Solubilities of N-phenylacetamide, 2-methyl-N-phenylacetamide and
4-methyl-N-phenylacetamide in supercritical carbon dioxide
Shi-Yue Huang, Muoi Tang, Sheau Ling Ho, Yan-Ping Chen
∗Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan, ROC Received 31 January 2006; received in revised form 6 April 2007; accepted 6 April 2007
Abstract
The solubilities of N-phenylacetamide, 2-methyl-N-phenylacetamide and 4-methyl-N-phenylacetamide in supercritical carbon dioxide were measured using a semi-flow apparatus. The experimental data were taken at 308.2, 318.2 and 328.2 K, and over the pressure range from 10 to 22 MPa. A plug flow fluid–solid mass transfer model was applied under the experimental conditions, and it showed that the corresponding solid solubility data were measured in the steady state region with low mass transfer effects. The experimental solid solubility data were then correlated using the Peng–Robinson and the Soave–Redlich–Kwong equations of state with van der Waals mixing rules. These data were also correlated with the semi-empirical equation presented by Chrastil, or that presented by Mendez-Santiago and Teja. The solid solubility data calculated from all the correlation models with optimally fitted parameters yielded absolute average deviation of 6%.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Solid solubility; Supercritical CO2; Experimental data
1. Introduction
Supercritical fluid technology is becoming increasingly important in diversified fields of extraction, reaction, particle
formation and materials processing[1,2]. Solid solubility data
in supercritical fluids are among the most important thermo-physical properties that are essential to the efficient design of supercritical processes. Solid solubility data in supercritical
CO2 have been reviewed by several authors[3–6], who have
concluded that more experimental data and proper correlation models for specialty chemicals are still needed.
We have measured the solid solubility of various aromatic
compounds in supercritical CO2 [7]. In this study, we used
the similar semi-flow apparatus to measure the equilibrium solubility of N-phenylacetamide, 2-methyl-N-phenylacetamide
and 4-methyl-N-phenylacetamide in supercritical CO2at
tem-peratures of 308.2, 318.2 and 328.2 K over the pressure range 10–22 MPa. 2-Methyl-N-phenylacetamide and 4-methyl-N-phenylacetamide are isomers which were used as dyestuff. N-Phenylacetamide was used in organic synthesis and the phar-maceutical industry. All three selected polar compounds consist
∗Corresponding author. Tel.: +886 2 2366 1661; fax: +886 2 2362 3040. E-mail address:[email protected](Y.-P. Chen).
of the NHCOCH3 functional group. As far as we know, no
solid solubility data regarding these compounds have yet been reported in literature. In this study, we therefore report novel data for further applications and modeling. A fluid–solid mass
transfer model investigated by Abaroudi et al.[8]was applied
under our experimental conditions. It was used to examine whether the measured solid concentration in the fluid at the exit of the experimental cell approached the equilibrium sol-ubility. The measured solid solubility data were then correlated
using the Soave–Redlich–Kwong [9] and the Peng–Robinson
[10]equations of state (EOS) with van der Waals (VDW2)
mix-ing rules that included two adjustable parameters. Correlation results from the EOS models were then compared with those
from the semi-empirical equations presented by Chrastil[11],
or Mendez-Santiago and Teja[6].
2. Experimental
2.1. Chemicals
Carbon dioxide was supplied by San-Fu Chemical Co. (Taiwan) with a minimum purity of 99.8%. 2-Methyl-N-phenylacetamide and 4-methyl-2-Methyl-N-phenylacetamide were purchased from Merck Co. N-Phenylacetamide was purchased
0896-8446/$ – see front matter © 2007 Elsevier B.V. All rights reserved.
Table 1
Physical properties of the pure compounds used in this study
Compound Mw (×10−3kg/mol) Tm(K) Vs(×10−3m3/mol) Tc(K) Pc(MPa) ω
Carbon dioxide 44.01 304.19[15] 7.382[15] 0.228[15]
N-Phenylacetamide (C8H9NO) 135.17 387.5[14] 0.1109[14] 735.85[12] 4.011[12] 0.577[13]
2-Methyl-N-phenylacetamide (C9H11NO) 149.19 383.2[14] 0.1277[14] 761.01[12] 3.501[12] 0.625[13]
4-Methyl-N-phenylacetamide (C9H11NO) 149.19 421.7[14] 0.1231[14] 761.01[12] 3.501[12] 0.625[13]
Fig. 1. Structures of three organic compounds in this study.
from Acros Co. All three pure compounds had a minimum purity of 99%, and were used without further purification. The prop-erties of the pure compounds used in this study are tabulated inTable 1. However, the critical constants and acentric factors for pure solid compounds were not available in literature. The critical temperature and pressure were estimated using the
cor-relation equation of Joback[12], and the acentric factors were
estimated from by Ambrose method[13]. The structures of these
pure compounds used for experiments are illustrated inFig. 1.
2.2. Experimental apparatus and procedures
A semi-flow type apparatus used in this study for measuring
the solid solubility in supercritical CO2is shown inFig. 2. The
experimental system consisted of three sections: (1) the
sup-ply of supercritical CO2, (2) the equilibrium between solid and
supercritical phases and (3) the analysis of experimental results. The experimental procedures were similar to those described
in our previous study[7]. Pure CO2was liquefied to 272.2 K and
then was compressed to the desired pressure by a HPLC pump (Thermo Separation Product). The pressure was controlled by a
back pressure regulator. The high pressure CO2passed through
a pre-heating coil that was immersed in a water bath. It was then charged into the pre-equilibrium and equilibrium cells. The
pre-equilibrium cell had a volume of 150 cm3 and 25 g solid
sample was then distributed into five layers packed with glass
beads. The main equilibrium cell had a volume of 300 cm3and
50 g solid sample was distributed into10 layers packed also with glass beads. The equilibrium cells were equipped with filters to prevent any physical entrainment. The temperature and pressure were measured using a calibrated quartz thermocouple and a cal-ibrated Heise gauge, respectively. The temperature and pressure
measurements displayed accuracy of±0.1 K and ±0.03 MPa,
respectively in this study.
After flowing through the equilibrium cell, the supercritical
CO2 was expanded to atmospheric pressure through a needle
valve wrapped with heating tape. The heating tape was kept in the temperature range of 20–30 K above the melting point of the solid solute in order to avoid any precipitation in the line. After the expansion, solid was separated from the gas phase and then
was dissolved in a flask with organic solvent. The volume of CO2
Fig. 2. Schematic diagram of the experimental apparatus: 1, CO2cylinder; 2, cooler; 3, HPLC pump; 4, pre-heater; 5, pre-equilibrium cell; 6, filter; 7, equilibrium cell; 8, pressure transducer; 9, thermometer; 10, heating tape; 11, ice bath; 12, saturator; 13, wet test meter; 14, solvent delivery pump; 15, solvent reservoir.
flow was measured by a wet test meter (Ritter TG1). A UV–vis spectrometer (Jasco UV-975) was used to analyze the composi-tions of the organic solution in the flask. The organic solution in the collection flask was sonicated for 10 min to ensure complete dissolution before it was analyzed using the UV–vis spectrom-eter. In this study, ethyl acetate was chosen as the solvent. A sharp absorption peak in the UV–vis spectrometer for both 2-methyl-N-phenylacetamide and 4-methyl-N-phenylacetamide was observed at the band of 263 nm. The optimal absorption band for N-phenylacetamide was also observed at 261 nm. Cali-brations for the UV analyses were made before the experiments using standard solutions of known concentrations. The
experi-mental data were taken after CO2flowed through the equilibrium
cell for 30 min. In each experiment, at least three measurements were taken at a given temperature and pressure. The repro-ducibility of the solid solubility measurements was observed at ±5%, and the accuracy of the solid solubility data was estimated
as±0.002 mol fraction.
3. Results and discussion
A fluid–solid mass transfer model presented by Abaroudi et
al.[8]was solved in this study under our experimental
condi-tions. The purpose of solving this model was to ensure that the mass transfer effects were insignificant to our measurements. In
this model, the supercritical CO2was assumed to pass through
the packed equilibrium cell in a one-dimensional plug flow. A mass balance over a differential bed length (z) in the cell was
written as ε∂C
∂t +u
∂C
∂z =kgas(Csat− C) (1)
where C is the solid concentration in the fluid phase, ε the poros-ity of the equilibrium cell, asthe mass transfer area, kgthe solid to
fluid mass transfer coefficient and u is the interstitial fluid veloc-ity in the equilibrium cell. The initial and boundary conditions were:
t = 0, C = 0 for any z > 0 (2)
z = 0, C = 0 for any t > 0 (3)
The Laplace transform method was applied to solve Eq.(1)
and the following dimensionless groups were introduced:
X = CC
sat
, τ = Lεu , θ = τt, ξ = Lz, St=kgausL (4) where X is the ratio of the solid solute concentration in super-critical fluid phase (C) to its saturated solubility (Csat) and L is
the length of the equilibrium cell. It was solved as a function of the dimensionless mean residence time θ, the dimensionless bed
distance ξ and the modified Stanton’s number St. The solution
for Eq.(1)yielded:
X = [1 − exp(−ξ St)][1− exp(−θ St)] for θ > St (5)
X = 1 − exp(−Stθ) for St> θ > 0 (6)
Table 2
Properties and approach to equilibrium for CO2(1) + N-phenylacetamide (2) at various operation conditions T (K) P (MPa) ρCO2(kg/m3) μCO
2(×10 5Pa s) D12(×108m2/s) Sc Re St Minimum value of X (=C/Csat) 308.2 10.44 671.80 6.25 1.83 5.09 2.70–8.11 136.9–405.6 1.00 12.16 728.35 7.09 1.58 6.17 2.38–7.15 125.3–371.0 1.00 13.89 769.00 7.80 1.41 7.17 2.17–6.50 116.5–345.0 1.00 15.61 800.96 8.44 1.30 8.13 2.00–6.00 109.5–324.1 0.99 17.33 827.64 9.06 1.20 9.09 1.87–5.60 103.5–306.2 0.99 19.06 850.76 9.66 1.13 10.07 1.75–5.25 98.2–290.4 0.99 20.78 871.02 10.26 1.06 11.07 1.65–4.94 93.5–276.5 0.99 22.50 889.18 10.85 1.01 12.10 2.56–4.67 89.2–263.9 0.99 318.2 10.44 502.73 4.36 2.95 2.94 3.88–11.64 171.4–508.2 1.00 12.30 615.88 5.58 2.19 4.15 3.03–9.08 151.1–447.7 1.00 13.88 672.43 6.31 1.89 4.97 2.68–8.04 139.8–414.2 1.00 15.61 717.69 6.97 1.67 5.80 2.43–7.28 130.3–386.1 1.00 17.33 753.14 7.55 1.52 6.58 2.24–6.71 122.7–363.3 1.00 19.05 782.59 8.11 1.41 7.36 2.08–6.25 116.1–343.8 1.00 20.78 808.00 8.64 1.31 8.15 1.96–5.87 110.3–326.6 0.99 22.50 830.18 9.17 1.23 8.95 1.84–5.53 105.2–311.4 0.99 328.2 10.44 356.70 3.14 4.64 1.89 5.39–16.16 194.4–576.2 1.00 12.30 487.46 4.26 3.17 2.75 3.97–11.92 177.5–526.1 1.00 14.02 572.26 5.13 2.53 3.55 3.30–9.89 162.6–482.1 1.00 15.75 632.00 5.83 2.16 4.27 2.90–8.70 151.1–447.7 1.00 17.47 677.17 6.42 1.92 4.93 2.63–7.90 141.8–420.2 1.00 19.19 713.65 6.95 1.75 5.58 2.43–7.30 134.0–397.1 1.00 20.92 744.46 7.45 1.61 6.22 2.27–6.81 127.3–377.0 1.00 22.50 768.89 7.89 1.51 6.81 2.14–6.43 121.8–360.6 1.00
The detail procedures for the determination of the modified Stanton’s number, and the calculation of parameters in the mass
transfer model have been presented in our previous study[7].
The flow rates of CO2, converted to the values at the STP
condi-tion, ranged from 5 to 15 L/h in this study. The measured solid solubility at a given temperature and pressure should not vary
with the CO2flow rates, according to the phase rule. We applied
this criterion to examine if the correct experimental data were obtained. Following a similar approach and employing the same experimental conditions, the minimum values of X were also evaluated at various temperatures and pressures for each solid
compound. Table 2 demonstrates an example for the
1calcu-lated minimum relative saturation values in the solid solubility measurements of N-phenylacetamide.
Since the X values shown inTable 2were very close to unity, it
is verified that the mass transfer has negligible effect on all
mea-sured solid solubility data in supercritical CO2. Similar results
have been observed for the other two solids in this study.
The measured solid solubilities in supercritical CO2
for N-phenylacetamide, 2-methyl-N-phenylacetamide and
4-methyl-N-phenylacetamide are presented in Tables 3–5,
respectively. The densities of pure CO2shown in these tables
were calculated using the Peng–Robinson EOS. The solubil-ities for three compounds increased with pressure at each isotherm. At the same temperature and pressure, the solid solubilities increased in an order of N-phenylacetamide > 4-methyl-phenylacetamide > 2-4-methyl-phenylacetamide. N-phenylacetamide had the lowest molecular weight and it showed
the largest solubility in supercritical CO2. Although we know
4-methyl-N-phenylacetamide and 2-methyl-N-phenylacetamide are isomers, it is still difficult to discuss the specific interactions
Table 3
Solubilities of N-phenylacetamide (2) in supercritical carbon dioxide (1) T (K) P (MPa) y2(×104) ρ1(kg/m3) 308.2 10.44 0.508 671.80 12.16 0.794 728.35 13.89 1.109 769.00 15.61 1.246 800.96 17.33 1.497 827.64 19.06 1.695 850.76 20.78 1.756 871.02 22.50 2.025 889.18 318.2 10.44 0.410 502.73 12.30 0.810 615.88 13.88 1.224 672.43 15.61 1.741 717.69 17.33 2.386 753.14 19.05 2.783 782.59 20.78 3.124 808.00 22.50 3.245 830.18 328.2 10.44 0.293 356.70 12.30 0.782 487.46 14.02 1.356 572.26 15.75 2.376 632.00 17.47 2.817 677.17 19.19 3.487 713.65 20.92 4.225 744.46 22.50 4.562 768.89 Table 4
Solubilities of 2-methyl-N-phenylacetamide (3) in supercritical carbon dioxide (1) T (K) P (MPa) y3(×104) ρ1(kg/m3) 308.2 12.16 0.358 728.35 13.89 0.492 769.00 15.61 0.708 800.96 17.33 0.861 827.64 19.06 1.163 850.76 20.78 1.354 871.02 22.50 1.676 889.18 318.2 12.30 0.301 615.88 13.88 0.525 672.43 15.61 0.931 717.69 17.33 1.455 753.14 19.05 1.997 782.59 20.78 2.278 808.00 22.50 2.762 830.18 328.2 12.30 0.197 487.46 14.02 0.548 572.26 15.75 1.042 632.00 17.47 2.022 677.17 19.19 2.912 713.65 20.92 3.815 744.46 22.50 4.633 768.89
for these solid compounds with supercritical CO2since no dipole
moments of these solids were available in literature. 4-Methyl-N-phenylacetamide had smaller solid molar volume than that of 2-methyl-N-phenylacetamide. The former solid was expected
to have higher solubility upon extraction by CO2, as the solid
was surrounded by clusters of CO2molecules. The
experimen-tal solid solubility data were then correlated using either the equation of state or the semi-empirical equations.
Table 5
Solubilities of 4-methyl-N-phenylacetamide (4) in supercritical carbon dioxide (1) T (K) P (MPa) y4(×104) ρ1(kg/m3) 308.2 12.16 0.527 728.46 13.88 0.836 768.93 15.61 1.022 800.97 17.33 1.078 827.69 19.06 1.221 850.72 20.78 1.389 871.02 22.50 1.664 889.21 318.2 12.16 0.480 609.89 13.88 0.892 672.64 15.61 1.344 717.69 17.33 1.482 753.20 19.06 1.997 782.69 20.78 2.236 808.00 22.50 2.452 830.22 328.2 12.16 0.384 479.18 13.89 0.966 566.80 15.61 1.222 627.82 17.33 2.034 673.95 19.06 2.947 711.06 20.78 3.601 742.14 22.50 4.802 768.93
Table 6
Correlated results of solid solubility data in supercritical carbon dioxide using various EOS and VDW2 mixing rules
Peng–Robinson EOS Soave–Redlich–Kwong EOS
k1j l1j AADyj(%) k1j l1j AADyj(%)
CO2(1) + N-phenylacetamide (2), ln P2sat (Pa)= 42.06 − 14036.33/T (K)
0.036 0.001 6.54 0.045 0.018 7.03
CO2(1) + 2-methyl-N-phenylacetamide (3), ln Psat
3 (Pa)= 54.89 − 19570.25/T (K)
−0.064 0.111 4.32 −0.060 0.120 4.71
CO2(1) + 4-methyl-N-phenylacetamide (4), ln P4sat (Pa)= 46.15 − 15826.82/T (K)
0.088 0.126 6.21 0.088 0.118 6.40 AADyj (%)=100n n k=1 |yexp j,k−ycalj,k| yexp
j,k , the summation was over all kth experimental points for solid j.
3.1. Equation of state method
At the phase equilibrium condition, the solid (component j)
solubility in supercritical CO2(component 1) was calculated by
yj = Psat j exp((Vjs(P − Pjsat))/RT ) ϕSCF j P (7)
where Vjsis the solid molar volume, Pjsatthe solid vapor pressure
and ϕSCFj is the fugacity coefficient of the solute in the
super-critical phase. In this study, the vapor pressure of solute was expressed by the following empirical equation:
ln Pjsat= A −B
T (8)
where A and B were two adjustable parameters that were opti-mally fitted into the solid solubility data. Two EOS with mixing rules were employed in this study to calculate the fugacity coef-ficient in the supercritical phases: the Soave–Redlich–Kwong
EOS[9]:
P = RT
v − b −
a
v(v + b) (9)
and the Peng–Robinson EOS[10]:
P =v − bRT −v(v + b) + b(v − b)a (10)
The EOS parameters were evaluated from the critical con-stants of pure compounds.
The van der Waals mixing rules with two parameters were used to calculate the EOS parameters for fluid mixtures:
am= yiyj(aiaj)0.5(1− kij) (11) bm= yiyj(bi+ bj) 2 (1− lij) (12)
where kijand lijwere two adjustable binary interaction
param-eters, considered as temperature-independent in this study. The binary interaction parameters and the parameters in the solid vapor pressure equations were optimally fitted into the exper-imental solubility data by minimizing the following objective function: obj= |y exp j − ycalj | yexp j (13) The correlation results using the EOS method are shown in
Table 6. With the optimally fitted parameters (A, B, k1j and
l1j), satisfactory accuracy for the calculated solid solubility was
observed by the EOS method with an absolute average deviation around 6%.
3.2. Semi-empirical equation method
Two empirical equations presented by Chrastil[11]and by
Mendez-Santiago and Teja [6] were commonly employed to
correlate the solid solubility in supercritical CO2. The Chrastil
model was based on the hypothesis of molecular association. It expressed a linear relationship between the logarithm of the
Table 7
Correlated results of the solubility data in supercritical carbon dioxide using the Chrastil equation and the Mendez-Santiago and Teja equation
System Chrastil equation Mendez-Santiago and Teja equation
n C D AADyj(%) E (×104) F G AADyj(%) CO2(1) + N-phenylacetamide (2) 5.08 −7.44 × 103 −10.97 6.82 −1.22 2.85 26.07 4.82 CO2(1) + 2-methyl-N-phenylacetamide (3) 8.38 −1.13 × 104 −21.16 5.56 −1.69 4.30 36.83 7.33 CO2(1) + 4-methyl-N-phenylacetamide (4) 6.29 −9.07 × 103 −14.08 6.69 −1.39 3.38 29.82 6.42 AADyj (%)=100n n k=1 |yexp j,k−ycalj,k| yexp j,k
Fig. 3. Solubility for N-phenylacetamide (2) in supercritical carbon dioxide (1): () 308.2 K; (䊉) 318.2 K; () 328.2 K; (—) Mendez-Santiago and Teja method.
solid solubility and the logarithm of the density of the pure CO2
(component 1): ln Sj (kg/m3)= n ln ρ1 (kg/m3)+ C T +D (14) Sj= Mρ1Mjyj 1(1− yj) (15) where T is the temperature, n the association number and M is the molecular weight. The optimal values of n, and the other two parameters C and D were optimally fitted into the experi-mental data in this study. Mendez-Santiago and Teja proposed
Fig. 4. Solubility for 2-methyl-N-phenylacetamide (3) in supercritical carbon dioxide (1): () 308.2 K; (䊉) 318.2 K; () 328.2 K; (—) correlation results from the Mendez-Santiago and Teja equation.
Fig. 5. Solubility for 4-methyl-N-phenylacetamide (4) in supercritical carbon dioxide (1): () 308.2 K; (䊉) 318.2 K; () 328.2 K; (—) correlation results from the Mendez-Santiago and Teja equation.
an equation that also had three adjustable parameters:
T ln(yjP (MPa)) = E + Fρ1 (kg/m3)+ GT (16)
The empirical parameters (E, F and G) in Eq.(16)were also
optimally fitted using the measured solid solubility data. The cor-relation results using the above two semi-empirical equations are
shown inTable 7. Both equations yielded the absolute average
deviation in solid solubility around 6%. Graphical presentations of the solid solubility data for various solid solutes are shown inFigs. 3–5, respectively. The cross-over pressures of the
cor-Fig. 6. Solubility of various compounds in supercritical CO2 at 308.2 K: () N-phenylacetamide; (䊉) 2-methyl-N-phenylacetamide; () 4-methyl-N-phenylacetamide; (—) correlation results from the Mendez-Santiago and Teja equation.
responding solids were between 12 and 14 MPa. The correlated results using the Mendez-Santiago and Teja equation with its optimally fitted parameters are also demonstrated in these fig-ures. It is observed that the correlation results were satisfactory.
Fig. 6shows a typical plot of the comparison of the solid solu-bilities at 308.2 K and various pressures. The correlation results were again found satisfactory for all solid solutes.
4. Conclusion
In this study, new solid solubility data of N-phenylacetamide, 2-methyl-N-phenylacetamide and 4-methyl-N-phenylacetamide in supercritical carbon oxide are presented at 308.2, 318.2 and 328.2 K over the pressure range from 10 to 22 MPa. Subse-quently, it was demonstrated that the mass transfer effects were negligible at the experimental conditions. Besides, in order to correlate the solubility data, the Peng–Robinson and the Soave–Redlich–Kwong EOS with VDW2 mixing rules, the Chrastil and the Mendez-Santiago–Teja semi-empirical equa-tions were used. We further verified that all methods yielded satisfactory correlation results for solid solubility with absolute average deviation around 6%.
Acknowledgement
The authors are grateful to the support for this research from the National Science Council, Taiwan, ROC.
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