Solubility of HFCs in lower alcohols

Fluid Phase Equilibria 303 (2011) 115–119

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Solubility of HFCs in lower alcohols J.M.M.V. Sousa b , J.P.B. Almeida a , A.G.M. Ferreira a , H.C. Fachada c , I.M.A. Fonseca a,∗ a

Departamento de Engenharia Química, Universidade de Coimbra, Pólo II, Rua Sílvio Lima, 3030-790 Coimbra, Portugal Departamento de Engenharia Química e Biológica, Instituto Politécnico de Coimbra, 3030-199 Coimbra, Portugal c Departamento de Engenharia Electrotécnica, Instituto Politécnico de Coimbra, 3030-199 Coimbra, Portugal b

a r t i c l e

i n f o

Article history: Received 24 August 2010 Received in revised form 23 December 2010 Accepted 7 January 2011 Available online 15 January 2011 Keywords: G/L solubility HFCs Alcohols Acceptor number Reduced dipole moment

a b s t r a c t This work is inserted in a research program that consists mainly in the experimental and theoretical study of the effect of association between solute and solvent molecules in the solubility of gases in liquids. The solubilities of hydrofluorocarbons, HFCs, (CH3 F, CH2 F2 , CHF3 ) in lower alcohols (methanol, ethanol, 1-propanol, 1-butanol) have been determined in the temperature range [284, 313] K, at atmospheric pressure. An automated apparatus based on Ben-Naim–Baer and Tominaga et al. designs was used, which provides an accuracy of 0.6%. A precision of the same order of magnitude was achieved. To represent the temperature dependence of the mole fraction solubilities, the equation R ln x2 = A + B/T + C ln T was used. From this equation, the experimental Gibbs energies, enthalpies and entropies of solution at 298 K and 1 atm partial pressure of the gas, were calculated. A semiempirical correlation has been developed between the solubilities of HFCs in alcohols at 298 K and the Gutmann acceptor number of solvents, AN, and reduced dipole moment of the gases, *. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The available literature studies that aim to quantify, at least in a semiquantitative way, the effect of chemical forces on gas solubility are very scarce [1]. In particular, for hydrofluorocarbons (HFCs) the available solubility data in organic associated solvents is almost non-existent which enables these kinds of studies. Recently we have determined the solubilities of tetrafluoromethane in lower alcohols and a semiempirical correlation between the solubility of CF4 in the alcohols at 298 K and the Gutmann acceptor number of the solvents has been developed [2]. In the present work we have determined the solubility of CHF3 , CH2 F2 and CH3 F in primary alcohols (methanol, ethanol, 1propanol and 1-butanol) as a function of temperature, using an automated apparatus based on Ben-Naim–Baer and Tominaga et al. designs with an accuracy of 0.6% in the experimental method, checked by measuring the solubility of carbon dioxide and nitrous oxide in water in the range 290–303 K [3]. The solubility of these gases in alcohols is much lower than in other organic solvents, because alcohols are highly associated liquids. Actually, the dissolution process of the gas in the solvent is accomplished with a complex formation between the HFC and the alcohol molecules by means of hydrogen-bonding C–H· · ·O. The presence of the strongly electron-attracting halo-

∗ Corresponding author. Tel.: +351 239 798 728; fax: +351 239 798 703. E-mail address: [email protected] (I.M.A. Fonseca). 0378-3812/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2011.01.003

gen atom(s) on the carbon of the solute molecules loosens the hydrogen(s) and makes it available for coordination to the donor atom of the solvent molecule [4]. This scenario was confirmed by ab initio calculations of intermolecular interactions between fluoromethanes and fluoroethers, which show that fluorine atoms of fluoromethanes withdraw electrons and polarize the C–H bond, therefore increasing the C–H· · ·O interaction. The results of these ab initio calculations provided the undoubtable conclusion that the interaction Fn H3−n C–H· · ·O (n = 1, 2, 3) is substantially enhanced with the increase in fluorinated ratio of methane [5]. Another theoretical study by ab initio calculations of C–H· · ·O hydrogen bonds in H2 O–CH3 F, H2 O–CH2 F2 and H2 O–CHF3 shows that the inclusion of additional fluorine atoms on the carbon results in a shortening of the optimal interaction distance and an increase of strength of the hydrogen bond [6]. Zellhoefer et al. [4] have stated that the series of solutes, CH3 X, CH2 X2 , CHX3 and CX4 where X is a halogen atom, show that the solubilities in solvents containing donor atoms (oxygen or nitrogen) increase to a maximum with CHX3 and drop markedly on passing to the CX4 type. The knowledge of the solubilities of gases in liquids, allows the development of the gas/liquid solubility correlations. Abraham et al. [7] used five factors (excess molar refraction, the dipolarity/polarizability, the effective hydrogen-bond acidity and basicity and the McGowan characteristic volume) to fit the solubilities of 408 gaseous compounds in water at 298 K. Hildbrand and Scott obtained correlations for nonpolar gases solubility in nonpolar solvents at 298 K and 1 atm partial pressure, which shows that these

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Nomenclature List of symbols A parameter in Eq. (5) AN Gutmann acceptor number B parameter in Eq. [5] Bmix second virial coefficient of the binary mixture C parameter in Eq. [5] Henry coefficient H2,1 M1 molar mass of solvent molar mass of solute M2 ms mass of solution amount of solvent (mol) n1 n2 amount of dissolved gas (mol) P pressure vapour pressure of the pure solvent P1∗ R gas constant (J mol−1 K−1 ) T temperature (K) x2 mole fraction solubility of solute mole fraction of solute in vapour phase y2

Table 1 Purities and origin of the compounds used in this work. Compound

Formula

Origin

Purity (%)

Methanol Ethanol 1-Propanol 1-Butanol Fluoromethane Difluoromethane Trifluoromethane

CH3 OH C2 H5 OH C3 H7 OH C4 H9 OH CH3 F CH2 F2 CHF3

Riedel and Häen Carlo Erba Lab Scan-Anallytical Sciences Panreac Linde Gas UK Limited Linde Gas UK Limited Praxair

99.9 99.8 99.5 99.5 99.0 99.0 99.0

is to bring an accurately known volume of solvent into contact with a known volume of gas at a given temperature and pressure. After the equilibrium has been attained the change in the gas volume yields the amount of gas dissolved in the liquid and hence the solubility. An accuracy better than 0.6% was achieved [3]. The origin and purities of the compounds used in this work are summarized in Table 1 with all purities specified as minimum purities, in mol%. 3. Calculations

Greek letters G20 molar Gibbs energy of solution (J mol−1 ) 0 H2 molar enthalpy of solution (J mol−1 ) S20 molar entropy of solution (J mol−1 ) V variation of volume of the gas in the burette fugacity coefficient of pure solvent in saturation ϕ1∗ conditions ϕ1G fugacity coefficient of solvent in the vapour phase ϕ2G fugacity coefficient of the solute in the vapour phase  dipole moment (Debye) * reduced dipole moment  collision diameter of the Lennard-Jones potential (Å) ε/k well-depth of the Lennard-Jones potential (K) k Boltzmann constant (J K−1 )

The quantities obtained directly from experiment are: the displaced volume in gas burette due to the gas dissolution, V, the mass of solution, ms , and the equilibrium pressure and temperature, P and T, respectively. The mole fraction solubility of the solute, x2 , is obtained from Eq. (1), x2 =

(1)

where n1 and n2 represent the amounts of solvent and solute (in mol), in the liquid phase, respectively. n1 is directly obtained from, n1 = (ms − n2 M2 )/M1 , where M1 and M2 are the molar masses of the solvent and solute, respectively. And n2 is obtained from Eq. (2), n2 =

solubilities can be correlated in terms of two parameters: the solubility parameter of the solvent and the Lennard-Jones energy parameter for the solute [8]. Demyanovich and Lynn [9] present an empirical correlation at 298 K of a macroscopic thermodynamic property (infinite dilution activity coefficients for sulphur dioxide in organic solvents) with a specify solvent molecular characteristic (the Gutmann donor number, a basicity scale). In this work a semiquantitative correlation between the solubility of the HFCs in the alcohols studied has been developed at 298 K. Two parameters have been used in this correlation: the acceptor number, AN, which is a measure of the association of the alcohol [10] and the reduced dipole moment, * used as dimensionless ratio of the effective polarity of a molecule [11], which is related with the dipole moment and the parameters of the Lennard-Jones potential of the gas molecules [12]. This study is also important from the practical point of view. Indeed the HFCs are considered good alternatives to replace the chlorofluorocarbons (CFCs), which have been widely used as solvents, refrigerants, foaming agents and propellants. The substitution of the chloride atom by fluorine originates “green refrigerants”, with low ozone depletion potential, less inflammables and with low toxicity [13].

n2 n1 + n2

y2 PV RT + Bmix P

where Bmix is the second virial coefficient of the binary mixture. Since we need to know y2 to obtain n2 , this calculation requires an iterative procedure. The calculation begins with estimates of vapour and liquid phases compositions obtained from Raoult and Dalton laws. In the iterative procedure, the compositions are improved using the expressions of x2 , n2 and also the following expression, y2 = 1 −

(1 − x2 )(P1∗ ϕ1∗ ) Pϕ1G

(3)

where ϕ1G is the fugacity coefficient of solvent in the vapour phase, ϕ1∗ represents the fugacity coefficient of pure solvent in saturation conditions, P1∗ represents the vapour pressure of component 1. The calculation ends when convergence is obtained between two consecutive x2 values. The determination of Henry’s constant, H2,1 (T,P) is then straightforward, H2,1 (T, P) =

ϕ2G y2 P x2

(4)

being ϕ2G , the fugacity coefficient of the solute in the vapour phase. The dependence of solubility of the gases on temperature has been represented by the equation:

2. Experimental R ln x2 = A + The solubility apparatus and procedure employed in this work have been described in detail in Ref. [3]. The principle of the method

(2)

B + C ln T T

(5)

with the parameters fitted to the data by a least-squares method.

J.M.M.V. Sousa et al. / Fluid Phase Equilibria 303 (2011) 115–119 Table 2 Solubility of CHF3 in the alcohols expressed as mole fraction, x2 , at a partial pressure P2 = 101,325 Pa, and the Henry coefficient, H2,1.

117

Table 3 Solubility of CH2 F2 in the alcohols expressed as mole fraction, x2 , at a partial pressure P2 = 101,325 Pa, and the Henry coefficient, H2,1 .

Solvent

T (K)

x2 (10−4 )

H2,1 (MPa)

Solvent

T (K)

x2 (10−4 )

H2,1 (MPa)

Methanol

284.15 287.75 291.40 295.28 299.26 303.13 307.11 287.45 292.40 294.27 296.17 300.04 302.05 304.02 306.21 308.09 288.25 291.30 295.45 299.29 303.03 307.02 287.65 291.23 295.45 299.18 303.03 307.02

310.5 278.8 264.5 245.1 235.3 232.3 228.7 352.0 312.5 300.3 284.5 267.6 261.9 255.8 255.5 253.2 403.3 391.7 375.6 346.4 335.0 320.0 538.9 500.2 465.8 433.4 404.4 372.9

3.263 3.615 3.830 4.133 4.306 4.361 4.431 2.879 3.242 3.375 3.561 3.786 3.869 3.961 3.965 4.002 2.512 2.587 2.698 2.925 3.025 3.167 1.880 2.026 2.175 2.338 2.505 2.717

Methanol

287.75 290.25 293.35 297.25 301.06 303.05 307.03 287.75 290.25 293.15 297.30 301.06 305.04 313.00 287.35 290.55 293.65 297.25 301.05 305.04 308.81 287.35 290.25 293.15 297.45 301.05 305.03 309.02

193.2 187.8 174.0 164.3 158.1 149.1 142.6 257.6 248.6 224.5 206.3 189.8 173.2 136.1 312.1 312.3 290.4 279.9 270.7 257.4 243.4 383.4 366.7 346.8 341.6 333.0 317.8 301.0

5.246 5.396 5.824 6.165 6.411 6.795 7.108 3.934 4.076 4.513 4.911 5.338 5.851 7.445 3.155 3.244 3.489 3.620 3.743 3.936 4.163 2.643 2.763 2.922 2.966 3.043 3.188 3.366

Ethanol

1-Propanol

1-Butanol

Ethanol

1-Propanol

1-Butanol

The thermodynamic functions of solution are obtained from Eq. (5) by standard expressions:



H20 = RT



S20

∂ ln x2 ∂ ln T



= −B + CT

∂ ln x2 + ln x2 =R ∂ ln T

(6)

 = A + C(1 + ln T )

G20 = H20 − TS20

(7) (8)

To characterize the gas in the developed correlation is used the reduced dipole moment (*) [12] as a descriptor of the gas, which characterizes the effective polarity of a gas molecule with a permanent electric dipole moment,  [11], where ε is the Lennard-Jones potential well depth and  is the collision diameter of gas molecule.



∗

 =

2 ε 3

(9)

The solubility of CH3 F in lower alcohols was already determined by Silva et al. [16] with an accuracy of 3%. As the improved method employed in the present work is more accurate (0.6%), we repeated these experiments for CH3 F, which have shown that Table 4 Solubility of CH3 F in the alcohols expressed as mole fraction, x2 , at a partial pressure P2 = 101,325 Pa, and the Henry coefficient, H2,1 . Solvent

T (K)

x2 (10−4 )

H2,1 (MPa)

Methanol

288.15 290.65 293.15 295.65 298.15 300.65 303.25 305.75 288.05 290.71 293.55 295.73 298.35 300.75 303.25 305.69 308.05 288.15 290.75 293.65 295.67 298.29 300.73 303.05 308.23 288.25 290.77 293.23 295.71 298.25 300.67 303.25 308.23

74.28 68.10 58.82 52.88 46.14 43.65 39.45 37.19 87.82 78.61 71.13 67.08 63.53 61.50 61.21 58.73 57.88 106.2 101.8 96.77 92.05 89.38 86.05 82.49 75.46 124.1 119.5 115.1 109.9 105.9 102.5 99.49 91.95

13.642 14.879 17.226 19.162 22.020 23.206 25.684 27.243 11.538 12.890 14.245 15.105 15.950 16.474 16.552 17.233 17.505 9.540 9.954 10.471 11.008 11.337 11.775 12.283 13.427 8.162 8.479 8.805 9.220 9.568 9.884 10.184 11.020

Ethanol

4. Results and discussion The solubilities found in this work were corrected to 101,325 Pa partial pressure of the gas using Henry’s law, since the most literature values are referred to this pressure. The experimental solubilities data and the Henry’s coefficients for CHF3 , CH2 F2 and CH3 F in the alcohols obtained in this work are shown in Tables 2, 3 and 4, respectively. These tables show that among the solvents the solubilities of the CHF3 , CH2 F2 and CH3 F studied in this work are the lowest in methanol, increasing with the C-content of the alcohol. This feature is a consequence of the association made by H-bonding in the alcohols through the hydroxyl group, being this hydroxyl group protected by steric hindrance of adjacent carbon groups [14] causing a weaker H-bonding or a less association between the alcohol. Being that the H-bonding in the solvent has the effect of “exclude” the solute molecules and therefore reduce the solubility below what would be without such molecular interaction [15].

1-Propanol

1-Butanol

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Fig. 2. Solubility x2 of CH3 F (* = 1.504), CH2 F2 (* = 1.476) and CHF3 (* = 1.139) as a function of Gutmann acceptor number (AN) of alcohols and reduced dipole moment of the gases (*). Open symbols represent experimental values, the lines represent the correlation (Eq. (10)).

Fig. 1. Solubility of CH3 F, CH2 F2 and CHF3 in 1-propanol. Table 5 Parameters for CHF3 , CH2 F2 and CH3 F molecules used in Eq. (9).

Table 6 Gutmann acceptor number of alcohols.

Gas

 (D) [18]

 (Å) [19]

ε/k (K)[19]

*

Alcohol

AN [20]

CHF3 CH2 F2 CH3 F

1.65 1.98 1.847

4.40 4.10 3.80

178.5 189.0 199.0

1.139 1.476 1.504

Methanol Ethanol 1-Propanol 1-Butanol

41.3 37.1 35.3 32.2

the solubilities were underestimated in relation to the new values obtained. In the literature we have found three solubility values for CH2 F2 in methanol and three for ethanol [17] in the temperature range  of this study. The average absolute deviations |x2exp − x2lit |/x2lit × 100) are 2.4% for methanol and (AAD = (1/N) 3.0% for ethanol, respectively. The solubilities data of CHF3 , CH2 F2 and CH3 F in 1-propanol are plotted in Fig. 1, showing that the solubilities of CH3 F, CH2 F2 and CHF3 in 1-propanol increase as the number of fluorine atoms increases. This is related to the presence of the strongly electronattracting fluorine atom(s) on the carbon of the solute molecules that loosens the hydrogen(s) and makes it available for coordination to the donor atom of the solvent molecule [4]. A similar behaviour is found for the other alcohols, as can be observed in Tables 2–4. In Fig. 2 we can observe a correlation between the solubilities of CH3 F, CH2 F2 and CHF3 in alcohols at 298 K and atmospheric pressure, as function of the acceptor number of the alcohols, AN, and the reduced dipole moment of the gases, *, calculated through Eq. (9). In Tables 5 and 6 we present the parameters used in the developed correlation, described by Eq. (10). ln(x2 ) = −0.0818AN − 125.43∗ + 194.73(∗ )2 − 74.59(∗ )3 (10)

The average absolute deviation, obtained with this correlation is 5% which is acceptable taking into account that it is a semiempirical correlation with a strong empirical basis, since are used two descriptors, one for the alcohol, the AN (Gutmann acceptor number) and the other for the gas, the reduced dipole moment of the gas molecule. The AN descriptor is used as a measure of the association of the alcohols [10] and the reduced dipole moment of the gas molecule, that takes into account the polarity of the molecule (), its size through , the collision diameter. To represent the temperature dependence of the mole fraction solubilities, Eq. (5) was fitted to the corrected x2 values. The optimized parameters at 298 K and 1 atm of Eq. (5) and the AAD (%) of x2 are listed in Table 7. The thermodynamic functions, H20 , S20 which are related through Eq. (8) to give the molar Gibbs energy of a solution (G20 ), were calculated at 298 K with the optimized parameters of Eq. (5), being the values listed in Table 8. In Fig. 3 we have plotted the solubilities of CH3 F, CH2 F2 , CHF3 and CF4 [2] in methanol, ethanol, 1-propanol and 1-butanol at 298 K, being observed a linear correlation between molar Gibbs energy of solution and ln x2 , which shows that lower values of (G20 ) correspond to a more favourable process of dissolution and to an higher solubility.

Table 7 Parameters in the equation, R ln x2 = A + B/T + C ln T.

CHF3

CH2 F2

CH3 F

a

AAD = (1/N)



System

A (J mol−1 K−1 )

B (J mol−1 )

C (J mol−1 K−1 )

AADa (%)

Methanol Ethanol 1-Propanol 1-Butanol Methanol Ethanol 1-Propanol 1-Butanol Methanol Ethanol 1-Propanol 1-Butanol

−5738.54 −6168.75 521.98 725.83 −70.95 2333.98 −308.05 −144.79 −7525.79 −9689.15 150.90 −255.10

260064.05 283139.32 −16362.66 −21648.80 11477.77 −89952.78 20386.06 11593.79 356968.42 441624.50 2171.05 19057.74

848.64 910.78 −86.84 −119.20 −0.32 −362.37 36.84 13.64 1102.92 1433.23 −34.64 26.92

0.6 0.7 0.8 0.3 0.9 1.0 0.9 1.1 1.3 0.9 0.4 0.3

|x2exp − x2calc |/x2calc × 100.

J.M.M.V. Sousa et al. / Fluid Phase Equilibria 303 (2011) 115–119

119

Table 8 Molar Gibbs energy of solution, G20 , molar enthalpy of solution, H20 and molar entropy of solution, S20 , at 298 K and 1 atm partial pressure of the gases.

CF4 [2]

CHF3

CH2 F2

CH3 F

System

G20 (J mol−1 )

H20 (J mol−1 )

S20 (J mol−1 K−1 )

Methanol Ethanol 1-Propanol 1-Butanol Methanol Ethanol 1-Propanol 1-Butanol Methanol Ethanol 1-Propanol 1-Butanol Methanol Ethanol 1-Propanol 1-Butanol

20201.45 18969.94 18621.63 18480.83 9254.09 8884.89 8250.34 7720.77 10196.86 9639.87 8869.65 8390.15 13269.13 12513.84 11694.00 11263.07

−3834.18 −886.28 −1122.70 −1636.01 −7168.81 −11726.59 −9517.25 13872.79 −11570.75 −18034.80 −9407.77 −7527.62 −28131.63 −14306.78 −12501.06 −11029.76

−80.66 −66.63 −66.26 −67.51 −55.11 −69.17 −59.62 −72.46 −73.05 −92.87 −61.33 −53.42 −138.86 −89.96 −81.15 −74.77

22000 20000

methanol

CF4

ethanol

18000

∆G20 (J. mol-1)

presence of the strongly electron-attracting fluorine atom(s) on the carbon of the solute molecules that loosens the hydrogen(s) and makes it available for coordination to the donor atom of the solvent molecule. In this work a semiempirical correlation was developed for the solubilities of HFCs in the alcohols at 298 K and 1 atm partial pressure of the gases. This correlation embodies two descriptors, one for the solvent, the Gutmann acceptor number, and the reduced dipole moment for the gas. The correlation obtained gives an average absolute deviation of 5%.

1-propanol 1-butanol

16000 14000 CH3 F

12000

CH2 F2

10000

References

CHF3

8000 6000 -9

-8

-7

-6

-5

-4

-3

-2

ln (x2) Fig. 3. Molar Gibbs energy of solution at 298 K as function of the solubility; CF4 values from Ref. [2] and CH3 F, CH2 F2 , CHF3 values obtained in this work.

5. Conclusions The solubilities of CH3 F, CH2 F2 and CHF3 in lower alcohols (methanol, ethanol, 1-propanol, 1-butanol) have been determined in the temperature range [284, 313] K, at atmospheric pressure. The CH3 F, CH2 F2 and CHF3 solubilities increase with the Ccontent of the alcohol increases. This behaviour is due to the protection of hydroxyl group by steric hindrance of the increasing adjacent carbon groups which cause a weaker hydrogen bonds or a weaker alcohol association which determines that solvents with weaker H-bonding tendencies dissolve more the same gas than those with strong H-bonding tendencies; this behaviour is corroborated by the values of the standard Gibbs molar energy, G20 . The CH3 F, CH2 F2 and CHF3 solubilities in lower alcohols increase as the number of fluorine atoms increases. This is related to the

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