Article pubs.acs.org/jced
Solubility of Hydrogen Sulfide in N‑Methylacetamide and N,NDimethylacetamide: Experimental Measurement and Modeling Mohammad Shokouhi,* Hadi Farahani, Masih Hosseini-Jenab, and Amir Hossein Jalili Research Institute of Petroleum Industry (RIPI), P.O. Box 14665-137, Tehran, 0098, Iran ABSTRACT: The solubility of hydrogen sulfide in N-methylacetamide and N,Ndimethylacetamide were experimentally measured. Gas concentrations were systematically measured by the isochoric saturation method at temperatures from (303.15 to 363.15) K and pressures from the vapor pressure of solvent up to about 2.2 MPa. Results show that H2S solubility in N,N-dimethylacetamide is more than that in N-methylacetamide. The experimental data were correlated using (1) the Krichevsky−Ilinskaya equation and (2) a generic Redlich−Kwong (RK) cubic equation of state. Using the solubility data, the partial molar thermodynamic properties of solution such as Gibbs free energy, enthalpy, and entropy at infinitely diluted solution, and also the enthalpies of absorption of loaded solutions were calculated using the Gibbs−Helmholtz equation.
■
■
INTRODUCTION
Materials. The specifications and sources of the chemicals used in this work are summarized in Table 1. All the materials were reagent grade and used without further purification. All solvents were prepared by calibrated balance (Mettler model AE 200) with an uncertainty of ± 0.0001 g. Apparatus and Procedure. The details of the experimental method for the measurement of gas solubility have previously been presented18,19 and only a short description will be provided here. The double wall equilibrium cell was connected to a water recirculation bath (model T 2500 PMT Tamson) with temperature stability within ± 0.02 K, and the temperature was measured using a model TM-917 Lutron digital thermometer with a 0.01 K resolution equipped with a Pt100 sensor inserted into the cell. The equilibrium cell pressure was measured using a model PA-33X KELLER pressure transmitter sensor in the range of (0 to 25) bar, which was accurate to within 0.01 % of full scale, and that of the gas container was measured using a Baroli type BD SENSORS digital pressure gauge in the range of (0 to 25) bar, which was accurate to within 0.01 % of full scale. One can calculate the total number of moles of acid gas injected into the equilibrium cell using the procedure adopted by Park and Sandall20 and Hosseini Jenab et al.:19
Acid gases solubility in physical organic solvents is important for industrial application, particularly, for the treatment of natural gas as well as for the development of correlations and prediction methods in molecular thermodynamics.1−5 Among the amides group, the solubility of CO2 in dimethylformamide (DMF) is extensively reported6−11 in literature. Also the phase behavior measurements of binary carbon dioxide/N,Ndimethylacetamide and the carbon dioxide/N,N-diethylacetamide system at high pressure are reported by the Byun research group.12 Yet except for the solubility of hydrogen sulfide in DMF13 and also the solubility of SO2 and H2S in DMA14 at only one gas partial pressure equal to 0.101 MPa and temperatures 268.15 K, 298.15 K, and 333.15 K, we have not found any experimental data on the solubility of hydrogen sulfide in physical solvents with an amide functional group. In our ongoing research on the solubility of acid gases in physical organic solvents, in this work, solubility measurements of hydrogen sulfide in N-methylacetamide (NMA) and N,Ndimethylacetamide (DMA) are experimentally investigated. All experimental trials are carried out via the isochoric saturation method at the temperature range from (303.15 to 363.15) K and pressures from the vapor pressure of solvent up to 2.2 MPa. The solubility data are modeled using two distinct correlations related to two theoretical approaches: the new version of the Redlich−Kwong cubic equation of state proposed by Shiflett and Yokozeki for gas−ionic liquid systems15−17 known as the generic Redlich−Kwong (GRK) cubic equation of state, and the Krichevsky−Ilinskaya (KI) equation. Some characteristic partial molar thermodynamic properties of H2S dissolved at infinite dilution in those solvents and also the enthalpy of absorption of loaded solutions were calculated using the Gibbs−Helmholtz equation. © XXXX American Chemical Society
EXPERIMENTAL SECTION
nag =
Vgc ⎛ Pi P⎞ ⎜ − f⎟ RTa ⎝ Z i Zf ⎠
(1)
Received: May 28, 2014 Accepted: January 6, 2015
A
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 1. Specifications and Sources of Chemicals Used in This Work chemical name
molecular formula/
CAS registry number
purity
source
hydrogen sulfide N-methylacetamide N,N-dimethylacetamide
H2S C3H7NO C4H9NO
7783-06-4 79-16-3 127-19-5
99.95 % > 99 % > 99.9 %
Roham Gas Company Merck Aldrich Chemical
where Vgc denotes the volume of the gas container, Zi and Zf are the compressibility factors corresponding to the initial and final pressures, Pi and Pf, respectively, in the gas container before and after transferring gas, and Ta is the ambient temperature, which is equal to that in the gas container. Compressibility factors were calculated using NIST.21 Equilibration between liquid and vapor phases inside the cell were normally achieved within about 2 h after the start of stirring, and the partial pressure of gas at equilibrium in the equilibrium cell, Peag, was calculated as follows: Page = PT − PVP
nagg
VgPage ZagRT
= nag −
nagg
xag =
nagl (mole)
(3)
chemical name
wsolvent(g)
+
NMA
313.2−443.15
DMA
298.15−439.3
NMA
303.15−363.15
DMA
277.13−363.15
charged DMA
303.15−353.15
wsolvent(g) Msolvent(g)
Antoine Constants B= C= −6431.73 −9.41471 B= C= −4398.40 −36.6354 Density Equations ρNMA (g/cm3) = −(8.102 × 10−4)·T/K + 1.1956 (R2 = 0.9991) ρDMA (g/cm3) = −(8.800 × 10−4)·T/K + 1.1979 (R2 = 0.9995) ρCharged DMA (g/cm3) = −0.02654·mH2S − (8.800 × 10−4)·T/K + 1.1979 A= 18.3951 A= 15.5415
(5)
nagl (mole) nagl
temperature range (K)
(4)
1000
(7)
Table 2. Antoine Constants for the Equation ln(p/kPa) = A + B/(T/K + C), and Linear Correlation Equation for Density with Correlation Coefficient, R2
The molality and mole fraction of the loaded gas in the liquid phase is defined as mag =
)
1000
RESULTS AND DISCUSSION Validation of the experimental apparatus and accuracy of data were recently investigated for CO2/dimethylformamid and also CO2/MDEA aqueous solution in a previous work.13 The liquid phase molar volume for DMA was taken from the density data reported by Scharlin.22 Those data are correlated using a linear equation, and for the case of NMA, the liquid phase molar volume was obtained from linear correlation equation fitted through experimental data reported in the literature.23−25 Both density and temperature equations along with their correlation coefficients (R2) are reported in Table 2.
where Vg is the gas phase volume, T is the equilibrium temperature of the cell, and Zag and ρag are the compressibility factor and density of acid gas at Peag and T, respectively. The number of moles of gas in the liquid phase was then determined from nagl
+ wsolvent ⎞⎟ ⎟⎟ ρcharged solution ⎠
mag wsolvent
■
(2)
= Vgρag
(
where mag is the molality of acid gas obtained from the iteration technique or as an approximate estimation obtained from the molality calculated with eqs 3 through 6.
where PT and PVP denote the total pressure and vapor pressure of solution. A key issue is the determination of the vapor pressure of the mixture solution since this value must be subtracted from the total pressure to obtain the partial acid gas pressure. The moles of remaining acid gas in the gas phase, ngag, was determined from nagg =
⎛ ⎜ = ρag ⎜Vauto − ⎜ ⎝
Vapor pressures of pure NMA are obtained from Gopal et al.26 and Manczinger et al.,27 and those of pure DMA are obtained from Nasirzadeh et al.28 and Ishiguro et al.29 for which those data correlated with Antoine equation. The Antoine equations for vapor pressure with the set of constants for the two liquids are reported in Table 2. Experimental solubilities of H2S in both solvents are reported in Tables 3 and 4. Temperature and pressure dependency of H2S solubility, graphically have been shown in Figures 1 and 2. As expected H2S solubility in both solvents increases with increasing pressure and decreases with increasing temperature. In Figure 3, H2S solubility in DMA, NMA, and also two other typical organic solvents such as sulfolane (SFL)1 and dimethylformamide13 have been compared at T = 313.15 K. As may be seen, the solubility of H2S in DMA is higher than it is in others.
(6)
where nlag is the number of acid gas mole in the liquid phase, wsolvent is the weight of solvent in g, and Msolvent is molar mass of pure solvent in g. As mentioned above the amount of dissolved gas is calculated from the amount of gas charged to the cell by subtracting a correction for the amount of gas that is still present in the vapor phase. That correction is calculated assuming that the volume of the vapor phase is the difference between the cell volume and the volume of the unloaded solvent (which is known from the preparation of the solvent). However, that procedure neglects a volume change (mostly a volume expansion) when a gas is dissolved in a liquid. In this case, eq 3 may be corrected as B
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 3. Experimental Solubility of H2S in DMAa T
Pt ± 0.003
K
MPa
303.15 0.041 0.121 0.191 0.335 0.458 0.586 0.734 313.15 0.053 0.150 0.238 0.415 0.564 0.719 0.903 323.15 0.065 0.184 0.289 0.501 0.681 0.863 1.084 333.15 0.081 0.219 0.343 0.594 0.806 1.021 1.279 343.15 0.094 0.257 0.404 0.696 0.941 1.194 1.490 353.15 0.115 0.299 0.469 0.806 1.086 1.380 1.715
ΔHabs(GH)
PH2S xH2S ± ΔxH2S
MPa Pt −3.9 × 10−4 0.041 0.121 0.191 0.335 0.458 0.586 0.734 Pt −6.8 × 10−4 0.053 0.150 0.238 0.415 0.564 0.719 0.903 Pt −1.16 × 10−3 0.064 0.183 0.288 0.500 0.680 0.862 1.083 Pt −1.98 × 10−3 0.079 0.217 0.341 0.592 0.804 1.019 1.277 Pt −3.27 × 10−3 0.091 0.254 0.401 0.693 0.938 1.190 1.486 Pt −5.19 × 10−3 0.110 0.294 0.464 0.801 1.081 1.375 1.710
(xH2S ± ΔxH2S)Cor.
kJ/mol
0.047 0.123 0.181 0.279 0.349 0.409 0.472
± ± ± ± ± ± ±
0.003 0.003 0.003 0.004 0.004 0.004 0.004
0.047 0.124 0.182 0.280 0.350 0.411 0.474
± ± ± ± ± ± ±
0.003 0.003 0.003 0.004 0.004 0.004 0.004
−16.51 −16.07 −15.76 −15.27 −14.97 −14.72 −14.50
0.046 0.121 0.178 0.275 0.344 0.404 0.467
± ± ± ± ± ± ±
0.003 0.003 0.003 0.004 0.004 0.004 0.004
0.046 0.121 0.178 0.276 0.346 0.406 0.470
± ± ± ± ± ± ±
0.003 0.003 0.004 0.004 0.004 0.004 0.004
−17.64 −17.20 −16.89 −16.41 −16.10 −15.86 −15.63
0.045 0.119 0.175 0.270 0.339 0.398 0.461
± ± ± ± ± ± ±
0.003 0.003 0.003 0.004 0.004 0.004 0.004
0.045 0.119 0.175 0.271 0.340 0.400 0.464
± ± ± ± ± ± ±
0.003 0.003 0.004 0.004 0.004 0.004 0.004
−18.81 −18.37 −18.07 −17.59 −17.28 −17.03 −16.80
0.044 0.116 0.171 0.265 0.333 0.392 0.455
± ± ± ± ± ± ±
0.003 0.003 0.004 0.004 0.004 0.004 0.004
0.044 0.116 0.172 0.266 0.335 0.394 0.458
± ± ± ± ± ± ±
0.003 0.003 0.004 0.004 0.004 0.004 0.004
−20.01 −19.58 −19.28 −18.80 −18.49 −18.24 −18.01
0.043 0.113 0.167 0.260 0.327 0.386 0.449
± ± ± ± ± ± ±
0.003 0.003 0.003 0.004 0.004 0.004 0.004
0.043 0.113 0.168 0.261 0.329 0.388 0.452
± ± ± ± ± ± ±
0.003 0.003 0.003 0.004 0.004 0.004 0.004
−21.24 −20.82 −20.52 −20.05 −19.74 −19.49 −19.25
0.041 0.110 0.162 0.252 0.319 0.377 0.440
± ± ± ± ± ± ±
0.003 0.003 0.004 0.004 0.004 0.004 0.004
0.041 0.110 0.161 0.253 0.321 0.380 0.443
± ± ± ± ± ± ±
0.003 0.003 0.004 0.004 0.004 0.004 0.004
−22.52 −22.11 −21.81 −21.34 −21.03 −20.78 −20.53
T is temperature, Pt is total pressure, PH2S is partial pressure of H2S, xH2S and ΔxH2S are mole fraction and uncertainty of mole fraction of H2S, (xH2S)Cor is corrected mole fraction of loaded gas using density of charged solution and Habs is enthalpy of absorption. Standard uncertainties (u) are u(T) = ± 0.01 K and u(Pt) = ± 0.003 MPa (standard uncertainties in table are reported with 0.95 level of confidence). a
The measured quantity q is dependent upon the variables r... u which fluctuates in a random and independent manner. The experimental gas solubility data were evaluated to determine the Henry’s constant on the molality or mole fraction scale for the solubility of gas in solvents at zero (0) pressure, h(0) H,m or hH,x.
The error propagation theory was used to estimate the uncertainties of final results.30 In the base of this theory, the uncertainty δq of the interest variable q(r... u) is given by eq 8: ⎡⎛ ∂q ⎞ ⎤2 ⎡⎛ ∂q ⎞ ⎤2 δq = ± ⎢⎜ ⎟dr ⎥ + ... + ⎢⎜ ⎟du⎥ ⎣⎝ ∂u ⎠ ⎦ ⎣⎝ ∂r ⎠ ⎦
(8) C
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 4. Experimental Solubility of H2S in NMA
a
T ± 0.01
Pt ± 0.003
PH2S
xH2S
±ΔxH2S
ΔHabs(GH)
K
MPa
MPa
xH2S
± ΔxH2S
kJ/mole
0.024 0.089 0.151 0.228 0.296 0.348 0.383
0.002 0.003 0.004 0.005 0.005 0.006 0.006
−14.13 −13.91 −13.72 −13.50 −13.32 −13.19 −13.11
0.023 0.086 0.146 0.220 0.287 0.338 0.373
0.002 0.003 0.004 0.005 0.005 0.006 0.006
−15.08 −14.87 −14.68 −14.46 −14.29 −14.16 −14.08
0.022 0.082 0.141 0.213 0.278 0.328 0.364
0.002 0.003 0.004 0.005 0.005 0.006 0.006
−16.06 −15.86 −15.67 −15.46 −15.29 −15.16 −15.07
0.021 0.079 0.136 0.205 0.270 0.319 0.353
0.002 0.003 0.004 0.005 0.005 0.006 0.006
−17.08 −16.88 −16.70 −16.49 −16.31 −16.19 −16.10
0.020 0.076 0.130 0.198 0.261 0.310 0.344
0.002 0.003 0.004 0.005 0.005 0.006 0.006
−18.12 −17.93 −17.75 −17.55 −17.37 −17.24 −17.16
0.019 0.072 0.124 0.188 0.249 0.296 0.329
0.002 0.003 0.004 0.005 0.006 0.006 0.006
−19.20 −19.01 −18.84 −18.64 −18.47 −18.34 −18.26
0.018 0.070 0.121 0.185 0.244 0.291 0.323
0.002 0.004 0.004 0.005 0.006 0.006 0.007
−20.30 −20.12 −19.95 −19.75 −19.58 −19.45 −19.36
−5
303.15 0.050 0.179 0.318 0.511 0.705 0.867 0.978 313.15 0.060 0.214 0.385 0.613 0.855 1.043 1.175 323.15 0.069 0.251 0.449 0.722 1.001 1.222 1.360 333.15 0.079 0.289 0.515 0.832 1.151 1.405 1.589 343.15 0.089 0.326 0.582 0.941 1.306 1.593 1.798 353.15 0.100 0.364 0.650 1.053 1.462 1.785 2.023 363.15 0.112 0.402 0.721 1.165 1.621 1.981 2.260
Pt −3.2 × 10 0.050 0.179 0.318 0.511 0.705 0.867 0.978 Pt, −6.2 × 10−5 0.060 0.214 0.385 0.613 0.855 1.043 1.175 Pt −1.22 × 10−4 0.069 0.251 0.449 0.722 1.001 1.222 1.360 Pt −2.29 × 10−4 0.079 0.289 0.515 0.832 1.151 1.405 1.589 Pt −4.16 × 10−4 0.089 0.326 0.582 0.941 1.306 1.593 1.798 Pt −7.29 × 10−4 0.100 0.364 0.650 1.053 1.462 1.785 2.023 Pt, −1.24 × 10−3 0.111 0.401 0.720 1.164 1.620 1.980 2.259
It should be noted that the vapor pressure of NMA at the practical temperature range in this work is 3 × 10−5 MPa at T = 303.15 K through 1.2 × 10−3 MPa at T = 363.15 K, values which all are lower than the uncertainty of pressure sensor (0.003 MPa). T is temperature, Pt is total pressure, PH2S a
D
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Table 4. continued is the partial pressure of H2S, xH2S and ΔxH2S are mole fraction and uncertainty of mole fraction of H2S and Habs is enthalpy of absorption. Standard uncertainties (u) are u(T) = ± 0.01 K and u(Pt) = ± 0.003 MPa (standard uncertainties in table are reported with 0.95 level of confidence).
Figure 1. Experimental data for H2S−DMA system at different temperatures and pressure (points) compared with GRK EoS (dashed lines) and KI model (solid lines). The solid point (◆) in the figure is extracted from Hayduk et al. which shows a deviation of about 9% from our result.
Figure 2. Experimental data for H2S−NMA system at different temperatures and pressure (points) compared with GRK EoS (dashed lines) and KI model (solid lines).
E
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
Figure 3. Comparison of solubility of H2S in DMA, NMA, DMF, and sulfolane (SFL) at that given temperature. (0) hH, m (T ) =
lim
m / m0 → 0
(0) hH, x (T ) = lim
x→0
f (T , p) m/m
0
Table 5. Thermodynamic Properties of H2S Solubility in DMA and NMAa
(9)
f (T , p) x
T ± 0.01
h(0) H,x
ΔsolG∞ m
ΔsolH∞ m
ΔsolS∞ m
v∞ H2 S
K
MPa
kJ/mol
kJ/mol
J/mol
cm3/mol
(10)
where m is the molality of gas in the solvent, m0 = 1 mol·kg−1 IL and f is the fugacity of pure gas at temperature T and pressure p. The fugacities were calculated using the software package Thermofluids.31 For H2S, that software is based on the equation of state by Lemmon and Span.32 The procedure of Henry’s constant evaluation was adopted by Jalili et al.;33 therefore, it is not described here. The obtained h(0) H,x and the estimated uncertainty δh(0) H,x are given in Table 5. The influence of temperature on Henry’s constant was described by (0) ln(hH, x /MPa)
= Ah,x (T /K) + B h,x + C h,x /(T /K)
(11)
Henry’s constant in mole fraction scale and molality scale are correlated with (0) (0) −1 hH, = hH, m/MPakg x /MPa
Msolvent 1000
303.15 313.15 323.15 333.15 343.15 353.15 363.15
1.858 2.345 2.909 3.441 4.087 4.838 5.425
± ± ± ± ± ± ±
0.020 0.029 0.031 0.032 0.033 0.038 0.041
303.15 313.15 323.15 333.15 343.15 353.15
0.809 1.044 1.311 1.617 1.958 2.354
± ± ± ± ± ±
0.015 0.020 0.025 0.026 0.025 0.028
NMA−H2S 1.68 −14.12 2.22 −15.07 2.79 −16.05 3.38 −17.05 4.01 −18.09 4.67 −19.16 5.36 −20.26 DMA−H2S −0.44 −16.66 0.11 −17.78 0.70 −18.94 1.33 −20.13 1.99 −21.35 2.69 −22.62
−52.13 −55.20 −58.27 −61.35 −64.42 −67.49 −70.57
34.0 34.8 35.7 36.6 37.5 38.5 39.5
± ± ± ± ± ± ±
0.3 0.3 0.4 0.4 0.5 0.5 0.6
−53.52 −57.15 −60.77 −64.40 −68.02 −71.65
33.5 34.6 35.7 36.9 38.8 39.5
± ± ± ± ± ±
0.9 1.0 1.0 1.1 1.1 1.1
∞ T, temperature; h(0) H,x, Henry’s law constant; v , partial molar volume ∞ at infinite dilution obtained from GRK; ΔsolGm,x, Gibbs free energy of ∞ solution; ΔsolH∞ m,x, enthalpy of solution; ΔsolSm,x, entropy of solution at infinite dilution. a
(12)
where Ah,x, Bh,x, and Ch,x are adjustable parameters reported in Table 6. The correlation eq 11 was used to estimate the ∞ changes of the partial molar Gibbs energy ΔsolGm,x , the partial ∞ molar enthalpy ΔsolHm,x, the partial molar entropy ΔsolS∞ m,x of gas when it is transferred from the ideal gas state at temperature T and standard pressure p = p0 = 0.1 MPa to its reference state in the liquid solvent, and these properties are also given in Table 5.
Table 6. Numerical Values of the Parameters of eq 11, h(0) H,x/ MPa (Henry’s Law Constant on Mole Fraction Scale) DMA−H2S
■
MODELING Two models are used to correlate the experimental results for the solubility of a single gas in DMA and NMA. The Generic Redlich−Kwong Cubic Equation of State (EoS). A generic Redlich−Kwong (GRK) type of cubic equation of state, was proposed by Shiflett and Yokozeki15−17
NMA−H2S
Ah,x
Bh,x
Ch,x
Ah,x
Bh,x
Ch,x
0.02181
−6.7865
−0.0559
0.01848
−4.9349
−0.03481
to correlate the solubility of gases in an ionic liquid. For a pure component the RK EoS is P= F
a(T ) RT − υ−b υ(υ + b)
(13) DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data a(T ) = 0.427480
R2TC2 α(T ) PC
Article
Table 8. Optimal Binary Interaction Parameters in GRK and KI Equation, and also ARD % and MRD % of Both Models
(14)
RT b = 0.08664 C PC
l12 l21 τ12 = τ21 m12 = m21 A0 A1 ARD % (GRK) MRD % (GRK) ARD % (KI) MRD % (KI)
(15)
The mathematical form of α(T) as used by Shiflett and Yokozeki is ≤3
α (T ) =
∑ λk(Tr−1 − Tr)k
(16)
k=0
Pc and Tc are the critical pressure and critical temperature of the pure component, respectively, υ is the molar volume, Tr = T/Tc is the reduced temperature, and λk values are adjustable parameters. The critical properties for pure H2S were taken from the NIST database,21 those for DMA were calculated with the group contribution method34 and those for NMA were taken from the literature.35 All critical properties of H2S, DMA, and NMA are listed in Table 7. The parameters λ0 through λ3 were
molar mass Tc/K Pc/MPa λ0 λ1 λ2 λ3
NMA
DMA
34.08 373.60 9.008 0.99879 0.33206 −0.049417 0.0046387
73.09 718 5.00 1.0 0.453143 0 0
87.12 617.15 3.60 1.0 0.35819 0 0
ARD% =
aiaj fij (T )(1 − kij)xixj
i,j=1
b=
1 2
kij =
i=1
piexp (T , m)
ln γm = A(xs 2 − 1)
(21)
(22)
(24)
where A is binary parameters and xs is mole fraction of solvent. The influence of temperature on the binary interaction parameter is approximated by
(17)
A = A 0 + A1/(T /K)
(25)
39
Prausnitz et al. have discussed that the application of that type ∞ of equation needs to have information about h(0) H,x and v . 40 41 Bender et al. and also Deshmukh−Mather have presented the connection of the (KI) equation and the Peng−Robinson EoS to obtain the parameters of the KI equation from the EoS. The Henry’s law constants h(0) H,x were calculated from eq 10 at low pressure limit, and the partial molar volumes of solutes at infinite dilution were calculated by the GRK EoS and listed in Table 5. As observed in Table 5, the obtained values of vH∞2S are positive and linearly increase when temperature increases.
τij (19)
lijl ji(xi + xj) l jixi + lijxj
picor (T , m) − piexp (T , m)
where γx is the activity coefficient of gas on the mole fraction scale and vH∞2S is the molar volume of dissolved gas at infinite dilution. The activity coefficient, γx, was calculated from the two-suffix Margules equation39 on the mole fraction scale
(18)
T
N
∑
(23)
N
fij (T ) = 1 +
100 N
⎛ f (T , p) ⎞ vH∞2S(P − P s) HS (0) ⎟ = ln(hH, T ln⎜⎜ 2 ( )) + + ln(γx) x ⎟ RT x ⎝ ⎠
∑ (bi + bj)(1 − mij)(1 − kij)xixj i,j=1
0.042165 0.0049459 0 0.07939 0.62971 −440.93 1.11% 7.51% 2.38% 6.50%
Krichevsky−Ilinskaya equation. The solubility of a single gas in a pure NMA and DMA is described by the Krichevsky− Ilinskaya (KI) equation38 on the mole fraction scale
N
∑
0.091946 0.29908 0 −0.04846 0.21799 −219.05 1.43% 4.01% 2.99% 8.72%
⎛ pcor (T , m) − pexp (T , m) ⎞ i 100⎟⎟ MRD% = max⎜⎜ i exp pi (T , m) ⎝ ⎠
taken from Shiflett and Yokozeki36 for H2S, whereas for DMF and DMSO, they were considered as adjustable parameters and either set to zero (λ2 and λ3) or were obtained through a fit together with the binary parameters of the model to the new gas solubility data (see below). Table 7, shows all pure component parameters. The EoS was extended to mixtures by applying the modified van der Waals−Berthelot mixing rule proposed by Yokozeki:37 a(T ) =
H2S/DMA
the average relative deviation, ARD %, and the maximum relative deviation, MRD %, defined at eqs 21 and 22. The results of the RK correlation have been graphically shown in Figures 1 and 2 as well.
Table 7. Parameters of GRK EoS for Pure Compounds Used in the Present Study H2S
H2S/NMA
(20)
where τij = τji, τii = 0, mij = mji, mii = 0, and kii = 0. There are four interaction parameters per binary system: lij, lji, mij, and τij. These interaction parameters were adjusted to the experimental gas solubility data, and the pure component parameters (λ0 and λ1) of DMA and NMA were adjusted to the vapor pressure of pure solvent. Table 8 gives the numerical values of the binary interaction parameters and also the quality of correlation, using
vH∞2S ‐ NMA(cm 3/mole) = 6.3794 + 0.0908T (K) G
(R2 = 0.998) (26) DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data vH∞2S ‐ DMA(cm 3/mole)
■
ACKNOWLEDGMENTS We are thankful to the Research Council of the Research Institute of Petroleum Industry (RIPI) and the Research and Development of the National Iranian Oil Company (NIOC) for their support of this work.
(R2 = 0.998)
= −2.7857 + 0.1194T (K)
(27)
Parameters A0 and A1 were adjusted to minimize the sum of ARD % between the calculated and the experimental results for the pressure of the gas. The results of the correlations (interaction parameters) are given in Table 8. The quality of the correlation is reported using the average relative deviation ARD % and the maximum relative deviation MRD % as defined by eqs 21 and 22 in Table 8 as well, and graphically have been shown in Figures 1 and 2. The volume expansion or compression caused by dissolving an acid gas in liquid phase has been investigated using the sensitivity test on volume. It is empirically found out that if the ratio of uncharged injected liquid to the equilibrium cell volume is lower than one-third, the fluctuation of charged solution volume makes an error lower than that given for the solubility uncertainty. To further confidence and for a more realistic estimate, solubility data were recalculated using densities of the charged solutions obtained by the EoS for DMA and reported in Table 3, (xH2S)Cor, and also the densities of charged solutions were correlated by linear equations in terms of temperature and molality and reported in Table 2. Comparisons of data in columns 4 and 5 in Table 3 show that volume expansion causes the solubility increase with the deviations lower than 2% which is comparable with the uncertainty values of solubility. Enthalpy of Absorption. Using experimental pressuresolubility data of acid gases in solvent, one may be able to calculate the enthalpy of absorption via Gibbs−Helmholtz equation ΔHabs(GH), ⎛ ∂ ln pH S ⎞ ΔHabs(GH) 2 ⎜⎜ ⎟⎟ = − RT 2 ⎝ ∂T ⎠ P , x
■
(28)
ΔHabs(GH) is the enthalpy of absorption which is normally referred to as differential enthalpy in the literature. Enthalpies of absorptions were calculated using eq 28 and reported in Tables 3 and 4.
■
CONCLUSION
■
AUTHOR INFORMATION
Article
In this investigation, we have measured the solubility of H2S as a function of partial pressure of acid gas in N,Ndimethylacetamide and N-methylacetamide over a wide temperature range (between 303.15 K and 363.15 K) and pressure from vapor pressure of solvent up to about 2.0 MPa. The experimental data were correlated by using the (1) Krichevsky−Ilinskaya equation and (2) a generic Redlich− Kwong (GRK) cubic EoS. Results in Figures 1 and 2 and ARD % and MRD % in Table 8 show that both models have comparable abilities in the prediction of gas pressure.
Corresponding Author
*E-mail:
[email protected],
[email protected]. Tel: 98 21-48252467. Notes
The authors declare no competing financial interest. H
LIST OF SYMBOLS NIST = National Institute of Standards and Technology NMA = N-methylacetamide DMA = N,N-dimethylacetamide KI = Krichevsky−Ilinskaya equation RK EoS = Redlich−Kwong equation of state GRK = generic Redlich-Kowang equation of state R = universal gas constant Vgc = volume of the gas container (or gas sample) Vg = gas-phase volume in the equilibrium cell Vauto = volume of the autoclave (equilibrium cell) Zi and Zf = compressibility factors of the initial and final state in the gas container Ta = ambient temperature P0 = initial pressure of solution PT = total absolute pressure PVP or Ps = vapor pressure of pure solvent PH2S = partial pressure of H2S at equilibrium state Peag = partial pressure of acid gas at equilibrium state ngag = amount of acid gas in the gas phase at equilibrium state nlag = amount of acid gas in the liquid phase at equilibrium state nag = total number of moles of acid gas injected to equilibrium cell Msolvent = molar mass of pure solvent δ ni = uncertainty of amount of species i mj = molality of component j, mol. kg−1 wsolvent = weight of solvent charged into cell in g ρag = density of acid gas in gas phase at equilibrium state ρNMA = density of pure liquid N-Methylacetamide (g/cm3) ρDMA = density of pure liquid N,N-Dimethylacetamide (g/ cm3) ρcharged solution = density of charged solution (g/cm3) xH2S = mole fraction of loaded gas xs = mole fraction of solvent (xH2S)Cor = corrected mole fraction of loaded gas using density of charged solution Tr = reduced temperature Tc = critical temperature Pc = critical pressure α(T) = temperature dependent parameter in RK equation of state b = RK covolume constant R2 = correlation coefficients ARD = average of relative deviations MRD = maximum relative deviation h(0) H,x = Henry’s law constant on mole fraction base h(0) H,m = Henry’s law constant on molality base f H2S(T,p) = fugacity of H2S in gas phase γx = activity coefficient of gas on the mole fraction scale vH∞2S = molar volume of dissolved gas at infinite dilution λk′, lij, lji, mij, τij = adjustable parameters in GRK EoS ∞ ΔsolGm,x = partial molar Gibbs free energy of solubility at reference state ∞ ΔsolHm,x = partial molar enthalpy of solubility at reference state DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
ΔsolS∞ m,x = partial molar entropy of solubility at reference state GH = Gibbs−Helmholtz ΔHabs(GH) = enthalpy of absorption calculated using Gibbs−Helmholtz equation A(A0,A1) = adjustable parameters in KI equation
■
[bmim][BF4], and [bmim][Tf2N]. J. Chem. Eng. Data 2009, 54, 1844−1849. (19) Hosseini-Jenab, M.; Abedinzadegan Abdi, M.; Najibi, S.−H.; Vahidi, M.; Matin, N.-S. Solubility of carbon dioxide in aqueous mixtures of N-methyldiethanolamine + piperazine + sulfolane. J. Chem. Eng. Data 2005, 50, 583−586. (20) Park, M. K.; Sandall, O. C. Solubility of carbon dioxide and nitrous oxide on 50 mass % methyldiethanolamine. J. Chem. Eng. Data 2001, 46, 166−168. (21) NIST Scientific and Technical Databases, Thermophysical Properties of Fluid Systems. http://webbook.nist.gov/chemistry/ fluid/ (accessed Sep. 2012). (22) Scharlin, P.; Steinby, K. Excess thermodynamic properties of binary mixtures of N,N-dimethylacetamide with water or water-d2 at temperatures from 277.13 to 318.15 K. J. Chem. Thermodyn. 2003, 35, 279−300. (23) Victor, P. J.; Hazra, D. K. Excess molar volumes, viscosity deviations, and isentropic compressibility changes in binary mixtures of N-methylacetamide + 2-methoxyethanol and N-methylacetamide + water at (308.15, 313.15, and 318.15) K. J. Chem. Eng. Data 2002, 47, 79−82. (24) Pacak, P. Refractivity and density of some organic solvents. Chem. Papers 1991, 45, 227−232. (25) Gopal, R.; Rizvi, S. A. Physical properties of some mono- and dialkyl-substituted amides at different temperatures. J. Ind. Chem. Soc. 1966, 43, 179−182. (26) Gopal, R.; Rizvi, S. A. Vapor pressures of some monoalkyl and dialkyl substituted aliphatic amides at different temperatures. J. Ind. Chem. Soc. 1968, 45, 13−16. (27) Manczinger, J.; Kortuem, G. Z. Thermodynamic mixing effects in the system water−N-methylacetamide. Phys. Chem. 1975, 95, 177− 186 (Muenchen, Germany). (28) Nasirzadeh, K.; Neueder, R.; Kunz, W. Vapor pressures of propylene carbonate and N,N-dimethylacetamide. J. Chem. Eng. Data 2005, 50, 26−28. (29) Ishiguro, S. Thermodynamic and structural aspects on solvation steric effect in nonaqueous solution. Bull. Chem. Soc. Jpn. 1997, 70, 1465−1477. (30) Shoemaker, D. P.; Garland, C. W.; Steinfeld, J. I.; Nibler, J. W. Experiments in Physical Chemistry, 4th ed.; McGraw-Hill: New York, 1981. (31) Wagner, W.; Overhoff, U. ThermoFluids, (version 1.0, build 1.0.0); Springer: Berlin, Heidelberg (Germany), 2006. (32) Lemmon, E. W.; Span, R. Short fundamental equations of state for 20 industrial fluids. J. Chem. Eng. Data 2006, 51, 785−850. (33) Jalili, A. H.; Shokouhi, M.; Maurer, G.; Hosseini-Jenab, M. Solubility of CO 2 and H 2 S in the ionic liquid 1-ethyl-3methylimidazolium tris (pentafluoroethyl) trifluorophosphate. J. Chem. Thermodyn. 2013, 67, 55−62. (34) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Liquids and Gases, 4th ed.; McGraw-Hill: New York, 1987. (35) Perry, R. H.; Green, D. W.; Maloney, J. O. the Properties of Gases & Liquids, 7th ed.; McGraw-Hill: New York, 1997. (36) Shiflett, M. B.; Yokozeki, A. Separation of CO2 and H2S using room-temperature ionic liquid [bmim][PF6]. Fluid Phase Equilib. 2010, 15, 105−113. (37) Yokozeki, A. Solubility of refrigerants in various lubricants. Int. J. Thermophys. 2001, 22, 1057−1071. (38) Krychevsky, I.; Ilinskaya, A. Partial molal volume of gases dissolved in liquids. Acta Physicochim. U.R.S.S. 1945, 20, 327−348. (39) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd ed.; PrenticeHall: Englewood Cliffs, NJ, 1986; p 377. (40) Bender, E.; Klein, U.; Schmitt, W. P.; Prausnitz, J. M. Thermodynamics of gas solubility: Relation between equation-ofstate and activity-coefficient models. Fluid Phase Equilib. 1984, 15, 241−255.
REFERENCES
(1) Roberts, B. E.; Mather, A. E. Solubility of H2S and CO2 in sulfolane. Can. J. Chem. Eng. 1988, 67, 519−520. (2) Jou, F. Y.; Deshmukh, R. D.; Otto, F. D.; Mather, A. E. Solubility of H2S, CO2, CH4, and C2H6 in sulfolane at elevated pressures. Fluid Phase Equilib. 1991, 56, 313−324. (3) Murrieta-Guevara, F.; Romero-Martinez, A.; Trejo, A. Solubilities of carbon dioxide and hydrogen sulfide in propylene carbonate, Nmethylpyrrolidone, and sulfolane. Fluid Phase Equilib. 1988, 44, 105− 115. (4) Mundhwa, M.; Elmahmudi, S.; Maham, Y.; Henni, A. Molar heat capacity of aqueous sulfolane, 4-formylmorpholine, 1-methyl-2pyrrolidinone, and triethylene glycol dimethyl ether solutions from (303.15 to 353.15) K. J. Chem. Eng. Data 2009, 54, 2895−2901. (5) Zong, L.; Chen, C.−C. Thermodynamic modeling of CO2 and H2S solubilities in aqueous DIPA solution, aqueous sulfolane−DIPA solution, and aqueous sulfolane−MDEA solution with electrolyte NRTL model. Fluid Phase Equilib. 2011, 306, 190−203. (6) Zuniga-Moreno, A.; Luis, A.; Luna, G. Compressed liquid densities and excess volumes for the binary system CO2 + N,Ndimethylformamide (DMF) from (313 to 363) K and pressures up to 25 MPa. J. Chem. Eng. Data 2005, 50, 1224−1233. (7) Melzer, W. M.; Schroedter, F.; Knapp, H. Solubilities of methane, propane and carbon dioxide in solvent mixtures consisting of water, N,N-dimethylformamide, and N-methyl-2-pyrrolidone. Fluid Phase Equilib. 1989, 49, 167−186. (8) Duran-Valencia, C.; Galicia-Luna, L. A.; Richon, D. Isothermal vapor−liquid equilibria of the carbon dioxide (CO2)−N,N-dimethylformamide (DMF) system at temperatures from 293.95 to 338.05 K and pressures up to 12 MPa. J. Chem. Eng. Data 2001, 46, 1589−1592. (9) Chang, C. J.; Chen, C.−Y.; Lin, H.−C. Solubility of carbon dioxide and nitrous oxide in cyclohexanone, toluene and N,Ndimethylformamide at elevated pressures. J. Chem. Eng. Data 1995, 40, 850−855. (10) Jö decke, M.; Perez-Salado Kamps, A.; Maurer, G. An experimental investigation of the solubility of CO2 in (N,Ndimethylmethanamide + water). J. Chem. Eng. Data 2012, 57, 1249−1266. (11) Jö decke, M.; Perez-Salado Kamps, A.; Maurer, G. An experimental investigation on the influence of NaCl on the solubility of CO2 in (N,N-dimethylmethanamide + water). Fluid Phase Equilib. 2012, 334, 106−116. (12) Byun, H.−S.; Kim, N.−H.; Kwak, C. Measurements and modeling of high-pressure phase behavior of binary CO2−amides systems. Fluid Phase Equilib. 2003, 208, 53−68. (13) Shokouhi, M.; Farahani, H.; Hosseini-Jenab, M. Experimental solubility of hydrogen sulfide and carbon dioxide in dimethylformamide and dimethylsulfoxide. Fluid Phase Equilib. 2014, 367, 29−37. (14) Hayduk, W.; Pahlevanzadeh, H. The solubility of sulfur dioxide and hydrogen sulfide in associating solvents. Can. J. Chem. Eng. 1987, 65, 299−307. (15) Shiflett, M. B.; Yokozeki, A. Solubility of CO2 in room temperature ionic liquid [hmim][Tf2N]. J. Phys. Chem. B 2007, 111, 2070−2074. (16) Shiflett, M. B.; Yokozeki, A. Solubilities and diffusivities of carbon dioxide in ionic liquids: [bmim][PF6] and [bmim][BF4]. Ind. Eng. Chem. Res. 2005, 44, 4453−4464. (17) Yokozeki, A.; Shiflett, M. B.; Junk, C. P.; Grieco, L. M.; Foo, T. Physical and chemical absorptions of carbon dioxide in roomtemperature ionic liquids. J. Phys. Chem. B 2008, 112, 16654−16663. (18) Jalili, A. H.; Rahmati-Rostami, M.; Ghotbi, C.; Hosseini-Jenab, M.; Ahmadi, A. N. Solubility of H2S in ionic liquids [bmim][PF6], I
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
Journal of Chemical & Engineering Data
Article
(41) Deshmukh, R. D.; Mather, A. E. On the thermodynamics of gas solubility: Relation between equation-of-state and activity coefficient models. Fluid Phase Equilib. 1987, 35, 313−314.
J
DOI: 10.1021/je500478t J. Chem. Eng. Data XXXX, XXX, XXX−XXX
