capacity by using super-base
derived ionic liquids. Yang et al. (2011) also described task specific ionic
liquids having amine for carbon dioxide capture, while Galan Sanchez (2007)
employed that, amine functionalized ionic liquid shows thirteen times higher
solubility then non-amine functionalized ionic liquids. In post-combustion
system, large amount of solvent is required to treat the carbon di-oxide at low
pressure. Conventional ionic liquids are costly and exhibit relatively low
absorption capacities at low pressure (Astarita, 1983). Another challenge with
ionic liquid is their high viscosities. Due to the columbic interactions among
the ionic liquid constituents contribute to the high viscosity of ionic liquids.
The carbon dioxide adducts with amine further increases the viscosity due to
the presence of hydrogen bonding between them results in high mass-transfer
resistance (Tsuzuki et al., 2009). High cost and slow rates of absorption and
desorption process make it unsuitable for a large-scale application.
Athens Journal of Sciences
September 2015
189
The objective of the present study was, therefore, to explore the carbon
dioxide absorption capacity of new low-cost protic ionic liquid (PIL)
containing multi-amine functionalized sites. Protic ionic liquids are produced
by proton transfer from a Bronsted acid to a Bronsted base. Ionic liquid used in
this study was composed of two primary and two secondary amine groups. Due
to the more basic nature of secondary amine, the proton removed from an acid
is going to attach with the secondary-amine nitrogen. It is found that by
converting the existing amines and alkanolamine solvents into ionic form by
protonation technique avoided the evaporative loss of solvent at elevated
temperatures. The protic ionic liquid (PIL) investigated in this study is a novel
ionic liquid TETAL shown in Figure 1. The PIL TETAL was made as per the
literature procedure (Wasserscheid & Welton, 2003). The structure of
synthesized IL has been elucidated on the basis of FT-IR, 1H NMR, 13C NMR
and mass spectroscopy. The solubility of carbon dioxide into the reaction
mixture was measured by volumetric titration. The capacities of carbon dioxide
uptake at the ambient conditions, i.e. 1 atmospheric pressure and 298K for both
neat and the different v/v% s of aqueous solutions of TETAL were
investigated. The results are shown in Figure 12. Industrial carbon dioxide-
capturing systems mostly use 30 % w/w aqueous solutions of conventional
solvents. We also investigated the carbon dioxide absorption in 0.7M aqueous
solutions of TETAL for 70 hours in temperature and pressure controlled
experiments.
Reactions Pathways
In an amine- based carbon dioxide capturing plant, the primary and
secondary amines are converted into carbamate salt upon absorbing carbon
dioxide.
RNH2 + CO2 RNHCOO- +H+ … (1)
R2NH + CO2 R2NCOO- + H+ … (2)
The reaction of CO2 with tertiary amines results in the formation of a
bicarbonate salt.
R3N + CO2+ H2O R3NHCO3- + H+ … (3)
In the reaction mixture, nine main species are present: precursor amines
(RNH2/ R2NH/R3N), protonated amines (amH+), carbamates (RNHCOO-,
R2NCOO-), carbonate (CO32-), bicarbonate (R3NHCO3-), hydronium ion
(H3O+), hydroxyl ion (OH-), CO2, and water.
The reaction between carbon dioxide and amines took place either by a
two-step zwitterion mechanism (Caplow, 1968; Danckwerts, 1979) or by a
single-step termolecular mechanism (Crooks, 1989).
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Chaudhary et al.: A Novel Ionic Liquid for Carbon Capture
190
Zwitterion Mechanism
In this mechanism, zwitterion is formed as an intermediate in the reaction
between carbon dioxide and amine:
… (4)
This zwitterion undergoes de-protonation by a base B like water, amine,
OH- etc and results in carbamate formation:
(5)
Due to the low stability of carbamate, it readily undergoes hydrolysis
forming bicarbonates and releasing free amine molecules. The regenerated
amine again reacts with carbon dioxide. Initially the carbamate species are
dominant and later corresponding quantities of bicarbonate ions can be
confirmed by 13C NMR.
The contributions of the three reactions of carbon dioxide with water to the
overall rate are assumed to be negligible on account of low solubility of carbon
dioxide in water.
At steady state, the overall reaction rate between carbon dioxide and
aqueous solution of amine can be expressed as
… (6)
As here,
k2 = second-order reaction rate constant, L·mol−1·s−1
k-1 = backward rate constant, s−1 and
kB = the kinetic constant representing the de-protonation of the zwitterion by
any base,s-1.(Vaidya, 2007)
Termolecular Mechanism
The termolecular mechanism proposed by Crooks and Donnellan (1989)
assumes that the amine reacts simultaneously with one molecule of carbon
dioxide and one molecule of a base. The reaction proceeds in a single step via a
loosely-bound encounter complex as the intermediate rather than a zwitterion.
… (7)
When water is the base then the reaction is first order with respect to the
initial concentration of amine.
As carbon dioxide reaction with water is negligible, the rate equation will
be
H3O+
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191
As here,
k' =
Experimental Work
Chemicals
All chemicals used in the experiments were of analytical grade.
Triethylene tetramine (TETA, CDH), Lactic acid (LOBA CHEMIE),
concentrated hydrochloric acid (Sigma Aldrich), methyl orange indicator
(Sigma Aldrich) were used without purification. Carbon dioxide (CO2,
99.99%) and nitrogen (N2, 99.99%) gases were purchased from Sigma Aldrich.
Purity of gases was checked by ULTIMA-2100 series gas chromatograph of
Nettle make. All solutions were prepared using de-ionised water in volumetric
glassware.
Synthesis of [Triethylene tetrammonium] [Lactate]
Equi-molar quantities of triethylenetetramine and lactic acid were taken in
a three –necked round bottom flask equipped with a reflux condenser, a
pressure funnel, and a mechanical stirrer. Initially, triethylenetetramine was
taken in the round bottom flask and then lactic acid added drop by drop using a
pressure funnel with constant stirring at 120 rpm using the mechanical stirrer.
As the neutralization reaction produces a lot of heat, which is equal to -9 kcal/
mol, the round bottom flask was kept in an ice-water mixture. To avoid any
contamination with air, the reaction mixture was placed under N2 atmosphere.
It was then stirred for several hours at room temperature. The completion of
reaction was monitored by TLC. The product was a pale yellow viscous liquid.
Product was then washed with dichloromethane 2-3 times to remove
impurities. Residual water is removed by vacuum heating at 80 0C for 12
hours. The ionic liquid was finally stored-in an air tight flask. The water
content of the ionic liquid was analysed using the TGA analysis and found to
be 0.01% (w/w).
Proposed Reaction and Mechanism
H2N
H
NN
H
NH2
triethylenetetramine
OH
OOH
lactic acid
H2N
H
NN
H2
NH2
OH
O
-O
[Triethylenetetrammonium][Lactate]
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Chaudhary et al.: A Novel Ionic Liquid for Carbon Capture
192
Figure 1. Mechanism of Reaction
Figure 1 shows the mechanism of reaction between triethylenetetramine
(TETA) and lactic acid.
Characterization
The structure of synthesized protic ionic liquid was elucidated using FT-
IR, 1H NMR, 13C NMR, and Mass spectroscopy.
FT-IR Data
IR spectra of triethylenetetrammonium lactate before (Figure 2) and after
the carbon dioxide absorption (Figure 3) were compared for identification of
changes due to carbon-dioxide absorption is given in Table 1.
Table 1. FT-IR Data
Compound Type
Frequency range (cm-1)
C=O asymmetric stretching
band of carbamate
1734
C-N stretching band of
carbamate
1408.93
C=O symmetric stretching
band of carbamate
1125.45
C–N stretching band
1262
COO- symmetric stretch
1383
NH3+ bending
1460
Figure 2. FT-IR of Neat Triethylenetetrammonium Lactate without Absorbing
Carbon Dioxide
Protonated amine
Deprotonated acid
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193
Figure 3. FT-IR of Neat Triethylene Tetrammonium Lactate after Absorbing
Carbon Dioxide
NMR Measurement
Qualitative 1H and 13C NMR experiments for molecular- structural
determination were run at room temperature using a Bruker 300 MHz
spectrometer. An NMR sample of TETAL was prepared in deuterated DMSO-
d6. To avoid any disturbance between the deuterated solvent and the analyzed
mixture, a capillary tube was use to load DMSO-d6 with the sample in NMR
tube. The residual proton in DMSO-d6 was used as the 1H NMR external
reference at 2.50 ppm. The proton present in Triethylenetetrammonium Lactate
in different environment is shown in Figure 4.
Figure 4. 1H NMR of Triethylene tetraammonium Lactate
13C NMR spectra were obtained for the neat TETAL and after absorbing
carbon dioxide in order to investigate the nature of the carbon dioxide bound
species being formed. There was no signal for the carbamate carbon around
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Chaudhary et al.: A Novel Ionic Liquid for Carbon Capture
194
159–165 ppm in neat TETAL. In carbon di-oxide absorbed TETAL sample a
signal is observed at 163.54 ppm that is attributed to the carbamate carbon
(Figure 5(a) & Figure 5(b)).
13C NMR: δC (300 MHz; DMSO-d6) 39.5 ppm: For Lactate ion: 179.38(-
COOH), 67.68(-CHOH), 22.1(CH3); TETA ion: 40, 45, 50 (CH2N, NH2, NH)
1HNMR: δH (300 MHz; DMSO-d6): 1.119 (s, 3H, CH3), 2.347, 2.724,
2.593(CH2N), 4.4, (br s, NH, NH2);
Figure 5. (a) 13C NMR of Triethylene tetrammonium Lactate
(a)
(b) 13C NMR of Triethylenetetrammonium Lactate with Carbon Dioxide
Athens Journal of Sciences
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Figure 6. Mass Spectrum of triethylenetetrammonium Lactate
The molecular mass of Triethylenetetrammonium Lactate is 244.44 g
mole-1 depicted from the mass spectrum of TETAL in Figure 6.
Physicochemical Properties
Thermal Stability
Thermogravimetric analysis (TGA) was performed using a Thermo
Gravimetric Analyzer of Netzsch Instruments under a nitrogen atmosphere.
The samples were weighed, and then heated from room temperature to 300 °C
at a ramping rate of 10 °C·min−1. TGA analysis for the pure TETAL shows that
the sample is stable and does not loss weight until 150 oC, Figure 7 indicating
that TETAL is more stable than the corresponding polyamine TETA as a result
of the salt formation.
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Figure 7. Thermogravimetric Analysis of Triethylenetetrammonium Lactate
Viscosity
The dynamic viscosity was measured for the system TETAL as a function
of temperature from 273 to 388 K using Anton Paar MCR302 SN81193479.
Watanabe et al. (Tsuzuki et al., 2009) reported that the three main factors for
viscosity of ionic liquids are size, shape, and interaction between the anion and
the cation. The interaction forces between anion and cation are columbic
forces, van der Waals forces, and hydrogen-bonding. Out of these forces in
neat ionic liquid the columbic forces are responsible and in carbon dioxide
absorbed ionic liquid hydrogen-bonding mainly cause viscosity. The viscosity
of ionic liquid directly influences the diffusivity of ions in the solution. The
experimental viscosity of TETAL as a function of temperature is given by
Figure 8:
η (Pa.s) = 1×106 e-0.047 T(K)
Figure 8. Variation of Viscosity of TETAL with Temperature
Density Measurement
The experimental values for the density of TETAL as a function of
temperature from 293 to 363 K were measured using DE45 Mettler Toledo
density meter having a precision of 0.00005g/cm3. The value of density at
Athens Journal of Sciences
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197
atmospheric pressure was a linear function of temperature as shown in Figure
9:
ρ(kg m-3) = 1310.1 - 0.6571× T(K)
Figure 9. Density vs Temperature
Conductivity Measurement
Conductivity measurements were carried out using Mettler Toledo
conductivity meter. The instrument conductivity ranges from 0 to 2000 S/cm
with an accuracy of 1%. Before measurements, the instrument was calibrated
with 3M KCl solution. The temperature of the sample was kept at 25 0.1oC.
Measurement was repeated three times and the average value was calculated.
The measured value of ionic conductivity of TETAL under the given
conditions was 0.065mS/cm.
Application in Carbon Dioxide Capture
Along with their many promising properties, the ionic liquids also present
several challenges for large-scale carbon dioxide capture from flue gases. Flue
gases are mainly composed of low partial pressures of carbon dioxide. The
carbon dioxide solubility can be improved by tethering carbon dioxide-philic
groups on ionic liquid. Another challenge is the high viscosities of the ionic
liquids. The carbon dioxide absorbed ionic liquids possess even more viscous
due to the formation of hydrogen bonding. As a result the absorption and
desorption rates in ionic liquids becomes too slow for industrial processes.
Carbon Dioxide Absorption Study
All experiments were performed at atmospheric pressure with pure carbon-
dioxide gas. The gas was passed through in-line 3 A˚ molecular sieve drying
tubes. The flow rate was 0.002 m3 min-1. Experiments were conducted in a
round bottom glass reactor with an effective volume of 500 cm3. The
equilibrium study of carbon dioxide absorption was conducted in a 0.7 M
solution of the ionic liquid at a temperature of 16 oC and 1 atm for 70 hours.
The reactor was loaded with approximately 300 cm3 of the 0.7 M ionic-liquid
solution. The reactor was then sparged with nitrogen to remove all the air
above the interface of the solution before the experiment started. The vapour
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Chaudhary et al.: A Novel Ionic Liquid for Carbon Capture
198
pressure of the ionic-liquid and solvent in the gas phase of the reactor was
assumed to be constant, and equal to the total equilibrium pressure before the
introduction of solute gas carbon dioxide to the reactor. Carbon dioxide was
introduced into the reactor via a GFC mass flow controller and a carbon
dioxide rota-meter. Absorption reached a thermodynamic equilibrium after a
sufficient time period, corresponding to the solubility limit of the gas in the
ionic liquid at that temperature. Sample about 1ml of the reaction mixture were
taken out at regular intervals of 5 minutes and weighed. The samples were then
titrated with 2M HCl solution to analyse the carbon dioxide loading at those
time intervals. The experimental setup is depicted in Figure 10.
Figure 10. Experimental Setup for CO2 Absorption. 1. CO2 Cylinder, 2. Digital
Mass Flow Controller, 3. CO2 Rotameter 4. Reaction Vessel, 5. Magnetic
Stirrer, 6. Gas Inlet Port, 7. Gas Outlet Port
The amount of carbon dioxide absorbed in the solution was calculated
assuming ideal-gas behaviour, from the following equation:
Moles of CO2 absorbed (α) =
As here
α = Moles of CO2 absorbed (moles of CO2/gram of ionic-liquid solution),
T = Room temperature (K),
V.P.= Vapour pressure of water at room temperature (mm Hg),
Vfluid = Volume of displaced solution in the graduated tube (ml), and
VHCl = Volume of 2M HCl used (ml).
Athens Journal of Sciences
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199
Figure 11. Carbon Dioxide Absorption in 0.7M Aqueous Solution of TETAL
The absorption study reveals that 0.7 M aqueous solution of TETAL can
absorb up to 1.57 mole of carbon dioxide per mole of TETAL at ambient
conditions as shown in Figure 11.
Effect of Water on Carbon Dioxide Absorption Capacity
The viscosity of carbon dioxide adducts which is formed upon reacting IL
with carbon dioxide increases by double of the initial magnitude (Yang, 2011).
The increase in viscosity is caused by the formation of a hydrogen bonding
network (Wang, 2013). Due to increase in viscosity the mass transfer resistance
in liquid phase is increases which limit the carbon dioxide absorption capacity
of TETAL. However, small quantities of water reduce the viscosity, with some
ILs having a 50% reduction in viscosity with 2% water by volume (Khupse,
2013). Ren et al. (2009) demonstrated that mainly 7% water is present in the
flue gas stream. However, the effect of water on the absorption of carbon
dioxide into chemically reacting ILs has not been quantitatively reported to our
knowledge. So, in this study the quantitative analysis of addition of water on
absorption capacity of TETAL was done. The effect of different percentage of
water addition on the rate and carbon dioxide absorption capacity of TETAL
was shown in Figure 12.
Figure 12: Effect of Addition of Water on Carbon Dioxide Absorption
Capacity of TETAL
Vol. 2, No. 3
Chaudhary et al.: A Novel Ionic Liquid for Carbon Capture
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A 50 % (v/v) of water addition to TETAL increased its absorption
efficiency from 0.98 to 1.56 moles carbon dioxide per mole of TETAL (Figure
12). During the carbon dioxide absorption by the ionic liquid, two basic sites
get protonated which limits its absorption capacity. On adding a base, i.e.
water, the extra protons from those basic sites get removed thus providing the
sites for further absorption of carbon dioxide. From the quantitative analysis, it
was found that addition of water up to 50% increased the absorption capacity
of TETAL to a maximum of 1.56 mole/mole of TETAL, and further addition
led to a decrease in the absorption capacity.
It was also found that after 70 hours of bubbling pure carbon dioxide in the
reaction mixture the end product was a white precipitate. Initially, the
carbamate formation predominated but the end of the absorption the product
was a white precipitate which was water soluble. By wet chemistry, it was
confirmed as ammonium bicarbonate. A lower energy is required to break the
bicarbonate bond in comparison to the carbamate has calculated from Gaussian
03. Thus, carbon dioxide rich solvent requires less energy for regeneration.
NH4HCO3 ↔ NH3 + CO2 + H2O, ΔH=15.8 kcal/mol
RNHCOOH ↔ RNH2 + CO2, ΔH=38.6 kcal/mol
Cost of Ionic Liquid
The cost of an ionic-liquid solvent is obviously an important factor for its
industrial applications. In general, ionic liquids are relatively very expensive in
comparison to the common organic solvents used. Still, the ionic liquids are
important as solvents due to their non-volatile nature and low melting points.
Ionic liquids are the most expensive solvents amongst all the commercially
used solvents. Basically, the cost of an ionic liquid depends on the prices of the
starting materials that form the cation and anion components (Wilkes, 2002).
For example, [bmim][PF6], [bmim][BF4],[omim][Cl] used widely in carbon
dioxide capture studies at lab scale are Rs 17,004.59/5g (€ 252.7), Rs 15171.40
(€225.46), and Rs 4,660.16 (€ 69.25) per litre. The cost of these ionic liquid are
very high due to the costs of source of these ions like Na[BF4] and H[PF6]. The
1-alkyl-3 methylimidazolium cations are more expensive in comparison to the
alkyl amines. The comparison between the cost of different cations and anions
are given in the Table 2.
Table 2. Rough Estimates of the Prices of Cation/Anion Components of Ionic
Liquids
Cheap Expensive
[HNR3]+
[HPR3]+
[NR4]+
[PR4]+
R-Pyridinum
R-Methylimidazolium
R,R-
Dialkylimidazolium
Cl-
[MeSO4]-
[AlCl4]-
[MeCOO]-
[NO3]-
[PF6]-
[BF6]-
[CF3SO3]-
[SbF6]-
Cost of Triethylenetetramine = Rs 5923.17 / litre
Athens Journal of Sciences
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201
Cost of Lactic acid = Rs 5481.93/ litre
Cost of DCM = Rs 4,328 / litre
Total cost for 1 litre of ionic liquid = Rs 7145.21
The cost of 1ethyl-3methyl imidazolium bromide in conversion is ₨
1,82,562.4 /litre. These cost estimates are from Sigma Aldrich catalogue.
Observations and Conclusions
In this work we have reported the absorption capacity and
physicochemical properties of TETAL. TETAL protic ionic liquid is easy to
synthesize and also a low-cost ionic liquid. The carbon dioxide absorption
capacity may further be enhanced by improving the basic nature of the ionic-
liquid which in turn can be adjusted by playing with the concentrations of acid
and base used during synthesis. The carbon dioxide absorption capacity in
aqueous solution of TETAL reached up to 1.57 mole of carbon dioxide
absorbed /mole of TETAL. This represents the highest absorption capacity to
cost ratio in comparison with all ionic liquids reported till date. This makes
TETAL more attractive than all other solvents. The decomposition temperature
of TETAL is 150 0C. So, it has the capability of carbon dioxide absorption at a
high temperature. This may be further improved in future work. In addition,
substantial viscosity and density decreases have been observed with an increase
in temperature, making it further attractive in practice.
Acknowledgments
We thank Chemical Engineering department, Indian Institute of
Technology, Delhi, and University Grants Commission, India, for the support
and funds provided for this research, including a doctoral fellowship for Amita
Chaudhary.
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