On the Solubility of Carbon Dioxide in Binary Water–Methanol Mixtures

Article pubs.acs.org/jced

On the Solubility of Carbon Dioxide in Binary Water−Methanol Mixtures N. Schüler,* K. Hecht, M. Kraut, and R. Dittmeyer Institute for Micro Process Engineering, Karlsruhe Institute of Technology, Karlsruhe, Germany ABSTRACT: The solubility of carbon dioxide in binary mixtures of water and methanol containing up to 12.37 mass % methanol has been measured at temperatures between 298 K and 333 K at atmospheric pressure. The solubility increases with increasing methanol content, but the influence is, at least at low temperatures, much smaller than linear interpolation would suggest. Employing the van't Hoff equation for ideal solutions, a correlation has been proposed that fits the measurements for up to 8.16 mass % methanol in water.

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INTRODUCTION Because of the ever-increasing mobility of the population, there is a growing interest in portable electronic devices. The power density of batteries cannot fulfill the needs of these applications. The conversion of methanol and water yielding carbon dioxide and electricity in micro direct methanol fuel cells (μDMFC) seems to be a promising alternative. For the simulation of such systems as well as for the characterization of system components, reliable data for the solubility of carbon dioxide in the working fluid under the actual process conditions are needed. In the literature the solubility of CO2 is reported only for the pure components, water1−4 and methanol,5−10 and for mixtures under absolute pressures between 200 kPa and 10 000 kPa.11,12 A good overview on experimental data for the solubility of CO2 in methanol is given in the review by Staby and Mollerup.10 This study presents new data on the solubility and Henry's constants of CO2 in water−methanol mixtures at atmospheric pressure for temperatures of up to 333.15 K and methanol content of up to 12.37 mass %. Furthermore, a model for the prediction of the Henry's constants for mixtures with a methanol content up to 8.16 mass % and temperatures between 298 K and 320 K has been evaluated.

Figure 1. Schematic of the experimental apparatus: A, syringe filled with carbon dioxide, B, syringe filled with liquid.

The complete apparatus was heated and insulated; the temperature was measured using Ni/CrNi-thermocouples with a measurement tolerance of 1.1 K. Pressure was measured using a transducer (Fi. Wika SE & Co. KG). The pressure transducer has a precision of 5 kPa. All experiments were performed using an absolute pressure of 103 ± 5 kPa. Syringe A and the connecting tubing were filled with a defined volume of carbon dioxide, syringe B with a defined volume of the liquid. Gas and liquid were brought in contact and agitated until equilibrium was reached. Equilibrium is reached when the volume of the system is unchanged over time at a given pressure. The liquid was initially oversaturated by applying pressure to the mixture. Then a relative pressure of 3 kPa was adjusted by retracting the cock of the syringe. Under equilibrium conditions the pressure remains constant. A time of 5 min was determined to be sufficiently long to establish equilibrium. Titration. To verify the experimental setup used in this study, the amount of CO2 dissolved in a saturated liquid sample was measured by titration. The comparison of the volumetric method with titration was carried out using pure water. Based on the described volumetric method, water and CO2 were brought in contact. After reaching the equilibrium state a defined amount of the saturated liquid

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EXPERIMENTAL SECTION Chemicals. Carbon dioxide (Basi 4.5) with a minimum purity of 99.995 %, methanol (Merck, analytical grade >99.9 %), and deionized water were used. Apparatus. A schematic of the experimental apparatus is shown in Figure 1. A defined volume of gas was brought into contact with a defined volume of liquid. Equilibrium was achieved by agitation. The remaining gas volume was measured; the change in the volume equals the amount of gas dissolved in the liquid. Each gastight syringe (A, B; Valco Instruments Company Inc., Magnum) contained a volume of 50 mL ± 0.1 %. The volume in the piping was measured to be 9 mL. © 2012 American Chemical Society

Received: April 5, 2012 Accepted: July 19, 2012 Published: July 30, 2012 2304

dx.doi.org/10.1021/je300332b | J. Chem. Eng. Data 2012, 57, 2304−2308

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was directly filled in a 0.5 mol·L−1 concentrated NaOH solution. 2NaOH + CO2 → Na 2CO3 + H 2O

(1)

The carbonate formed was precipitated using BaCl2. BaCl 2 + Na 2CO3 → 2NaCl + BaCO3↓

(2)

The CO2 concentration could be determined by titrating the sample with 0.01 M HCl. BaCO3 + 2HCl → BaCl 2 + CO2 ↑ +H 2O

(3)

The experimental results of the volumetric method were found to be in good agreement with the measured titration data (Table 1). Table 1. Comparison Volumetric Method: Titration, xCO2 T/K

mCO2/molCO2·kgsolvent−1

xCO2,volumetric

xCO2,titration

Δx/x

298 303 308 322

3.584·10−2 3.286·10−2 2.879·10−2 2.295·10−2

6.31·10−4 5.38·10−4 5.20·10−4 4.09·10−4

6.45·10−4 5.92·10−4 5.18·10−4 4.13·10−4

0.022 0.090 −0.003 0.010

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EXPERIMENTAL RESULTS Preliminary Experiments. The influence of dissolved air in methanol and water was analyzed in preliminary experiments. The mole fractions of CO2 in the liquid at equilibrium conditions in both degassed and nondegassed solvents are shown in Figure 2. Dissolved air reduced the solubility of CO2 in pure methanol but did not affect the solubility of CO2 in water. The solubility of CO2 in degassed methanol was about 20 % higher than in nondegassed samples. Consequently, pure water and methanol were degassed separately in a rotary evaporator, and all experiments were performed using degassed liquids. The volume of each degassed sample was 0.5 L, and the degassing process took 1 h. Solubility of CO2. Pure Components. The solubility of CO2 in pure water and pure methanol at various temperatures is presented in Table 2 and plotted in Figure 3. The solubility decreases with rising temperature for both species. Xia et al.11 reported Henry's constants for CO2 in water and methanol mixtures for pressures up to 10 000 kPa. Their measurements fit very well with our measurements. The observations of Xia et al.11 indicate that the model which was evaluated by Xia is comparable to our model at atmospheric pressure. The solubility of carbon dioxide in methanol is about 3.5 times higher than in water at ambient temperatures. However, the solubility in methanol decreases rapidly with rising temperature and falls below that of water at about 326 K because methanol boils at 338 K. The CO2-solubility in water decreases nearly linearly in the observed temperature range. The experimental data of this study compares well with the literature values for water as shown in Figure 4. At lower temperatures the measurements fit well with the data measured by Kunerth.3 With increasing temperature the data agree with the data of Morrison and Billet.4 Mixtures. The solubility of CO2 measured for mixtures of methanol and water is shown in Table 3 and depicted in Figure 5. Estimating CO2 solubility by linear interpolation between the values for pure water and pure methanol results in large errors

Figure 2. Influence of degassing on the solubility of CO2 in water and methanol, at absolute pressure 103 ± 5 kPa. Top: ●, H2O; ○, degassed H2O. Bottom: ●, MeOH; ○, degassed MeOH.

Table 2. Solubility of CO2 in Water and Methanol, xCO2, with Relative Error ± 5 % H2O

MeOH

T/K

xCO2

T/K

xCO2

303 308 313 318 324 328 333

7.13·10−4 6.08·10−4 5.31·10−4 4.70·10−4 3.99·10−4 3.54·10−4 3.15·10−4

299 307 313 318 322 327

5.37·10−3 5.18·10−3 4.68·10−3 3.43·10−3 1.99·10−3 3.66·10−4

even at very low concentrations of methanol. The absolute amount of dissolved CO2 in the water−methanol mixtures is low compared to pure methanol and only slightly higher than for pure water. The curves (Figure 5) for the mixtures show at low temperatures a slightly higher solubility of CO2. However, the solubility is decreasing with rising temperature below that of pure water, depending on the methanol content of the mixture. The CO2 solubility increases with increasing methanol content, up to 12.37 mass % at each temperature. Methanol concentrations between 0.8 mass % and 12.37 mass % are relevant concentrations for DMFC applications. Henry's Constants. The Henry's constants for pure water are given in Table 4. The calculated data fits well with the data 2305

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Figure 5. Solubility of CO2 in water−methanol mixtures relative to solubility in pure water, at absolute pressure 103 ± 5 kPa. ●, 0.80 mass % MeOH; ○, 2.41 mass % MeOH; ▼, 4.04 mass % MeOH; △, 8.16 mass % MeOH; ■, 12.37 mass % MeOH.

Figure 3. Solubility of CO2 in water and methanol, at absolute pressure 103 ± 5 kPa. ●, H2O; ○, MeOH.

Table 4. Henry's Constants for Pure Water at Different Temperatures T/K

1/T

ln kH

kH

303 307 312 318 324 329 333

3.30·10−3 3.26·10−3 3.21·10−3 3.14·10−3 3.09·10−3 3.04·10−3 3.00·10−3

7.86 8.02 8.16 8.28 8.44 8.56 8.68

2.60·103 3.05·103 3.49·103 3.95·103 4.64·103 5.23·103 5.89·103

kH = Figure 4. Solubility of CO2 in water: comparison with literature data, at absolute pressure 103 ± 5 kPa. ●, Austin;1 ○, Markham;2 ▼, Kunerth;3 △, Morrison;4 ■, this work.

pCO

2

mCO2

=

pCO

2

(

M H2O 1−b

+

MMeOH b

)

xCO2

(4)

where b is the methanol mass fraction, kH is Henry's constant (kgsolvent·molCO2−1·kPa), M is the molecular weight (kg·mol−1), mCO2 is the mass of CO2 (molCO2·kgsolvent−1), p is the pressure (kPa), and xCO2 is the mole fraction of CO2 in the liquid phase. Figure 6 shows the Henry's constants calculated from the measured solubilities of CO2 in water−methanol mixtures in comparison to the data evaluated by Xia et al.11 The evaluated constants from Xia et al.11 are in a good agreement with the constants calculated in this work. The solubility of CO2 for higher concentrations of methanol decreases because of the increasing constants over the analyzed range.

from Yaws and Yang.13 Yaws and Yang evaluated a Henry's constant of 2380 kgH2O·molCO2−1·kPa at 298 K. Table 5 lists the Henry's constants of CO2 in water− methanol mixtures at temperatures up to 323 K at atmospheric pressure which were calculated with eq 4. Pure CO2 is used for the calculation. The partial pressure of CO2 is reduced by the vapor pressure of the water−methanol mixture.

Table 3. Solubility of CO2 in Water−Methanol Mixtures, xCO2, with Relative Error ± 7 % 0.8 mass % MeOH T/K 302 308 313 318 323 328 333

xCO2 −4

7.73·10 6.35·10−4 5.07·10−4 4.34·10−4 2.81·10−4 4.63·10−5 0.00E+00

2.41 mass % MeOH

5.68 mass % MeOH

8.16 mass % MeOH

12.7 mass % MeOH

44.44 mass % MeOH

T/K

T/K

T/K

T/K

T/K

xCO2

302 308 314 319 323 328 333

5.95·10−4 4.76·10−4 3.80·10−4 2.87·10−4 1.46·10−4 1.46·10−4 2.27·10−6

302 308 313 318 323 328 332

xCO2 −4

7.50·10 6.47·10−4 5.23·10−4 4.56·10−4 3.37·10−4 1.37·10−4 3.17·10−5

301 307 313 318 323 328 333

xCO2 −4

9.21·10 8.16·10−4 6.81·10−4 5.91·10−4 4.03·10−4 1.99·10−4 5.25·10−5

303 308 313 319 322 327 333 2306

xCO2 −4

8.65·10 8.19·10−4 7.05·10−4 6.21·10−4 5.45·10−4 2.16·10−4 4.41·10−5

302 308 313 318 325 327 334

xCO2 −3

1.05·10 9.59·10−4 8.50·10−4 7.74·10−4 6.57·10−4 5.65·10−4 1.75·10−4

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Table 5. Henry's Constants of CO2 in Different Concentrated Water−Methanol Mixtures at Different Temperatures 0.8 mass % MeOH T/K

−3

302 308 313 318 323

2.41 mass % MeOH ln kH

1/T 3.31·10 3.25·10−3 3.19·10−3 3.14·10−3 3.10·10−3

T/K

7.79 7.99 8.21 8.37 8.80

302 308 313 318 323

5.68 mass % MeOH ln kH

1/T −3

3.31·10 3.25·10−3 3.19·10−3 3.14·10−3 3.10·10−3

T/K

7.84 7.98 8.20 8.33 8.63

301 307 313 318 323

8.16 mass % MeOH ln kH

1/T −3

3.32·10 3.26·10−3 3.19·10−3 3.14·10−3 3.10·10−3

7.66 7.78 7.96 8.10 8.49

T/K

ln kH

1/T −3

301 303 308 313 319 322

3.32·10 3.30·10−3 3.25·10−3 3.19·10−3 3.13·10−3 3.11·10−3

7.74 7.80 7.95 8.08 8.21 9.13

Figure 7. Dependence of ln(kH) on (1/T)/K−1 for 0.8 mass % methanol in water.

Figure 6. Henry's constants of CO2 in different concentrated water− methanol mixtures at a temperature of 313.75 K. ●, Xia et al.;11 ○, this work.

⎛ d ln kH ⎞ ⎜ ⎟ = −3626 K + 155 K·bMeOH ⎝ d(1/T ) ⎠

(7)

Henry's constants have been evaluated up to a methanol content of 8.16 mass % in water and temperatures up to 323 K. At higher methanol concentrations and temperatures a substantial amount of methanol evaporated from the liquid to the gaseous phase caused the boiling point at 338 K. As seen in Figure 5, the variation in solubility with temperature is linear up to this temperature. The temperature dependence of the Henry's constants could be fitted with the van't Hoff equation for temperatures up to 320 K. d ln kH ΔH 0 =− d(1/T ) R

(5) −1

where ΔH is the reaction enthalpy (J·mol ) and R is the universal gas constant (J·mol−1·K−1). Employing the van't Hoff equation for ideal solutions, the measured data could be fit very well until for methanol concentrations up to 8.16 mass % in water and temperatures up to 320 K (Figure 5). The relationship between ln(kH) and 1/T for 0.8 mass % methanol in water is shown in Figure 7. The measurements at temperatures above 320 K do not fit the linear trend of the points at lower temperatures due to beginning evaporation. With the linearization it is possible to calculate the Henry's constants for different concentrations at different temperatures according to a van't Hoff-based equation: 0

⎛⎛ d ln k ⎞ 1 ⎞ H kH(T ) = kH0·exp⎜⎜ ⎟· ⎟ ⎝⎝ d(1/T ) ⎠ T ⎠

Figure 8. Temperature dependence coefficients for water−methanol mixtures.

The value of the Henry's constant at 298 K, k0H, can also be calculated as a linear function of the methanol content: kH0 = exp( −0.50155bMeOH + 7.6782)

kg H O· kPa 2

mol CO2

(8)

A comparison between the values predicted by the model and the experimental measurements is shown in Figure 9. The model is able to predict the Henry's constants for water and methanol mixtures with up to 8.16 mass % methanol for temperatures between 298 K and 320 K. At higher temperatures methanol evaporates so that the starting concentration and the liquid composition cannot be considered to be the

(6)

The temperature dependence constant (d ln kH/d(1/T)), which is the slope of the line in Figure 7, has units of K and can be calculated as a function of the methanol content (see Figure 8). 2307

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(6) Chang, C. J.; Day, C.-Y.; Ko, C.-M.; Chiu, K.-L. Densities and Px-y diagrams for carbon dioxide dissolution on methanol, ethanol, and acetone mixtures. Fluid Phase Equilib. 1997, 131, 243−258. (7) Leu, A.-D.; Chung, S. Y.-K.; Robinson, D. B. The equilibrium phase properties of (carbon dioxide + methanol). J. Chem. Thermodyn. 1991, 23, 979−985. (8) Joung, S. N.; Yoo, C. W.; Shin, H. Y.; Kim, S. Y.; Yoo, K.-P.; Lee, C. S.; Huh, W. S. Measurements and correlation of high-pressure VLE of binary CO2-alcohol systems (methanol, ethanol, 2-methoxyethanol and 2-ethoxyethanol. Fluid Phase Equilib. 2001, 185, 219−230. (9) Hong, J. H.; Kobayashi, R. Vapor-Liquid Equilibrium studies for the carbon dioxide−methanol system. Fluid Phase Equilib. 1988, 41, 269−276. (10) Staby, A.; Mollerup, J. Mutual solubilities of mono-alcohols and carbon dioxide: a review of experimental data. Fluid Phase Equilib. 1993, 89, 351−381. (11) Xia, J.; Jödecke, M.; Pérez-Salado Kamps, A.; Maurer, G. Solubility of CO2 in (CH3OH + H2O). J. Chem. Eng. Data 2004, 49, 1756−1759. (12) Urukova, I.; Vorholz, J.; Maurer, G. Solubility of Carbon Dioxide in Aqueous Solutions of Methanol. Predictions by Molecular Simulation and Comparison with Experimental Data. J. Phys. Chem. B 2006, 110, 14943−14949. (13) Yaws, C. L.; Yang, H.-C. Henry’s law constant for compound in water in Thermodynamic and Physical Property Data; Yaws, C. L., Ed.; Gulf Publishing Company: Houston, TX, 1992; pp 181−206.

Figure 9. Comparison of Henry's constant model to measurements, at absolute pressure 103 ± 5 kPa. ●, 0.80 mass % MeOH; ▼, 2.41 mass % MeOH; ■, 5.68 mass % MeOH; ◆, 8.16 mass % MeOH; ▲, 12.37 mass % MeOH.

same. The measured solubility of CO2 does not account for methanol evaporation. The model may still be valid at higher temperatures if the methanol concentration is accurately described. However, a full consideration of nonidealities in ternary mixtures is beyond the scope of this paper. For the range of concentrations and temperatures and low pressures expected in a DMFC, the suggested correlation can be used.

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CONCLUSIONS Data on the solubility of CO2 in water−methanol mixtures have been presented. At temperatures up to 333.15 K and under atmospheric pressure, the solubility of CO2 increases with the increasing amount of methanol in the mixture and decreases at higher temperatures. It could be shown that the experimental data of the solubility in water match with existing literature data well. Henry's constants were evaluated for water−methanol mixtures up to a methanol content of 8.16 mass % and temperatures up to 320 K at atmospheric pressure. Under these conditions the constants fit the van't Hoff equation well. The model from Xia et al.11 should be extrapolated to atmospheric pressure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Austin, W.; Lacombe, E.; Rand, P. W.; Chatterjee, M. Solubility of carbon dioxide in serum from 15 to 38 C. J. Appl. Physiol. 1963, 18 (2), 301−304. (2) Markham, A. E.; Kobe, K. A. The Solubility of Carbon Dioxide and Nitrous Oxide in Aqueous Salt Solutions. J. Am. Chem. Soc. 1941, 63, 449−454. (3) Kunerth, W. Solubility of CO2 and N2O in Certain Solvents. Phys. Rev. 1922, 2, 512−524. (4) Morrison, T. J.; Billet, F. The Salting-out of Non-electrolytes. Part II. The Effect of Variation in Non-Electrolyte. J. Chem. Soc. 1952, 3819−3822. (5) Miyano, Y.; Fujihara, I. Henry's constants of carbon dioxide in methanol at 250−500 K. Fluid Phase Equilib. 2004, 221, 57−62. 2308

dx.doi.org/10.1021/je300332b | J. Chem. Eng. Data 2012, 57, 2304−2308