Solubility of CO2, H2S, and their mixture in the ionic liquid 1-octyl-3-methylimidazolium bis(trifluoromethyl)sulfonylimide

Article

pubs.acs.org/JPCB

Solubility of CO , H S, and Their Mixture in the Ionic Liquid

2

1

-Octyl-3-methylimidazolium Bis(trifluoromethyl)sulfonylimide

,†

‡

†

Amir Hossein Jalili,* Mohammadali Safavi, Cyrus Ghotbi, Ali Mehdizadeh, Masih Hosseini-Jenab,

and Vahid Taghikhani^‡

^†Gas Science Department, Gas Research Division, Research Institute of Petroleum Industry (RIPI), P.O. Box 14665-137, West Blvd.,

Azadi Sport Complex, Tehran, Iran

‡

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran

ABSTRACT: Gaseous solubilities of carbon dioxide (1), hydrogen sulfide (2), and their

binary mixture (x ≈ 0.2, 0.5, 0.8) have been measured in the ionic liquid 1-octyl-3-

2

methylimidazolium bis(trifluoromethyl)sulfonylimide ([C mim][Tf N]) at temperatures

8

2

ranging from (303.15 to 353.15) K and at pressures under 2 MPa. The observed PTx

solubility data were used to obtain Henry's law constants and correlated by three models:

(

1) the simple Krichevsky−Kasarnovsky (KK) equation, (2) a model comprised of the

extended Henry's law and the Pitzer's virial expansion for the excess Gibbs free energy,

and (3) the generic Redlich−Kwong (RK) cubic equation of state proposed for gas−ionic

liquid systems. The correlations from the three models show quite good consistency with

the experimental data for IL/CO and IL/H S binary mixtures within experimental

2

uncertainties. For IL/CO /H S ternary mixtures, the RK model shows the best correlation

2

with the experimental data. The comparison showed that the solubility of H S is about

2

two times as great as that of CO in the ionic liquid studied in this work. It was further

2

found, by comparison of the experimental data of this study with those of previous reports, that the solubility of H S in

2

[

C mim][Tf N] ILs increases as the number of carbon atoms in the alkyl substituent of methylimidazolium cation, n, increases.

n 2

In addition, quantum chemical calculations at DFT/B3LYP level of theory using 6-311+G(d) and 6-311++G(2d,2p) basis sets

were performed on the isolated systems studied in this work to provide explanations from a molecular point of view for the

observed experimental trends.

INTRODUCTION

Room temperature ionic liquids (RTILs), also known as liquid

salts, ionic melts, and liquid electrolytes, have emerged as an

coefficient data of acid gases (CO and H S) at various

2 2

■

temperatures and pressures are important in the evaluation of

ionic liquids (ILs) for use in industrial natural gas treating as

well as other industrially important processes. A growing

1

important family of organic compounds since 1995. Due to

ⁿ^u^m^b^e^r^o^f^e^x^p^e^rⁱ^m^eⁿ^t^a^l^d^a^t^a^f^o^r^s^o^l^u^bⁱ^lⁱ^t^y^aⁿ^d^dⁱ^f^f^u^sⁱ^oⁿ^o^f^C^O2

their tunable chemical structures, they show various promising

applications such as gas storage, separation, and catalysis. This

class of compounds are comprised of an organic cation like

quaternary ammonium, imidazolium, and pyridinium ions and

in various ILs have become available in the past few years,

+

which in the case of [C mim] -based ILs include the following:

8

(

1) the high-pressure phase equilibrium data presented by

8

−

Blanchard et al. for CO with six imidazolium-based ILs

an inorganic or organic anion such as [Cl] , [BF ] , [PF ] , or

2

4

6

−

including [C mim][BF ] and [C mim][PF ] at temperatures of

[

Tf N] and are molten salts, which are liquid over a wide

8

4

8

6

2

3

13.15, 323.15, and 333.15 K and pressures of up to 9.6 MPa.

temperature range including ambient temperature (below the

boiling point of water). Due to the existence of Coulombic

1

The authors concluded that the volume expansion of liquid IL

phase is negligible even for large amounts of dissolved CO and

attraction between the ions of ILs, they exhibit negligibly small

vapor pressure, meaning that ionic liquids are essentially

nonvolatile and could facilitate the absorption of gases without

loss of the capture agent into the gas stream. They also have

high thermal and electrochemical stability.

Nowadays, given the tendency for green processes and

sustainable technology, one of the active research areas is

exploring ionic liquids as an alternative or even replacement to

2

also that the solubility of ILs in the CO phase is exceedingly

2

low; (2) subsequent high-pressure phase behavior of CO in

2

1

0 different imidazolium-based ILs including [C mim][Tf N]

8 2

at temperatures of 298.15, 313.15, and 333.15 K and pressures

9

up to 15 MPa, reported by Aki et al. In their investigation, the

latter group concluded that the solubility of CO is greater in

2

−

ILs with anions having −CF groups such as [Tf N] and also

3

2

that the solubility increases by increasing the alkyl group chain

conventional alkanolamine solutions for removal of acid gases

3

−7

(

CO₂and H S) in gas sweetening processes.

Another

2

research area is concerned with the fixation and sequestration

Received: August 6, 2011

Revised: February 8, 2012

Published: February 28, 2012

of CO , which is regarded as the most important greenhouse

2

8

gas by employing ionic liquids. Solubility and diffusion

©

2012 American Chemical Society

2758

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

2

3

length in the cation part of the IL; (3) Henry's law constant at

ethylsulfate ([C mim][EtSO ]), and most recently the

2 4

10

+

2

98.15 K, reported by Baltus et al. for CO in [C mim]-

solubility of H S in [HOC mim] -based ILs containing

[PF ] , [OTf] , and [Tf N] anions, and [C mim] -based

6 2 2

ILs containing [PF ] and [Tf N] anions. All of the data

obtained have been used to estimate Henry's law constants or

diffusion coefficients at different temperatures.

2

8

2 2

−

24

+

[

Tf N] as well as eight different imidazolium-based ILs from

2

−

25

the low-pressure solubility data obtained by using a quartz

crystal microbalance apparatus; (4) Henry's law constant due to

6 2

1

Chen et al. for the solubility of CO in imidazolium-based

2

−

tetrafluoroborate [BF ] ILs at T = 307.55, 312.45, 317.45, and

We are interested in examining the potential of ILs for the

separation of CO and H S from natural gas and also for the

4

322.15 K. They concluded that the solubility increases by

2

increasing the alkyl chain length of the imidazolium cation ring

in the sequence: [C mim][BF ] > [C mim][BF ] > [C mim]-

separation of H S and CO gases from each other in the

gaseous streams containing them. The data reported by other

2 2

8

4

6

4

12

[

BF ]; (5) measurements made by Zhang et al. for the

researchers (mentioned above) for the CO −[C mim][Tf N]

4

2

8

2

10

solubility at infinite dilution of CO in [C mim][BF ] as well as

system except those of Baltus et al. at 298.15 K are mainly

obtained at high pressures, which are neither of sufficient

accuracy for extrapolation to low pressure regions nor for

estimating the Henry's law constants at various temperatures.

Also to our best knowledge, there is no reported solubility data

for H S−[C mim][Tf N] system in the open literature. Thus,

2

8

4

a series of 1-butyronitrile substituted imidazolium-based ILs at

T = 303, 313, and 323 K by using the gas chromatography

technique; (6) high-pressure phase behavior of CO₂

+

1

3

[

C mim][BF ], which has been measured by Gutkowski et al.

8 4

in the pressure and temperature range of 0.1−100 MPa and

2

8

2

3

03−363 K, respectively, 7) high-pressure solubility data of

2

this paper focuses on solubility of CO and H S in the ionic

2 2

CO in 1-alkyl-3-methylimidazolium bis(trifluoromethyl)-

liquid [C mim][Tf N] in the low to medium pressure range

8 2

sulfonylimide ([C mim][Tf N], n = 2, 4, 6, 8), reported by

(up to about 2.0 MPa) at temperatures from 303.15 to 353.15 K.

This way we will have sufficient experimental data in addition

to the ones previously reported for the other members and will

be able to follow the solubility behavior of CO and H S acid

n

2

1

4

Shin et al. at pressures up to 45 MPa and temperatures

between 298.15 and 343.15 K, and finally (8) subsequent high-

pressure phase equilibrium data of carbon dioxide with 1-alkyl-

2

3

-methylimidazolium trifluoromethanesulfonate ([C mim]-

gases in [C mim][Tf N] ionic liquids. In addition, because of

n

n 2

[

OTf], n = 2, 4, 6, 8) ILs at pressures up to 40 MPa and

the inconsistency between the Henry's law constants at zero

pressure for solubility of H S in [C mim][Tf N] reported in

at temperatures between 303.85 and 344.55 K reported by Shin

2

6

2

1

5

21

et al. The latter group used the Peng−Robinson equation of

state to correlate the obtained experimental data. For hydrogen

sulfide, however, experimental data for solubility and diffusion

in ILs are not as versatile as those for carbon dioxide. Jou and

our previous work and the other members of [C mim][Tf N]

n

2

family, the PTx data for H S/[C mim][Tf N] system were

2

6

2

again measured in this study. The solubilities determined are

used to estimate zero pressure Henry's law constants and partial

molar thermodynamic functions of solution of H S and CO at

1

6

Mather provided the first report regarding the solubility of

H S in ILs, that is, 1-butyl-3-methylimidazolium hexafluor-

2

different temperatures. Correlation equations for the obtained

Henry's law constants with temperature are presented here.

Also the solubility of CO /H S mixtures in [C mim][Tf N] is

ophosphate ([C mim][PF ]) at temperatures from 298.15 to

4

6

4

03.15 K and pressures up to 9.6 MPa. Subsequently, Pomelli

2

8

2

17

+

et al. reported the solubility of H S in different [C mim] -

based ILs with different anions and in a series of [Tf N] ILs

2

4

investigated in this study to explore the facility of separation of

these gases from each other in streams containing them. The

notion behind this consideration is the large difference in

Henry's law constants for the solubility of H S and CO in the

−

2

with different cations at 298.15 K and 1400 kPa, using a

medium pressure NMR technique. They observed that H S is

2

19−25

stable with no sign of reaction under the investigated

experimental conditions. Their quantum chemical calculations

ionic liquids studied to date,

which suggests that the

selective capturing and separation of these gases may also be

possible using [C mim][Tf N]. In the next step, the obtained

show that the interaction energy between H S and the anion

2

8

2

part of the ILs is comparable in strength to that of traditional

hydrogen bonds and concluded that this is the main factor

responsible for the high solubility of hydrogen sulfide in ILs.

solubility data are modeled by using two distinct correlation

equations, that is, the extended Henry's law combined with

26,27

Pitzer's activity coefficient model for electrolytes,

which

1

8

Heintz et al. measured the solubility of CO as well as a

2

takes into account the nonideality of solute in liquid solvent

through activity coefficients, and a generic Redlich−Kwong

type equation of state proposed by Shiflett and Yokozeki for

mixture of N /H S in a polymeric ammonium polyether-based

2

IL with chloride anion in the temperature range from 300 to

2

8−31

5

00 K and pressures up to 0.23 and 3.0 MPa for H S and CO ,

2

gas−ionic liquid systems.

The two models are compared

1

9

respectively. Shiflett and Yokozeki reported the phase

equilibrium VLLE measurements of binary mixtures of H₂S

and CO with [C mim][PF ] at temperatures from (273.6 to

with each other and with the simple Krichevsky−Kasarnovsky

equation, through comparison of the predicted results with

32

2

4

6

that of experimental data. The experimental results obtained in

this work are also compared with the corresponding data for

[C mim][Tf N], [C mim][Tf N], and [C mim][Tf N] re-

3

42.2) K for H S and at T = 283.1 and 293.0 K for CO and

2

ternary mixture of H S/CO /[C mim][PF ] at T = 298.15 and

2

4

6

2

4

2

333.15 K and pressures up to 6.5 MPa. The remaining data

ported in the literature. Finally, ab initio density functional

concerning the solubility of H S in ILs have been produced

2

theory (DFT) quantum chemical calculations on the [C mim]-

n

in our laboratory at temperatures ranging from 303.15 to

[

Tf N] ionic liquids and their interaction with CO and H S

2

353.15 K and pressures up to about 2.0 MPa. This includes the

molecules were performed to understand the observed

solubility behaviors investigated in this work.

solubility of H S in [C mim][PF ], [C mim][BF ], and

2

4

6

4

2

0

[

C mim][Tf N], the solubility of H S in [C mim][PF ],

4 2 2 6 6

21

C mim][BF ], and [C mim][Tf N], the solubility and

6

4

6

2

EXPERIMENTAL METHODS

diffusion of H S and CO in 1-(2-hydroxyethyl)-3-methylimida-

■

2

22

zolium tetrafluoroborate ([HOC mim][BF ]), the solubility and

Materials. Carbon dioxide and hydrogen sulfide (c.p. grade

99.95% min) were obtained from Roham Gas Company.

2

4

diffusion of H S and CO in 1-ethyl-3-methylimidazolium

2

759

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

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Figure 1. Apparatus for the measurement of the solubility of pure and mixtures of CO and H S acid gases in liquids: 1, CO gas cylinder; 2, H S gas

2

cylinder; 3, He gas cylinder; C1−C3, CO , H S, and He gas containers, respectively; C4, gas mixture container; P1−P5, pressure sensors

2

(

transmitters); V1−V13, valves; CV, check valve; GSV, gas sampling valve; GC, gas chromatograph; AB, air bath; EC, equilibrium cell; MB, magnetic

bar; MS, magnetic stirrer; VP, vacuum pump; T, trap (acid gas scrubber).

The ionic liquid [C mim][Tf N] was supplied by Merck

Apparatus and Procedure. The experimental apparatus of

6

2

20

Chemical Company with a nominal purity of >99%. [C mim]-

Jalili et al. for the solubility of pure gases in ILs was modified

to measure pure and mixed gas solubility. The experimental

setup is shown schematically in Figure 1. It consists of a high-

pressure equilibrium cell (EC) and three gas containers (C1 to C3)

for introducing known amounts of CO , H S, and He into the

8

[

Tf N] was synthesized according to a known literature pro-

2

1,33

cedure.

A mixture of 8.2 g (0.10 mol) of 1-methylimidazole

(

>

Merck, 99%) and 16.4 g (0.11 mol) of n-octyl chloride (Merck

98%) was refluxed for 29 h at 373 K. The reaction mixture

2

was then washed with ethyl acetate to remove unreacted

starting materials. The oily product obtained was then heated at

gas mixture container (C4). All wetted compartments of the

apparatus are constructed from stainless steel (SS 316 L). The

equilibrium cell was equipped with a magnetic bar (MB) driven

by a magnetic stirrer (MS) at the bottom of the cell to facilitate

heat and mass transfer inside the cell. The equilibrium cell was

connected through a ball valve (V10) to the gas mixture

container (C4). The equilibrium cell and the gas mixture

container were placed inside an air bath (AB), the temperature

of which was controlled to within 0.05 K. The equilibrium

temperature was measured with a Lutron model TM-917 digital

thermometer with a 0.01 K resolution using a Pt-100 sensor

inserted into the air bath (AB). The equilibrium cell and the gas

container pressures were measured using a Keller model PA-

33X pressure transmitter sensors in the range of 0−2 MPa,

which were uncertain to within 0.01% of their full scale. The

calibration of pressure sensors was carried out against a

pneumatic dead-weight gauge (DH-Budenberg, model 550).

The volumes of different compartments of the apparatus were

measured using a calibrated bulb of known volume. First, the

calibrated bulb was connected to the apparatus via valve 13

(Figure 1). The whole system was evacuated through valve 11,

and then valve 13 was closed. The apparatus was pressurized to

atmospheric pressure by opening valve 12 to atmospheric air,

and the temperature was allowed to equilibrate. Using the ideal

gas law, the volume of the system was calculated from the

pressure drop when valve 13 was again opened while valve 12

was closed. The volume of the calibrated bulb was measured

3

43 K for 7 h at reduced pressure to remove the residual water.

A sample of 18.5 g of 1-octyl-3-methylimidazolium chloride

1

([C mim][Cl]) was obtained (80% yield). H NMR (300 MHz,

8

CDCl , 25 °C) δ (ppm) = 0.47 (3H,t, NCH (CH ) CH ), 0.89

3

2

2 6

3

(

10H, m, NCH CH (CH ) CH ), 1.54 (2H, m, NCH CH -

2 2 2 5 3 2 2

(CH ) CH ), 3.75 (3H, S, NCH ), 3.95 (2H, t, NCH (CH ) CH ),

2

5

3

2

2 6

3

7

.27 (1H, d, H-4), 7.50 (1H, d, H-5), 10.12 (1H, S, H-2).

To a mixture of 18.5 g (0.08 mol) of 1-octyl-3-methylimida-

zolium chloride in 67 mL of deionized water, 25.8 g (0.09 mol)

of lithium bis(trifluoromethyl)sulfonylimide (Merck >98%) was

added at room temperature. The two-phase mixture obtained was

magnetically stirred at room temperature for 24 h. Upon

completion of the reaction, as monitored by thin layer

chromatography (TLC), the IL was separated from the

reaction mixture as a dense phase. The upper aqueous phase

was washed with CH Cl (2 × 20 mL). The washings were

2

combined with the organic layer, and the latter was dried over

anhydrous MgSO . After filtration, the solvent was removed

4

using a rotary evaporator, and the product was then heated at

reduced pressure for 7 h at 343 K to remove residual water.

1

The yield was 90%. H NMR (300 MHz, CDCl , 25 °C): δ

3

(

ppm) = 0.98 (3H, t, NCH (CH ) CH ), 1.40 (10H, m,

2 2 6 3

NCH CH (CH ) CH ), 1.89(2H, m, NCH CH (CH₂)₅

2

5

3

2

CH ), 3.97 (3H, S, NCH ), 4.20 (2H, t, NCH (CH ) CH ),

3

2

2 6

3

7.34 (1H, d, H-4), 7.35(1H, d, H-5), 8.77 (1H, S, H-2).

2

760

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

within a tenth of a milliliter by filling the bulb with distilled

water and then measuring the mass of the water by using an

analytical balance (Mettler model AE 200) with an uncertainty

V10 was opened to allow contacting and mixing between liquid

IL and vapor phases inside the equilibrium cell (EC). Equi-

libration, which was indicated by the constant pressure of the

EC with time, was achieved normally within about 12 h by

the continuous operation of a magnetic stirrer, after which valve

V10 was closed. Then a few microliters of the representative

equilibrated gas phase containing H S and CO was injected

±

0.0001 g. The measured volume of the various parts of the

apparatus was uncertain to within ±0.5 mL. The composition

of the gas phase, which was assumed to be solely composed of

H S and CO , was assessed by gas chromatography (GC). The

2

vapor phase was analyzed using an online gas chromatograph

KONIK model HRGC 4000B) equipped with a megabore

from C4 through gas sampling valve GSV into the GC to

analyze and determine the composition of the representative

gas mixture above the gas-saturated IL. The GC analysis was

performed many times for at least four repeatable outcomes,

and then the average value was employed for doing the

calculations. By knowing the composition of the gas phase

above the IL saturated with CO /H S gas mixture, together

(

column (Supel-Q PLOT, 30 m × 0.53 mm) and a thermal

conductivity detector working at a temperature of 523.15 K

with helium carrier gas. The temperature of the column and the

flow rate and pressure of the carrier gas were adjusted to 313.15 K,

−1

5

.0 mL·min , and 530 kPa, respectively. The vapor sample was

2

taken in the sampling loop of 10 μL by a valco six-way, gas-

sampling valve (GSV) the temperature of which was adjusted

to 313.15 K. For the calibration of gas chromatograph, the

volumetric procedure described below was used to determine

the mixed gas composition, the accuracy of which was checked

by the gravimetric method.

The operation of the apparatus was such that at first a known

mass (about 10 g) of an ionic liquid was introduced into the

equilibrium cell, and then the whole equipment (except for gas

containers C1 through C3) was evacuated to pressures below

with the equilibrium total pressure, P_e_q_u_i_l, the equilibrium

temperature, T, and the total volume of the gas phase (which is

the sum of C4 and the gas phase volume in the equilibrium cell EC),

g

the moles of remaining H S and CO in the gas phase, n ,

2

gas

were determined by using an appropriate equation of state and

g

mixing rule. In this work, n was calculated using the

gas

35

SUPERTRAPP, which employs the NIST extended corre-

sponding states model (EXCST) for the calculation of phase

properties. In cases where the final equilibrium pressure P_e_q_u_i_l

was low (below 200 kPa), the operation was altered in such a

way that at first an adequate amount of helium gas was injected

from C3 to the equilibrated H S + CO gas mixture in C4,

0

3

.1 kPa by a vacuum pump and the temperature was raised to

43 K. The ionic liquid inside the cell was kept at this

2

temperature under vacuum for at least 48 h to remove trace

amounts of water and volatile impurities. The water content of

ionic liquids was carefully determined before the solubility

measurements by a Mettler model DL-37 Karl Fischer

volumetric titrator. In all cases, the water mass fraction was

found to be below (1 ± 0.1) × 10 (Several tests were

performed to check the time and the conditions for drying and

degassing the ionic liquid samples. It was found that the IL was

appropriately degassed and dried after pumping it under a

pressure of 0.1 kPa for about 24 h at a fixed temperature of

while valve V10 was closed, and after an additional 12 h to

achieve a homogeneous composition gas mixture inside C4, the

analysis of the gas mixture was performed by the above-

mentioned procedure. The moles of H S and CO in the liquid

2

phase n¹were then determined from

gas

−4

l

⁼ⁿgas − n^g

n

gas

(2)

CORRELATION AND MODELING DETAILS

■

Three correlation methods were applied to the experimental

data obtained in this work. The first method used was the

3

43 K). The temperature was then adjusted to the desired

value through the air bath, and a known amount of H S was

2

32

Krichevsky−Kasarnovsky (KK) equation, which does not take

introduced through valves V9 and CV (check valve) into the

gas container C4 from the gas container C2 of known volume

while valve V10 was closed. Then the whole system except for

gas containers C1 through C4 was evacuated again after which

into account the nonideality of the solute in the liquid phase

∞

₋P^s

RT

f (T, P)

s

V (

i

P

)

i

(P )

ln

= ln K

(T) +

h,x

x

i

(3)

a known amount of CO was charged from C1 to C4 through

2

V9 and CV. The presence of check valve CV and also the

where f (T,P) is the fugacity of gas solute carbon dioxide or

i

higher pressure of C1 relative to C4 (filled at first with H S gas)

2

hydrogen sulfide in the gas phase at temperature T and

pressure P, x is the mole fraction of solute i in the solvent,

ensures that no flashback of H S into gas container C1 and the

2

s

i

P

^o^t^h^e^r^p^a^r^t^s^o^f^t^h^e^s^y^s^t^e^m^wⁱ^l^l^o^c^c^u^r^d^u^rⁱⁿ^g^t^h^e^eⁿ^t^r^aⁿ^c^e^o^f^C^O2

into the C4 container. One can calculate the total number of

K (T) is Henry’s law constant on mole-fraction scale of gas

solute i in solvent (at vapor pressure P of solvent), V is the

h,x

i

s

36

∞

i

^m^o^l^e^sⁿgas of H S and/or CO injected into the equilibrium cell

2

partial molar volume of gas solute i at infinite dilution, and R is

the universal gas constant. In this case, the vapor pressure of the

ionic liquid solvent is negligible, and it is reasonable to assume

from

⎛

⎞

V

s

gc

P

Z

P

i

f

the saturated vapor pressure P to be zero. Equation 3 can then

⎜

⎝

⎟

⎠

n

=

⁻Z

gas

RT

gc

be rearranged to eq 4

i

f

(1)

0

∞

f (T, P)

V P

i

where V denotes the volume of the gas container (C1 or C2),

i

(0)

gc

ln

= ln K (T) +

h,x

Z and Z are the compressibility factors corresponding to the

i

f

x

RT

(4)

i

initial and final pressures P and P , respectively, in the gas

i

f

Values of Kh⁽⁰, x⁾_i(T) and V

∞

at each temperature T can be

container before and after transferring H S or CO , and T is

i

2

gc

0

the temperature of the gas container. The most accurate PVT

obtained from the intercept and slope of plots of ln(f /x ) vs P

i

data presented by National Institute of Standards and

for binary CO /IL or H S/IL mixtures at the specified tem-

perature, respectively. Here, f is the fugacity of pure CO or

i 2

H S at equilibrated temperature T and pressure P for the gas

2

2 2

34

0

Technology (NIST) for pure compounds was used to

calculate compressibility factors of H S and CO gases, which

2

were needed for solubility calculations. In the next stage, valve

solute/IL binary system.

2

761

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The Journal of Physical Chemistry B

Article

40

The second method used was the extended Henry's law,

as a statistical weight. Yokozeki applied the random mixing

concept to the highly asymmetric mixtures by rescaling the

molecular sizes so that the number of neighboring interactions

becomes geometrically symmetric. This is equivalent to the

renormalization of the mole fraction: stretching and/or

which takes into account the nonideality of the solute, CO or

2

H S, in the liquid IL phase by Pitzer's activity coefficient model

2

K

(T, P)a (T, m ) = f (T, P)

m i

i

h,m

(5)

i

40

shrinking of mole fraction coordinates. It must be added

that each of cubic EoS's like Peng−Robinson, van der Waals,

and Redlich−Kwong can be equally well-applied for performing

the ϕ−ϕ calculations. In this study the RK type of EoS, as used

by Shiflett and Yokozeki for gas/IL systems, was arbitrarily

chosen. In this method, which is a conventional ϕ−ϕ approach,

the nonideality of gas solute in the liquid IL phase as well as in

the gas phase is both taken into account by the fugacity

coefficient of each component calculated from the RK cubic

K_h_,_m_i(T,P) is the molality-scale Henry's law constant of the ith

solute (CO or H S) in the IL at temperature T and pressure

2

P. a (T,m ) is the activity of the ith gas solute in the liquid

m

i

phase (IL), which is related to the molality m of the gas solute

i

and activity coefficient γ through eq 6:

i

m

i

a (T, m ) =

γ

o i

m

i

(6)

o

−1

where m = 1 mol·kg . The relation betweenK_h_,_m_i(T,P) and

Henry's law constant at zero pressure, K ⁰⁾_i(T), is expressed

28−31

EoS. The RK EoS is given in the following form

(

h,m

3

6

RT

− b

a(T)

as

^P⁼V

⁻V

(V

+ b)

̅

(11)

∞

⎛

⎝

⎞

⎟

V P

0)

i

K

(T, P) = K⁽(T)exp⎜

h,m

2 2

i

RT ⎠

R Tc

(7)

a(T) = 0.427480

α(T)

P

(12)

(13)

c

The activity coefficient of solute, γ, in the IL was calculated

i

using the Pitzer's virial expansion for the excess Gibbs free

RT

c

2

6,27

energy (molality scale):

b = 0.08664

P

c

m

i

ln γ = 2

∑

^·^β2i,j + 3

i

o

where P_cand T_care the critical pressure and critical

temperature of pure components, respectively, and V is the

molar volume. The mathematical form of α(T)is represented

j=CO ,H S

2

̅

m

⎛

j ⎞⎛ m ⎞

k

∑

⎜

⎝

⎟

⎜

⎟

^×^β3i,j,k

28−31

o

by eq 14

m ⎠⎝ m ⎠

j=CO ,H S k=CO ,H S

2

≤3

−1

(8)

α(T) = ∑ λ (T − T )^k

k

r

(14)

Here β and β are the parameters describing binary and ternary

k=0

2

3

interactions between gas molecules in the solvent, respectively.

Here T = T/T is the reduced temperature, and λ 's are simply

0

i

r

c

k

The fugacity of pure gas (H S or CO ), f (T,P), is the

2

adjustable parameters obtained by fitting eqs 11 through 14 to

experimental solubility PTx data for the systems of interest

product of the total pressure P and fugacity coefficient ϕ (T,P)

i

of pure gas

(

next section).

0

f

(T, P) = ϕ (T, P)P

i

(9)

COMPUTATIONAL DETAILS

■

Henry's law constant on the molality scale, K_h⁽⁰_,_m⁾ (T), is related

Quantum chemical calculations were performed using the

i

41

(

0)

Gaussian version 03 package. The geometries were optimized

to Henry's law constant on the mole fraction scale, K (T), by

h,x

i

at the DFT/B3LYP level of theory using the 6-311+G* and 6-

M

1

(

0)

(T) = K_h⁽⁰_,_x⁾ i⁽^T⁾^×

solv

000

3

11++G(2d,2p) basis sets. The calculations were carried out

K

h,m

i

(10)

under isolated conditions. The binding energies, E_b_i_n_d_i_n_g,

calculated according to eq 15 were corrected for the basis set

^w^h^e^r^e^Msolv is the relative molar mass of the solvent.

42

43

superposition error (BSSE) using the counterpoise method.

It must be added that the reason behind the selection of

Pitzer's activity coefficient model for electrolytes is its simplicity

E

= E_c_o_m_p_l_e_x− E_m_o_n_o_m_e_r₁− E_m_o_n_o_m_e_r₂

binding

(15)

2

4,25

and good correlative accuracy. Our previous studies

those made by Maurer and co-workers

and

37−39

revealed high

where Ecomplex and Emonomer stand for the counterpoise-corrected

optimized energy of the supermolecule (complex) and

optimized energy of each of the monomers constituting the

complex, respectively. For each of the complexes, two or three

initial configurations were constructed for geometry optimiza-

tion to explore the potential energy surface better. Frequency

calculations were carried out to verify whether the optimized

structures obtained are a transition state or correspond to the

most stable structure.

correlative accuracy of the Pitzer's model for gas/IL systems.

Finally the third model was the one proposed by Shiflett and

2

8−31

Yokozeki,

which is a generic Redlich−Kwong (RK) type

of cubic equations of state (EoS) with a simple modification to

be applicable to gas−ionic liquid binary systems. The notion

behind the selection of the RK EoS is the special form of the

semi-theoretical mixing rule proposed by Yokozeki in his

original work for the solubility of refrigerants in various

4

0

lubricants. Yokozeki argued that, for a binary mixture of two

species with very different molecular sizes, that is, in the case of

only geometrically constrained asymmetric mixtures, the

assumption of random mixing of molecular species with nearly

equal size is no longer valid. Then, quadratic and symmetric x_ix_j

terms of the second virial coefficient cannot theoretically work

RESULTS AND DISCUSSION

■

Experimental Data. The data corresponding to measure-

ment of carbon dioxide and hydrogen sulfide solubility in the

ionic liquid [C mim][Tf N] at temperatures of 303.15, 313.15,

8

2

323.15, 333.15, 343.15, and 353.15 K and pressures up to about

2

762

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The Journal of Physical Chemistry B

Article

Table 1. Mole Fraction Solubility of Carbon Dioxide Gas, x , in [C mim][Tf N]

2

8

2

p/MPa

x₂

p/MPa

x₂

p/MPa

x₂

T/K = 303.15

T/K = 313.15

T/K = 323.15

0

1

.1123

.2488

.4147

.6362

.9400

.2389

.5893

0.0415 ± 0.0010

0.0896 ± 0.0021

0.1380 ± 0.0032

0.2019 ± 0.0047

0.2753 ± 0.0064

0.3384 ± 0.0078

0.4012 ± 0.0093

0.1193

0.2645

0.4405

0.6761

1.0001

1.3171

1.6922

0.0385 ± 0.0008

0.0836 ± 0.0018

0.1297 ± 0.0027

0.1905 ± 0.0040

0.2612 ± 0.0055

0.3243 ± 0.0068

0.3846 ± 0.0081

0.1258

0.2793

0.4649

0.7138

1.0567

1.3932

1.7909

0.0362 ± 0.0007

0.0786 ± 0.0015

0.1227 ± 0.0024

0.1806 ± 0.0035

0.2486 ± 0.0048

0.3095 ± 0.0060

0.3685 ± 0.0071

T/K = 333.15

T/K = 343.15

T/K = 353.15

0.1321

0.2934

0.4880

0.7501

1.1105

1.4650

1.8856

0.0342 ± 0.0006

0.0746 ± 0.0013

0.1170 ± 0.0020

0.1725 ± 0.0030

0.2407 ± 0.0042

0.2975 ± 0.0052

0.3562 ± 0.0062

0.1381

0.3069

0.5101

0.7845

1.1616

1.5345

1.9760

0.0326 ± 0.0005

0.0711 ± 0.0011

0.1123 ± 0.0017

0.1659 ± 0.0025

0.2318 ± 0.0035

0.2881 ± 0.0044

0.3445 ± 0.0053

0.1440

0.3196

0.5314

0.8176

1.2116

1.6008

2.0628

0.0311 ± 0.0005

0.0686 ± 0.0010

0.1087 ± 0.0016

0.1614 ± 0.0024

0.2273 ± 0.0033

0.2841 ± 0.0042

0.3433 ± 0.0051

Table 2. Mole Fraction Solubility of Hydrogen Sulfide Gas, x , in [C mim][Tf N]

2

8

2

p/MPa

x₂

p/MPa

x₂

p/MPa

x₂

T/K = 303.15

T/K = 313.15

T/K = 323.15

0

1

.0935

.2007

.3456

.5132

.6824

.8714

.0755

.3654

.5087

0.0807 ± 0.0010

0.1672 ± 0.0021

0.2744 ± 0.0035

0.3840 ± 0.0048

0.4753 ± 0.0060

0.5556 ± 0.0070

0.6222 ± 0.0079

0.7045 ± 0.0089

0.7355 ± 0.0093

0.1025

0.2206

0.3815

0.5686

0.7593

0.9757

1.2116

1.5558

0.0770 ± 0.0010

0.1599 ± 0.0022

0.2626 ± 0.0036

0.3674 ± 0.0050

0.4521 ± 0.0061

0.5317 ± 0.0072

0.5982 ± 0.0081

0.6673 ± 0.0091

0.1111

0.2394

0.4153

0.6197

0.8324

1.0731

1.3411

1.7395

0.0719 ± 0.0008

0.1497 ± 0.0016

0.2472 ± 0.0027

0.3473 ± 0.0038

0.4309 ± 0.0047

0.5101 ± 0.0055

0.5756 ± 0.0062

0.6520 ± 0.0071

T/K = 333.15

T/K = 343.15

T/K = 353.15

0.1191

0.2576

0.4473

0.6706

0.9012

1.1663

1.4635

1.9119

0.0676 ± 0.0007

0.1413 ± 0.0015

0.2339 ± 0.0024

0.3305 ± 0.0034

0.4119 ± 0.0043

0.4899 ± 0.0051

0.5544 ± 0.0057

0.6300 ± 0.0065

0.1270

0.2748

0.4777

0.7175

0.9655

1.2539

1.5771

0.0662 ± 0.0006

0.1382 ± 0.0012

0.2279 ± 0.0021

0.3185 ± 0.0027

0.3952 ± 0.0033

0.4717 ± 0.0041

0.5357 ± 0.049

0.1343

0.2907

0.5062

0.7624

1.0270

1.3371

1.6869

0.0630 ± 0.0006

0.1316 ± 0.0011

0.2176 ± 0.0019

0.3048 ± 0.0027

0.3851 ± 0.0034

0.4576 ± 0.0040

0.5181 ± 0.0047

2

.0 MPa are summarized in Tables 1 and 2, respectively. As

The obtained parameters A of eq 16 are summarized in Table 5.

i

mentioned before, because of discrepancies observed between

the Henry's law constants previously reported by Rahmati

et al. and those obtained for other members of H S/[C mim]-

The deviation between experimental and correlated Henry's law

constants by means of eq 16 is within experimental

2

1

2

n

(0)

uncertainties for K_h_,_xgiven in Table 4. The Henry's law

[

Tf N], the binary system H S/[C mim][Tf N] was again

2 2 6 2

constants are compared with each other in Figure 5 as a

function of temperature. It can be observed that the solubilities

studied in this work to overcome this difficulty. The obtained

PTx data for the latter system are presented in Table 3. Figures 2,

3, and 4 graphically depict the experimental data in Tables 1, 2,

of hydrogen sulfide and carbon dioxide in [C

mim][Tf N] as

8 2

and 3 as Px isotherms for comparison with the correlations.

well as in [C mim][Tf N] decreases by increasing the

6

2

The reliability and accuracy of the method of measurement

temperature and that their solubility behavior is typical of

that of physical solvents, therefore obeying Henry's law. Also

2

0,23

(0)

have been checked in our previous works.

Values of K_h_,_xat

20

each temperature T are listed in Table 4 for the solubilities of

the solubility of H S is about two times as much as that of CO

2

H S and CO in the ILs studied in this work along with their

2

in [C mim][Tf N] in the entire temperature range studied in

8

2

standard deviations. The fugacity coefficients were calculated

using SUPERTRAPP developed by NIST for pure compounds

this work. We found that there exists a relatively good linear

3

5

(0)

and mixtures. The K_h_,_xvalues obtained showed good

correlation between Kh,x and n for dissolution of both H

S and

2

correlations with temperature by the following equation

CO in [C mim][Tf N] at each temperature (especially at

2

n

2

lower temperatures) represented by eq 17.

1

(

0)

i

ln(K /MPa) = ∑ A (T/K)

h,x

i

(0)

K

h,x

/MPa = δ + δ n

0 1

i=−1

(16)

(17)

2

763

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The Journal of Physical Chemistry B

Article

Table 3. Mole Fraction Solubility of Hydrogen Sulfide Gas, x , in [C mim][Tf N]

2

6

2

p/MPa

x₂

p/MPa

x₂

p/MPa

x₂

T/K = 303.15

T/K = 313.15

T/K = 323.15

0

1

.0685

.1466

.2276

.3150

.4863

.7703

.8705

.0105

.1789

.3578

.5043

0.0539 ± 0.0005

0.1118 ± 0.0010

0.1679 ± 0.0015

0.2245 ± 0.0021

0.3240 ± 0.0030

0.4563 ± 0.0042

0.4998 ± 0.0046

0.5517 ± 0.0050

0.6078 ± 0.0056

0.6619 ± 0.0060

0.7012 ± 0.0064

0.0767

0.1637

0.2543

0.3532

0.5459

0.8737

0.9910

1.1549

1.3568

1.5740

0.0503 ± 0.0003

0.1040 ± 0.0006

0.1554 ± 0.0009

0.2100 ± 0.0012

0.3039 ± 0.0018

0.4325 ± 0.0026

0.4757 ± 0.0028

0.5277 ± 0.0031

0.5840 ± 0.0035

0.6477 ± 0.0038

0.0846

0.1805

0.2804

0.3904

0.6039

0.9748

1.1091

1.2967

1.5317

0.0442 ± 0.0004

0.0962 ± 0.0009

0.1438 ± 0.0014

0.1957 ± 0.0018

0.2846 ± 0.0027

0.4093 ± 0.0038

0.4518 ± 0.0042

0.5036 ± 0.0047

0.5598 ± 0.0053

T/K = 333.15

T/K = 343.15

T/K = 353.15

0.0924

0.1966

0.3056

0.4262

0.6605

1.0726

1.2235

1.4352

1.7012

0.0421 ± 0.0003

0.0887 ± 0.0007

0.1332 ± 0.0010

0.1821 ± 0.0014

0.2616 ± 0.0020

0.3870 ± 0.0029

0.4288 ± 0.0032

0.4798 ± 0.0036

0.5359 ± 0.0040

0.0999

0.2123

0.3299

0.4609

0.7147

1.1665

1.3339

1.5683

1.8633

0.0391 ± 0.0004

0.0819 ± 0.0009

0.1236 ± 0.0013

0.1670 ± 0.0018

0.2452 ± 0.0026

0.3662 ± 0.0039

0.4069 ± 0.0043

0.4571 ± 0.0049

0.5131 ± 0.0054

0.1073

0.2271

0.3532

0.4942

0.7668

1.2570

1.4391

1.6950

2.0168

0.0368 ± 0.0004

0.0761 ± 0.0008

0.1151 ± 0.0012

0.1567 ± 0.0016

0.2298 ± 0.0024

0.3469 ± 0.0036

0.3868 ± 0.0040

0.4363 ± 0.0045

0.4922 ± 0.0051

Figure 3. Total pressure above the solution of H S + [C mim][Tf N]:

2

8

2

Figure 2. Total pressure above the solution of CO + [C mim]-

2

8

⧫

, 303.15 K; △, 313.15 K; ■, 323.15 K; ○, 333.15 K; +, 343.15 K; ×,

[

Tf N]: ⧫, 303.15 K; △, 313.15 K; ■, 323.15 K; ○, 333.15 K; +,

2

3

53.15 K; , correlation by Pitzer's model.

343.15 K; ×, 353.15 K; , correlation by Pitzer's model.

The temperature variation of coefficients δ and δ for H S/

0.8726564

0

1

2

δ₀=

− 19.4818533 + 0.0779534(T/K)

CO

2

(T/K)

[

C mim][Tf N] are expressed by eqs 18a and 18b and by eqs

n 2

(18c)

1

8c and 18d for CO /[C mim][Tf N], respectively

2 n 2

δ = ¹

.0679905

+ 1.8422710 − 0.0067911(T/K)

CO

−

1.9853795

1

2

(T/K)

δ₀=

+ 0.6055446 − 0.0022733(T/K)

H S

2

(T/K)

(18d)

(

18a)

Equations 17 and 18 yield K⁽values as a function of

0)

h,x

temperature for solubility of H S and CO in [C mim][Tf N]

2

through [C mim][Tf N] ILs. Also Figure 5 shows that the

8

2

δ = ¹

.0025309

− 10.4504372 + 0.0401737(T/K)

H S

solubilities of H S and CO increase in [C mim][Tf N] by

1

2

2 2 n 2

(T/K)

increasing n. This same conclusion has also been made by

8,9

(18b)

Brennecke et al. for the solubility of CO₂in classical

2

764

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The Journal of Physical Chemistry B

Article

Table 5. Numerical Values of the Parameters of Equations

16, 24, and 25a

B (cm ·mol⁻¹)

3

B (cm ·mol⁻¹·K⁻¹

3

)

A₋₁

A₀

A₁

0

1

CO /[C mim][Tf N]

2

8

2

−

2609.79 13.05286 −0.013971

1.017319

−0.231635

−3.834807

−1.24214

H S/[C mim][Tf N]

2

8

2

−2312.41 9.322106 −0.008083

−14.25479

a

H S/[C mim][Tf N]

2

6

2

−2358.34 8.705225 −0.00505

−154.181

a

For β₂_,_H₂_S₋_H₂_SC = 0.313928, and C = −110.588.

o

1

Figure 4. Total pressure above the solution of H S + [C mim][Tf N]:

2

6

2

⧫

, 303.15 K; △, 313.15 K; ■, 323.15 K; ○, 333.15 K; +, 343.15 K; ×,

53.15 K; , correlation by Pitzer's model.

3

Table 4. Thermodynamic Properties of CO and H S in

2

[

C mim][Tf N] and [C mim][Tf N]

8

2

6

2

∞

Δ G

Δ H

Δ S

sol

x

sol

x

sol

x

(

0)

(kJ·mol⁻¹)

(J·mol ·K⁻¹)

−1

T/K

K

(MPa)

h,x

CO /[C mim][Tf N]

2

8

2

3

03.15

13.15

23.15

33.15

43.15

53.15

2.60 ± 0.04

2.98 ± 0.04

3.34 ± 0.05

3.71 ± 0.05

4.07 ± 0.06

4.42 ± 0.07

8.22

−11.0

−10.3

−9.55

−8.79

−8.00

−7.19

−63.4

−61.1

−58.8

−56.4

−54.1

−51.8

3

8.84

9.44

10.0

Figure 5. Comparison between Henry's law constants as a function of

10.6

11.1

temperature for the solubility of H S and CO in [C mim][Tf N] ILs:

2

n

2

●

, H S + [C mim] (this work); ▲, H S + [C mim] (this work); ■,

2 8 2 6

H S/[C mim][Tf N]

2

8

2

⧫

○

H S + [C mim] (ref 20); , H S + [C mim] (ref 25); , CO +

2

4

2

3

03.15

13.15

23.15

33.15

43.15

53.15

0.99 ± 0.02

1.18 ± 0.02

1.36 ± 0.03

1.56 ± 0.03

1.74 ± 0.03

1.95 ± 0.04

5.47

−13.3

−13.1

−12.7

−12.3

−11.9

−11.4

−63.1

−62.5

−61.1

−59.8

−58.4

−57.1

◊

[

C mim] (this work); , CO + [C mim] (ref 62).

8 2 2

5.79

6.41

7.01

7.60

8.18

of H S as well as CO in [C mim][Tf N] ILs. As the molar

2

n

2

density of the solvent IL increases, the void (or free) volume of

the IL decreases. This phenomenon causes less free space to be

accessible to the H S or CO gas solute molecules, and

H S/[C mim][Tf N]

2

6

2

3

03.15

13.15

23.15

33.15

43.15

53.15

1.25 ± 0.03

1.51 ± 0.03

1.80 ± 0.04

2.12 ± 0.04

2.48 ± 0.05

2.86 ± 0.06

6.35

−15.5

−15.2

−14.9

−14.7

−14.4

−14.1

−71.9

−71.1

−70.2

−69.4

−68.6

−67.7

2

7.06

7.77

8.46

9.15

9.84

therefore the solubility increases from [C mim][Tf N] to

2

[C mim][Tf N]. Brennecke and co-workers have pointed out

8

2

this same conclusion in their earlier experimental studies on the

8

,47

high-pressure phase behavior of IL/CO₂systems.

Also

48

Noble and co-workers through the use of regular solution

methylimidazolium-based ILs. To explain the observed differ-

ence in solubility, the densities of pure ILs as a function of

temperature were compared to each other. A comparison

4

9,50

theory

derived a simplified linear relation between the

natural logarithm of the Henry's law constant for the solubility

4

4,45

reveals that the molar densities

decrease with increasing

of CO in imidazolium based ILs and the inverse of a rational

2

temperature for each pure compound and their values for the

ILs follow the order [C mim][Tf N] > [C mim][Tf N] >

power of molar volume (V ) of the ILs, that is, ln(K ⁽⁰⁾/atm)

m

h

2

4

2

= χ + κV⁻

⁴^/³. Their derived relation confirms the above

[

C mim][Tf N] > [C mim][Tf N]. The observed trend in

m

6

2

8

2

molar densities may be due to weaker interaction between the

discussions.

46

anion and cation, which increases from [C mim][Tf N] to

2

It can be shown that the Gibbs energy of solution,

corresponding to the change in Gibbs energy when the solute

is transferred at a constant temperature from the pure perfect

[

C mim][Tf N]. This effect give rise to higher free volumes in

8 2

the ionic liquid, which provides an explanation from energetic

and entropic point of view for the observed solubility behavior

2

765

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Article

gas at the standard pressure to the standard state of infinite

51

dilution of the solute in the solvent, is given by

⎛

(0)

⎞

K

∞

⎜

h,x

⎟

Δ

G

= RT ln

sol x

⎜

⎟

0

P

⎝

⎠

(19)

0

where P is the standard state pressure. The partial molar

differences in enthalpy and entropy between the two states can

be obtained by calculating the corresponding partial derivatives

of the Gibbs energy with respect to temperature

⎡

⎛

K

⎞⎤

(

0)

∞

⎛

⎜

⎞

∂

Δ

G

T

∂ ⎢ ⎜ h,x ⎟⎥

∞

= −T²

sol x

2

Δ

H

⎟ = −RT

ln

sol x

⎢ ⎜

⎟⎥

0

∂

T ⎝

⎠

∂T

⎜

⎟

P

⎢

⎥

Figure 6. Comparison of the partial molar heats of absorption at

⎣

⎝

⎠⎦

∞

infinite dilution, Δ H , for CO and H S in ionic liquids: gray

sol

x

2

(20)

columns, H S; white columns, CO .

2 2

∞

(

^Δsol

H

− Δ G )

sol x

T

∞

x

the interaction of H S with the cation and anion of the ILs is

Δ

S

=

2

sol x

(21)

stronger than that of CO . This is also confirmed in the next

2

section, where the ab initio quantum chemical calculations yield

this same conclusion in the case of interaction energy of H₂S

and CO with [C mim][Tf N]. In addition, it can be observed

The pressure range considered in this work is not high enough

to cause Henry's law constant to be a strong function of

2

0,21

2

n

2

pressure.

Therefore, one would not expect large errors if

∞

from Figure 6 that the Δ H values for the dissolution of pure

sol

x

one ignores this pressure dependency. By means of this

approximation and using eqs 19, 20, and 21, we estimated the

mole-fraction scale thermodynamic functions of solution at

infinite dilution for CO and H S in [C mim][Tf N] and

CO in the ILs are comparable with each other and except for

2

1

-(2-hydroxyethyl)imidazolium tetrafluoroborate ([HOemim]-

[

BF ]), there is no significant difference between their values.

4

2

6

2

This same behavior can be observed for dissolution of H S in

[

C mim][Tf N]. It may be worth mentioning that the relation

2

8

2

∞

the ILs. The comparison between the Δ H values reveals

that the interaction of H S is more energetic than CO with

between mole fraction scale and molality scale thermodynamic

functions of solution is straightforward and they can be

transformed to each other by using eqs 22 and 23,

sol

x

2

37

[

C mim][Tf N]. Also, the interaction of H S is more energetic

8

2

∞

with [C mim][Tf N] than with [C mim][Tf N]. The Δ S

6

2

8

2

sol x

∞

Δ

G

= Δ

G

⁺^R^T^lⁿ⁽^Msolv/1000)

⁻^R^lⁿ⁽^Msolv/1000)

(22)

(23)

sol m

sol x

values show the degree of ordering in the solution associated

with the gas dissolution. It can be seen from Table 4 that more

ordering occurs with H S than does with CO in the

∞

S

= Δ

S

sol m

sol x

2

[

C mim][Tf N] and [C mim][Tf N] ionic liquids, but the

6 2 8 2

The values for the mole fraction scale Gibbs free energy,

∞

difference is not so high to carry out further analysis indicating

that the energetic effect is more important than the entropic

Δ G , enthalpy, Δ H , and entropy Δ S of solution are

sol

x

sol

x

sol x

given in Table 4 at temperatures from 303.15 to 353.15 K for

CO /[C mim][Tf N], H S/[C mim][Tf N], and H S/

∞

effect. Table 4 reveals that, as in the case of Δ H , the Δ S

sol

x

sol x

2

8

2

8

2

values are negative and the variation with temperature of the

Δ S values are positive for CO /[C mim][Tf N], H S/

C mim][Tf N], and H S/[C mim][Tf N] binary mixtures;

[

C mim][Tf N], respectively. As it can be observed, the

6 2

∞

Δ G values are positive and increase with temperature in a

similar manner for the three systems, being the highest for

CO /[C mim][Tf N] and the lowest for H S/[C mim][Tf N].

sol

x

2

8

2

sol

x

[

8 2 2 6 2

that is, they increase with temperature.

The H S/CO /[C mim][Tf N] ternary system was also

2

8

2

6

2

∞

The Δ H values are negative, and the variations with

2

8

2

sol

x

∞

studied to assess the feasibility of the H S/CO gas separation

temperature of the Δ H values are positive for CO₂/

2 2

sol

x

by the selective absorption method. The solubility experiments

were performed under various T, P, and feed compositions.

Three levels were selected for the molar ratios of hydrogen

[

C mim][Tf N], H S/[C mim][Tf N], and H S/[C mim]-

8 2 2 8 2 2 6

[

Tf N] binary mixtures; that is, they increase with temperature.

2

The interaction of CO with ILs includes dispersion, dipole−

induced dipole, and electrostatic forces. In addition to the

2

sulfide to carbon dioxide in the feed, that is, H S/CO ≈ 4:1,

2

1

:1, and 1:4. Special care was taken when preparing the H S/

above interactions, H S also exhibits hydrogen bonding with

2

17

∞

CO gas mixtures to prevent the H S from condensing. The

the anion part of the ILs. The Δ H values of CO and H S

dissolution in [C mim][Tf N] and [C mim][Tf N] are similar

2

sol

x

2

saturation vapor pressure for H S at 298 K (2.0173 MPa) is

2

8

2

6

2

to those of polar solvents such as water, methanol, and ethanol,

which physically absorb these gases, where the interactions are

dispersion and dipole−induced dipole, but not electrostatic.

lower than that of CO at 298 K (6.4342 MPa). Therefore, the

2

total pressure for the three feed gas mixtures was set below 2.0

MPa. All measurements were carried out at temperatures of

303.15, 323.15, and 343.15 K and pressures less than 1.3 MPa.

∞

The Δ H values for CO and H S absorption into nonpolar

sol

x

2

solvents such as cyclohexane and heptane tend to be smaller

due to limited dispersion forces. Heat of absorption values for

The experimental results for the H S/CO /[C mim][Tf N]

2 2 8 2

47

ternary system are summarized in Table 6. Discussions about

modeling and gas separation feasibility are presented in the next

section.

Results of Correlation of Experimental Data. As

mentioned in previous section, the Pitzer's and RK models

were used to correlate the experimental solubility data. In case

compounds affording chemical reaction and complexation, such

2

as alkanolamines, are much larger. We have also compared the

∞

Δ H values for the dissolution of CO and H S in some ILs

sol

x

2

in Figure 6. Generally, it can be deduced that the absorption of

H S in ILs is more energetic than that of CO indicating that

2

766

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The Journal of Physical Chemistry B

Article

Table 6. Experimental VLE Data for CO /H S/[C mim][Tf N] Ternary Mixtures

2

8

2

a

feed

measured

calculated

CO₂

H₂S

IL

T/K

P/MPa

100·x_H₂_S

100·x_I_L

100·y_H₂_S

100·x_H₂_S

100·x_I_L

100·y_H₂_S

5

9

.1

20.1

34.4

49.8

14.7

23.7

30.0

4.8

74.8

56.5

37.7

71.7

54.2

42.7

76.0

55.5

39.3

74.9

55.9

37.0

71.6

54.2

44.1

75.9

55.9

39.1

75.5

56.0

37.6

71.7

54.3

43.2

76.2

55.9

39.5

303.15

323.15

343.15

0.1717

0.3821

0.7678

0.2275

0.4750

0.7214

0.2051

0.5005

0.9603

0.2039

0.4600

0.9249

0.2639

0.5496

0.8443

0.2325

0.5677

1.0900

0.2237

0.5330

1.0706

0.2972

0.6201

0.9592

0.2572

0.6297

1.2077

12.0

24.0

40.0

9.0

86.5

73.2

55.2

86.6

74.8

64.1

91.0

79.1

66.8

88.2

75.2

57.0

88.1

77.2

68.0

91.9

81.8

69.2

89.5

77.8

61.4

89.3

79.3

71.1

93.1

83.5

72.5

72.2

70.0

70.8

42.1

41.3

40.8

14.0

14.8

13.1

74.8

72.9

72.3

42.6

41.9

42.7

15.7

15.4

14.9

75.4

75.9

74.4

44.7

44.1

45.4

15.7

16.3

16.4

12.3

24.4

40.9

9.4

86.2

72.7

54.9

86.3

74.3

64.4

90.7

79.2

66.0

88.1

75.7

58.7

88.2

77.5

68.2

92.0

81.9

69.5

90.1

78.3

62.6

89.7

80.0

71.3

93.1

84.1

72.6

71.5

69.4

69.3

40.9

39.5

39.3

14.1

14.3

12.9

74.1

72.5

72.4

42.9

41.7

41.3

15.6

15.2

14.6

75.7

75.4

74.1

44.9

44.6

44.2

16.0

16.6

16.3

1

2

1

3

4

2.5

3.6

2.1

7.3

9.2

5.3

8.6

17.0

24.6

2.9

17.9

25.3

3.0

9.2

6.8

7.0

12.1

20.1

35.1

50.4

14.6

23.4

29.0

4.9

11.4

10.5

22.1

38.5

8.1

11.6

10.7

21.8

37.4

8.0

5

9

.0

1

2

1

3

4

2.6

3.8

2.4

6.9

9.2

5.2

8.6

15.5

21.7

2.6

15.5

22.3

2.6

8.9

6.0

12.3

19.7

35.5

49.9

14.6

23.7

29.6

4.7

10.3

9.3

10.5

8.9

4

8

.8

.5

19.8

34.4

7.2

19.6

33.9

7.0

1

2

1

3

4

2.5

3.7

2.0

7.2

9.1

4.9

7.9

14.4

19.4

2.2

13.9

20.2

2.2

9.2

5.6

5.4

12.6

9.5

9.6

a

Concentration units in mole %.

of Pitzer's model, the partial molar volume of gas solute i at

D , and D₁of eqs 25 for CO /[C mim][Tf N], H S/

0 2 8 2 2

[C mim][Tf N], and H S/CO /[C mim][Tf N] systems are

8 2 2 2 8 2

∞

infinite dilution, V , was considered a linear function of

i

absolute temperature T defined by eq 24

presented in Table 7, and the parameters C and C for H S/

0

1

2

∞

V (T) = B + B T

(24)

i

0

1

Table 7. Numerical Values of the Parameters of Equations

25a and 25b for Binary and Ternary Interactions of CO

where V^∞is in cm ·mol and T is in K. Parameters β and β₃

3

−1

,

2

i

2

were considered as a function of temperature T, defined by eqs

5a and 25b, respectively. Binary (β₂_,_C_O₂₋_C_O₂and β₂_,_H₂_S₋_H₂_S) as

well as ternary (β₃_,_C_O₂₋_C_O₂₋_C_O₂and β₃_,_H₂_S₋_H₂_S₋_H₂_S) interactions

in [C mim][Tf N] were described by eq 25a, and the other

H

2

S, and Their Mixture in [C mim][Tf N]

8 2

2

interaction

β₂or β₃

CO −CO₂

C_o= −0.054653

C_o= 0.746299

C₁= 3.907633

C₁= −226.762

2

8

2

H S−H S

2

^bⁱⁿ^a^r^y^aⁿ^d^t^e^rⁿ^a^r^yⁱⁿ^t^e^r^a^c^tⁱ^oⁿ^s⁽^f^o^r^e^x^a^m^p^l^e^β²,CO₂

−H

S^,

2

CO

2

−H

2

S

D

0

= 2.22527

D

1

= −0.012500

= −0.009390

β₃_,_C_O₂₋_H₂_S₋_H₂_S, etc.) were described by eq 25b. Neglect of

the parameter β does not have a considerable effect on the

accuracy of correlation for any of H S/IL and CO /IL binary

mixtures, but they need to be considered for improving the

accuracy of correlation for ternary H S/CO /[C mim][Tf N]

H

2

S−CO

CO −CO −CO

2

0

= 0.206944

1

2

^Co ⁼⁻⁰^.⁰⁰⁵¹¹⁰

^C1 ⁼¹^.⁵²⁴⁶⁵

3

H S−H S−H S

^Co ⁼⁻⁰^.⁰⁰⁴⁷⁵⁰

^C1 ⁼¹^.⁵⁴²⁵²⁰

2

H S−CO −H S

D = −1.61504

0

D = 0.006799

1

2

CO −H S−CO

2

8

2

mixtures. Also for H S/CO /[C mim][Tf N] ternary mixtures

the binary interaction parameters β₂_,_C_O₂_‑_H₂_Sand β₂_,_H₂_S₋_C_O₂were

considered different, that is, β₂_,_C_O₂_‑_H₂_S≠ β₂_,_H₂_S_‑_C_O₂, to improve

the correlation accuracy of the Pitzer's model, while in the case

of binary gas/IL mixtures they were considered equal.

2

8

2

[

C mim][Tf N] are presented at the footnote of Table 5. The

6 2

correlations made by the Pitzer's model for mole fraction of

CO and H S gas solutes, dissolved in the solvent IL at the

specified temperature and pressure, are graphically shown in

Figures 2, 3 and 4 for the three binary systems investigated in

this study. It can be seen that there is quite good agreement

between the correlated results and the observed experimental

2

C

T/K

1

X = C +

(i = j = k)

0

(25a)

(25b)

data in Tables 1, 2, and 3. Only in the case of the H S/

2

X = D + D (T/K)

(other cases)

0

1

[C mim][Tf N] binary system (Figure 4) at low temperature

8 2

whereX = β₂_i_,_jand β₃_i_,_j_,_k. The obtained parameters B and B of

of 303.15 K and pressures of above 1 MPa does the Pitzer's

model show relatively high positive deviations up to about 6.3%

0

1

eq 24 are summarized in Table 5; the fitted parameters C , C ,

0

1

2

767

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

a

Table 8. Pure Component Constants Used for the RK EoS

compound

CO₂

H₂S

molar mass (g·mol⁻¹)

T_c/K

P_c/kPa

λ₀

λ₁

λ₂

λ₃

44.010

34.082

475.48

447.43

304.13

373.10

1311.7

1287.3

7377

9000

2096

2390

1.00049

0.43866

0.33206

0.02012

0.05220

−0.10498

−0.049417

0.06250

0.99879

0.0046387

[

C mim][Tf N]

1

0

8

2

[

C mim][Tf N]

0

6

2

a

53,54

The critical parameters for [C mim][Tf N] and [C mim][Tf N] were estimated with the method proposed by Valderrama et al.

6

2

8

2

a

in mole fraction from the experimental data. We currently do

not have a reasonable explanation for this behavior.

Table 9. Binary Interaction Parameters of the RK EoS

system 1/2

l₁₂

l₂₁

m₁₂= m₂₁τ₁₂= τ /K

21

In the case of RK model, we need the critical properties of

pure compounds, extracted from NIST database for the pure

CO /[C mim][Tf N]

0.42943

0.21347

0.15623

0.31444

0.07944

0.13236

−0.32448

−0.03478

−0.12372

23.095

35.000

51.798

2

8

2

3

4

H S/[C mim][Tf N]

2 8 2

compounds CO₂and H S, and for the ionic liquids

2

H S/[C mim][Tf N]

2

6

2

[

C mim][Tf N] and [C mim][Tf N], they were estimated by

6 2 8 2

52

a

Determined by nonlinear least-squares analysis using the solubility

the modified Lydersen−Joback−Reid method, proposed by

Valderrama and co-workers.

5

3,54

data of this study.

The parameters λ through λ₃

0

for CO and H S were taken from ref 19, which were obtained

2

by Shiflett and Yokozeki from the corresponding vapor

pressure data, and those of the IL were obtained through

analysis of PTx solubility data for each of the three systems

binary and ternary systems of IL + CO + H S can be obtained

by applying the fundamental criterion for phase equilibrium:

2

investigated in this work. The parameters λ through λ₃

L

V

0

̂

x ϕ = yϕ

(i = 1, 2, 3)

where x and y are liquid and vapor mole fractions of the ith

i i

i

(32)

together with the critical constants are presented in Table 8

for each pure compound. The parameters a and b (eqs 12 and 13)

were modeled by the modified van der Waals−Berthelot mixing

i

̂

L

̂

V

species, and ϕ and ϕ stand for the fugacity coefficient of the

4

0

i

rule proposed by Yokozeki for general N-component

ith species in the liquid and vapor phases, respectively.

The average of relative deviations, ARD%, defined by eq 33

together with the maximum of relative deviations (MRD%) of

correlated mole fractions by using each of the three models,

mixtures as follows

N

a(T) =

∑

a a f (T)(1 − k )x x

i j ij i j

cor

i

exp

i

ij

x , from experimental data, x , are summarized and com-

i,j=1

(26)

(27)

pared with each other in Table 10 for a number of N data

points.

N

b = ¹∑ (b + b )(1 − m )(1 − k )x x

N

xi^c^o^r− x

exp

^A^R^D^%⁼¹N⁰⁰

i

j

ij

ij i j

i

2

∑

exp

i,j=1

x

i

(33)

i=1

τ_i_j

T

Table 10 shows that the Pitzer's model correlates the

solubility data of CO and H S in [C mim][Tf N] with a

higher accuracy than the RK EoS and the KK equation. In the

f_i_j(T) = 1 +

2

8

2

(28)

case of CO , the KK equation shows a higher correlation

2

l l (x + x )

ij ji

i

j

accuracy than RK EoS, but in the case of H S, the RK EoS

2

k_i_j=

shows a higher correlation accuracy than the KK equation.

In the case of CO /[C mim][Tf N], the solubility is lower

l x + l x

ji i ij j

(29)

2

8

2

compared to H S, and thus the nonideality in the liquid phase is

where τ = τ , τ = 0, m = m , m = 0, and k = 0. The

2

ij

ji

ii

ij

ji

ii

negligible. Hence, the KK approach seems to be able to

adequately describe the observed solubility behavior. In the case

of H S/[C mim][Tf N] binary system, the RK EoS shows the

parameters a and b are defined similar to eqs 12 and 13

i

2

R T

ci

2

6

2

a_i(T) = 0.427480

α_i(T)

highest correlation accuracy, while the Pitzer's model and KK

equation have comparable accuracy with each other. In the case

of the CO /H S/[C mim][Tf N] ternary system, the RK EoS

P

(30)

(31)

ci

2

8

2

RT

ci

shows the highest correlation accuracy. The KK equation did

not employ to correlate the experimental data of the CO /H S/

b_i= 0.08664 _P

2

ci

[

C mim][Tf N] ternary system. It must be noted here that the

8 2

There are four binary interaction parameters in this model: l_i_j,

l , m , and τ , which were obtained for each binary pair using

nonlinear regression analyses of experimental PTx data for

values of the critical constants, T and P , of the ILs estimated

c c

by different methods have a negligible effect on the correlation

accuracy of the RK EoS. For example in the case of

[C mim][Tf N] the values of T and P change respectively

ji

ij

CO /[C mim][Tf N], H S/[C mim][Tf N], and H S/

2

8

2

8

2

8

2

c

[

C mim][Tf N] binary systems. The numerical values of binary

from 1311.9 K and 2.10 MPa using the method of Valderrama

6

2

53

interaction parameters are summarized in Table 9. The

expression for fugacity coefficient ϕ of the ith species for the

RK EoS, which is needed for the phase equilibrium calculation,

is given in refs 28 through 31. The equilibrium solubility for the

et al. (method I) to 1088.7 K and 1.77 MPa by using the

55

group contribution method due to Shen et al. (method II).

In this case the values of ARD% change from 3.1% by

using method I to 3.2% when method II is employed for the

i

2

768

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

Table 10. Comparison between Average Relative Deviations (ARD %) and Maximum Relative Deviations (MRD %) Calculated

from Experimental Mole Fractions by the Three Models Considered in This Work

Pitzer's model

KK equation

RK equation

system

ARD%

MRD%

ARD%

MRD%

ARD%

MRD%

CO /[C mim][Tf N]

0.76

1.0

3.2

2.8

37

0.72

3.3

2.4

9.9

3.1

1.7

3.9

0.52

2.3

7.9

6.9

9.9

4.5

2

8

2

H S/[C mim][Tf N]

2

8

2

CO /H S/[C mim][Tf N]

8.9

2

8

2

H S/[C mim][Tf N]

0.92

2.9

6.3

1.1

1.7

5.1

2

6

2

overall

Figure 8. Plot of calculated selectivity defined by eq 34 versus

C mim][Tf N] mole percent at T = 303.15, 323.15, and 343.15 K,

[

8

2

P = 0.1 MPa, and CO /H S = 1:4 feed ratio. Continuous line (),

2

T = 303.15 K; broken line (- - -), T = 323.15 K; dotted line (···),

T = 343.15 K.

Figure 7. (a) Calculated selectivity defined by eq 34 versus

C mim][Tf N] mole percent with three different CO /H S mole

[

8

2

ratios at T = 303.15 K and P = 0.1 MPa. (b) Selectivity plots

without ionic liquid [C mim][Tf N] as a function of total pressure.

8

2

Continuous line (), 4:1 CO /H S feed mole ratio; broken line

2

(

- - -), 1:1 CO /H S feed mole ratio; dotted line (···), 1:4 CO /H S

2

feed mole ratio.

Figure 9. Plot of calculated selectivity defined by eq 34 versus

CO /[C mim][Tf N] binary system, and they change from

2

8

2

[

C mim][Tf N] mole percent at T = 303.15 K, P = 0.1 to 1.0 MPa,

8 2

1.77% by using method I to 1.80% using method II for

and CO /H S = 1:4 feed ratio. Continuous line (), P = 0.1 MPa;

2

H S/[C mim][Tf N] binary system. This is also the case for the

2

8

2

broken line (- - -), P = 0.5 MPa; dotted line (···), P = 1.0 MPa.

H S/[C mim][Tf N] binary system. The ARD% changes from

2

6

2

0.37% by using method I to 0.46% when method II is used.

separation by the absorptive method using [C mim][Tf N]

8 2

As mentioned before, the CO /H S/[C mim][Tf N] ternary

system was also studied to investigate the possibility of gas

ionic liquid. To do this, the RK EoS, a method experimentally

proven to be accurate in the present work (see Table 10) was

2

8

2

769

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

used to calculate the gaseous selectivity α_A_/_B, which is the ability

to separate gases A and B in the gas phase or gaseous

that, at high CO /H S feed ratios (1:1 and 4:1) without the

2

19

ionic liquid, no vapor−liquid equilibria exists and the gas

separation cannot be accomplished using traditional distillation

methods. Therefore, only with the addition of the ionic liquid is

the separation of CO and H S possible.

absorption selectivity S in the liquid phase. These factors are

A/B

1

9,56,57

defined as follows

2

y /x

A

α_A_/_B= S_B_/_A

=

COMPUTATIONAL RESULTS

y /x

B

(34)

■

B

In this section, discussions are presented from the molecular

point of view based on gas phase quantum chemical

calculations using geometrical optimizations to understand

the observed trends in the experimental data measured in this

article and previous related reports. As mentioned before, there

Here we denote CO as A and H S as B; the CO /H S

2

selectivity in the gas phase (α_A_/_B) has been computed according

to present EoS model at T = 303.15, 323.15, and 343.15 K, and

the results are summarized in Figures 7 through 9. In Figure 7a,

the CO /H S selectivity (α_A_/_B) is plotted as a function of the

2

is an inverse relation between the molar density of [C mim]-

n

[

C mim][Tf N] mole percent for three ternary mixtures with

[Tf N] ionic liquids and solubility of both CO and H S in

8

2

mole ratios 4:1, 1:1, and 1:4 at T = 303.15 K and P = 0.1 MPa.

In all three cases, α_A_/_Bremains relatively constant with

increasing ionic liquid concentration except at high IL

concentrations, in which they decrease steeply. Also it can be

observed that α_A_/_Bdecreases from about 3.1 to about 2.8 as the

CO /H S mole ratio decreases from 4:1 to 1:4. To understand

these ILs. Thus, the intermolecular interaction energy between

the isolated anion and cation of [C mim][Tf N] complexes as

n

2

well as the interaction energy between CO and H S molecules

2

with the anion and cation counterparts of the ionic liquids were

calculated to obtain an explanation for the observed

experimental results. The counter-poise corrected energies of

[C mim][Tf N] complexes were calculated using both the

2

the change in selectivity due to ionic liquid addition, Figure 7b

n

2

provides clear insights, where the selectivity with no [C mim]-

B3LYP/6-311++G(2d,2p) and B3LYP/6-311+G(d) levels to

compare the trends obtained from each of the two basis sets

and assess the basis set, which yields a proper description for

the molecular behavior of these systems. Results of com-

putation of molecular energies of single species, together with

the interaction energies, E_b_i_n_d_i_n_gfor each complex, are

summarized in Table 11. Figure 10 shows the geometry of

the minimum energy structures obtained at the B3LYP/6-311+

+G(2d,2p) level of theory for the monomers and complexes

studied in this work. In all [C mim][Tf N] complexes, the two

8

[

Tf N] at 303.15 K is plotted as a function of pressure for the

2

same CO /H S ratios (4:1, 1:1, and 1:4) in the absence of

2

[

C mim][Tf N]. The selectivity enhancement due to the ionic

8 2

liquid addition can be well-observed from the comparison of

Figure 7a and b. For example, the CO /H S feed ratio of 4:1

2

has a selectivity of about 2.8 with the ionic liquid, while the

corresponding case shows a selectivity of about 1.2 without the

ionic liquid (approximately the same as the value reported by

19

Shiflett and Yokozeki at 298.15 K). As the CO /H S feed

2

n

2

ratio decreases from 4:1 to 1:1 to 1:4, the improvement in

selectivity with the ionic liquid versus no ionic liquid also

decreases. The selectivity characteristics at higher temperatures

and pressures are shown in Figures 8 and 9, respectively. It can

be observed from Figure 8 that the selectivity (α_A_/_B) decreases

by increasing temperature. This behavior exists at all CO /H S

sulfur atoms together with the central nitrogen atom of the

−

[Tf N] anion are approximately coplanar with the imidazo-

2

+

lium ring of the [C mim] cation. The C −H hydrogen in the

cation (the hydrogen attached to the carbon between the two

nitrogen atoms) is directed toward the nitrogen atom of the

n

2

anion. The distance between C −H hydrogen of the cation, and

2

feed ratios and all pressures from 0.1 to 1.0 MPa. Figure 9

shows that the selectivity increases by increasing pressure. This

trend can be observed for all CO /H S feed ratios. Figure 9 also

the nitrogen atom of the anion does not vary considerably from

[C mim][Tf N] to [C mim][Tf N] and is relatively constant

2

8

2

in the small range of 2.017−2.027 Å, indicating that the size of

the alkyl chain substituent of imidazolium ring has no

considerable effect on the minimum distance between anion

and cation and only affects the interaction energy between the

2

shows that the selectivity enhancement is pronounced by about

3% in going from P = 0.1 MPa to P = 1.0 MPa. The most

important fact to consider at higher temperatures (343.15 K) is

4

−

Table 11. Energetic and Geometric Data on [C mim][Tf N], H S−[Tf N] and CO −[Tf N] Complexes

n

2

1

complex

B3LYP/basis set

6-311+G(d)

E₀+ ZPE

E_b_i_n_d_i_n_gkJ·mol⁻

minimum distance

OCO or H S angle

2

[

C mim][Tf N]

−2172.34931565

−2172.46602623

−2250.99393366

−2251.11740413

−2329.63818784

−2329.76969237

−2408.28243558

−2408.42119862

−2227.03107444

−2227.13641814

−2016.26154895

−2016.35258820

−744.041520141

−744.083507691

−533.272012803

−533.304590604

−309.8

−308.6

−306.6

−301.2

−306.0

−299.9

−306.5

−297.7

−19.26

−31.17

−11.06

−9.958

−19.16

−17.82

−11.01

−9.51

1.965

2.017

1.972

2.022

1.991

2.027

1.989

2.019

2.269

2.323

2.971

3.035

2.744

2.748

2.300

2.334

2

6

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

6-311+G(d)

-311++G(2d,2p)

C mim][Tf N]

4

2

6

C mim][Tf N]

6

2

6

C mim][Tf N]

8

2

6

−

H S−[Tf N]

91.83

91.13

176.3

176.8

93.82

93.24

179.98

179.97

2

6

−

CO −[Tf N]

2

6

+

H S−[C mim]

2

6

+

CO −[C mim]

2

6

2

770

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

+

Figure 10. Minimum energy structures for the dimers studied in this work: (a) CO /[C mim] ; (b) H S/[C mim] ; (c) [C mim][Tf N]; (d)

2

−

[

C mim][Tf N]; (e) [C mim][Tf N]; (f) [C mim][Tf N]; (g) H S/[Tf N] ; (h) CO /[Tf N] .

4

2

6

2

8

2

anion and cation (Table 11). Also it can be seen that as the size

of the alkyl substituent of the imidazolium ring increases no

folding results and it chooses the linear configuration. Since ab

initio calculations on the species are performed in the isolated

gas phase state, we certainly cannot conclude that chain folding

does not occur in the condensed liquid phase, where the

multiple interactions with other molecules surrounding each

molecule and reduction in volume are important and molecular

2

771

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

simulation studies need to be performed to clarify and fix the

problem. From Table 11, it can be deduced that the interaction

energy, E_b_i_n_d_i_n_gfor anion−cation complexes, decreases from

+G(2d,2p) and 6-311+G(d) basis sets, respectively. Also it

can be observed that the interaction of both CO and H S with

2

+

−

the prototype cation [C mim] is weaker than that of [Tf N]

2

+

[

C mim][Tf N] to [C mim][Tf N] and then increases for

anion being stronger in the case of H S−[C mim] complex

2

6

2

+

[

C mim][Tf N] by using the 6-311+G(d) basis set. However, a

relative to the CO −[C mim] complex.

8

2

decreasing trend in interaction energy can be observed from

There is a surprisingly excellent linear correlation (with R >

0.9999) between the absolute value of the energies of

[C mim][Tf N] complexes from ab initio calculations and

[

C mim][Tf N] to [C mim][Tf N] when using the 6-311+

2 2 8 2

+

G(2d,2p) basis set. Both basis sets indicate that the interaction

n

2

of H S with the anion and cation of the ionic liquid is more

correlated Henry's law constants generated by eqs 17 and 18

for the solubility of both CO and H S gases in [C mim][Tf N]

2

energetic than those of CO . This observation is pronounced

2

n

2

by the more polarized and diffused basis set 6-311++G(2d,2p),

ILs at each specified temperature. Equation 35 shows this

correlation

which implies that the interaction energy of H S with the

2

−

[

Tf N] anion is of the order of traditional hydrogen bond and

is about three times stronger than that of CO with [Tf N] .

2

K

⁽⁰⁾(T) = a(T)(|Ecomplex/Hartree|) + b(T)

h,x

−

2

(35)

However, the type of the hydrogen bond does not show strong

5

8

where a(T) and b(T) are linear functions of temperature in

kelvin

directionality. The hydrogen atoms of the H S molecule are

2

not directed toward the most electronegative fluorine atoms.

Instead, they are directed toward the less electronegative

^a⁽^T⁾⁼⁻⁰^.⁰⁰⁰¹⁷²⁹⁵⁽^T^/^K⁾⁺⁰^.⁰⁴⁷⁰¹³⁶⁴^C^O2

−

nitrogen atom of the [Tf N] anion. The gas phase ab initio

2

(

36a)

quantum chemical calculations using geometry optimizations at

both the B3LYP/CEP-121G(d,p) and the MP2/121G(d,p)

b(T) = 0.44005306(T/K) − 117.91173103 CO₂

levels of theory on H S-anion complexes made by Pomelli

2

1

7

(36b)

et al. as well as those performed on CO -anion complexes at

2

the B3LYP/6-311+G* and MP2/6-311+G* by Bhargava and

a(T) = −0.00005940(T/K) + 0.01582844 H S (36c)

59

2

Balasubramanian, qualitatively confirm this same conclusion.

−

The interaction energies for H S−[Tf N] complex are −5.11

2

b(T) = 0.16433102(T/K) − 43.60051328 H₂S

(36d)

−1

17

and −7.61 kcal·mol , respectively (interaction energy is in

the order of hydrogen bond), while the corresponding values

for the CO −[Tf N] complex are −2.37 and −2.80 kcal·mol

at the B3LYP and MP2 levels of theory, respectively.

This linear correlation between theoretically obtained absolute

energies of [C mim][Tf N] complexes on one hand and

−

−1

2

n

2

59

relations obtained from the experimental data on the other

hand further justifies the assumption that the solubility of acid

59

Furthermore, Bhargava and Balasubramanian concluded that

the optimized structures of CO -anion complexes are

gases CO and H S in [C mim][Tf N] ILs increases as the size

2 2 n 2

2

dominated by Lewis acid−base interactions, with the carbon

of the alkyl chain of the imidazolium ring in the cation increases

by decreasing the density or equivalent increase in free volume

of the IL. Furthermore, it provides theoretical support for the

experimental data reported in this work. Thus, by computing

the geometry optimized ab initio energy of an isolated

atom of CO as the electron acceptor (acid) and the anion as

2

the donor (base). From the above discussions, we can conclude

−

that the stronger interaction of H S with the [Tf N] anion

2

with respect to CO is responsible for the higher solubility of

2

H S in [C mim][Tf N] ionic liquids. Brennecke and co-

[C mim][Tf N] complex at B3LYP/6-311++G(2d,2p) level

n 2

2

n

2

6

0,61

workers

showed that the solubility of gases in ionic liquids

of theory using eqs 35 and 36, one can obtain Henry's law

constant in the limit of zero pressure at the specified

temperature, T, for dissolution of carbon dioxide or hydrogen

correlate well with gas polarizability, that is, the solubility

increases as the gas polarizability increases. Applying this

conclusion here it can be seen that H S with a higher dipole

sulfide in [C

mim][Tf N] ionic liquids.

n 2

2

−24

3

polarizability, α = 3.95 × 10 cm relative to CO , α = 2.911

10 cm shows a higher solubility in [C mim][Tf N] ionic

liquids too. The optimized structures corresponding to the

d

2

d

−24

3

CONCLUSIONS

×

n 2

■

New experimental data for the solubility and thermodynamic

functions of solutions of carbon dioxide and hydrogen sulfide

gases in the ionic liquid 1-octyl-3-imidazolium bis-

(trifluoromethyl)sulfonylimide, not previously reported in the

literature, have been measured and presented in this work. The

solubility of H S is higher than that of CO in [C mim][Tf N].

−

B3LYP/6-311++G(2d,2p) level of theory for the H S−[Tf N]

2

−

and CO −[Tf N] complexes are shown in Figures 10g and h,

2

−

respectively. In the case of the H S−[Tf N] complex, the

2

hydrogen atoms of H S are directed toward the two oxygen

2

−

atoms of the [Tf N] anion with a 1.6° decrease in H−S−H

2

8

2

angle and about 0.004 Å increase in H−S bond length. This

same orientation of interaction with less angle contraction can

be observed when using the B3LYP/6-311+G(d) level of

The solubility of both gases in the IL studied in this work is of a

physical nature. It has been shown that the solubility of both

CO₂and H S gases in [C mim][Tf N] ILs increases by

2

n

2

theory. The H−S−H angle in a free H S molecule is computed

increasing the number of carbons in the alkyl substituent of the

methylimidazolium cation ring. The solubility data for the

CO /H S/[C mim][Tf N] ternary system can best be

2

to be 92.70° at the B3LYP/6-311++G(2d,2p) level of theory.

−

In the case of CO −[Tf N] complex, Figure 10h shows that

2

8

2

the carbon atom of the CO molecule is aligned between the

correlated by means of the generic Redlich−Kwong cubic

equation of state proposed for gas/ionic liquid systems. The

addition of the ionic liquid makes feasible the separation of

CO and H S from each other especially at high temperatures

2

−

nitrogen and one of the oxygen atoms of the [Tf N] anion

2

with the oxygen atoms of CO positioned in the farthest

2

−

distance from the N and O atoms of the [Tf N] anion so as to

2

minimize the repulsive interaction of the oxygen atoms with the

where the traditional distillation procedure fails to work at these

conditions. Ab initio quantum chemical calculations provide

qualitatively useful clues to understand the nature of the

anion. The distortion of CO from a linear geometry upon

2

complexation is 3.2° and 3.7° when using the 6-311+

2

772

dx.doi.org/10.1021/jp2075572 | J. Phys. Chem. B 2012, 116, 2758−2774

The Journal of Physical Chemistry B

Article

solubility of CO and H S acid gases in [C mim][Tf N] ionic

liquids. Useful relations were presented in this work to calculate

the Henry's law constants for the solubility of acid gases in

(23) Jalili, A. H.; Mehdizadeh, A.; Shokouhi, M.; Ahmadi, A. N.;

Hosseini-Jenab, M.; Fateminassab, F. J. Chem. Thermodyn. 2010, 42,

2

n

2

1

(

298−1303.

24) Sakhaeinia, H.; Taghikhani, V.; Jalili, A. H.; Mehdizadeh, A.;

Safekordi, A. A. Fluid Phase Equilib. 2010, 298, 303−309.

25) Sakhaeinia, H.; Jalili, A. H.; Taghikhani, V.; Safekordi, A. A.

[

C mim][Tf N] ionic liquids by performing only quantum

n 2

chemical calculations on [C mim][Tf N] isolated complexes.

n

2

(

J. Chem. Eng. Data 2010, 55, 5839−5845.

AUTHOR INFORMATION

■

(26) Pitzer, K. S. Thermodynamics of Electrolytes. I. Theoretical

Basis and General Equations. J. Phys. Chem. 1973, 77, 268−277.

Corresponding Author

E-mail: jaliliah@ripi.ir, jaliliah@yahoo.com. Tel.: 98-21-

8252466; fax: 98-21-44739716.

(27) Activity Coefficients in Electrolyte Solutions; Pitzer, K. S., Ed.; CRC

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Press: Boca Raton, FL, 1991.

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4

(

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Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS

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■

2

074.

We are thankful to the research council of the Research

Institute of Petroleum Industry (RIPI) and also to the Research

and Development of the National Iranian Oil Company

NIOC) for their support of this work. The corresponding

author also gratefully acknowledges Prof. Gerd Maurer for his

kind guidance in correlating experimental data.

(

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Solubility of CO2, H2S, and their mixture in the ionic liquid 1-octyl-3-methylimidazolium bis(trifluoromethyl)sulfonylimide

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