SO2 Solubility in 50 wt % H2SO4 at Elevated Temperatures and

Article pubs.acs.org/jced

SO2 Solubility in 50 wt % H2SO4 at Elevated Temperatures and Pressures Andries J. Krüger,*,† Henning M. Krieg,† and Hein W. J. P. Neomagus‡ DST HySA Infrastructure Centre of Competence, †Faculty of Natural Science, ‡Faculty of Engineering, Focus Area: Chemical Resource Beneficiation, North-West University, Potchefstroom 2520, South Africa ABSTRACT: The SO2 solubility at various temperatures and pressures was evaluated to determine the SO2 content in a 50 wt % H2SO4 acid solution adding new experimental solubility data for the SO2−H2SO4 binary system currently available in literature. A setup was designed and commissioned to measure the SO2 solubility at temperatures ranging from 30 °C to 80 °C and pressures up to 1000 kPa in 50 wt % H2SO4. SO2 solubility measurements in water were used to benchmark the accuracy of the setup. According to the results, the solubility of SO2 in 50 wt % H2SO4 decreased with increasing temperature despite the increase in the system pressure found at higher temperatures. The highest amount of SO2 soluble in 50 wt % H2SO4 was attained at 30 °C and 3.658 kPa with 13.11 g of SO2 per 100 g of H2SO4 solution. A heat of solution of −36 kJ·mol−1 (uncertainty u(ΔH) = 5 kJ·mol−1) was determined.

1. INTRODUCTION The continual escalation in energy demand causes an increased pressure on current energy sources such as natural gas, coal, and oil. This has steered researchers among others to further develop alternative, specifically clean and renewable energy processes, including hydro-electrical, wind, solar, water electrolysis, and thermochemical processes. Hydrogen, a renewable source that can be used for the storage of energy, can for example be obtained by water electrolysis, in which water is split into oxygen and hydrogen.1 However, although traditional water electrolysis is a clean process, this reaction is usually operated in the 1.7 V to 2 V range with relatively low efficiencies and high operating costs.2 There are alternative and more efficient processes that can also be used to produce hydrogen from water including the sulfur iodine (SI) and hybrid sulfur (HyS) processes.3 Both these processes include a decomposition step wherein sulfuric acid is decomposed over a catalyst to produce sulfur dioxide, water, and oxygen (reaction eq 1.1). In the HyS process, the produced SO2 and added H2O after removal of the oxygen are fed to an electrolyzer.4 In the electrolyzer, the water, in the presence of sulfur dioxide, is oxidized at the cathode to produce sulfuric acid, protons, and electrons (reaction eq 1.2). Subsequently, the formed protons migrate through a proton exchange membrane (PEM) and recombine with the produced electrons to form H2 (reaction eq 1.3). H 2SO4 → SO2 + H 2O + 0.5O2

(1.1)

SO2 + 2H 2O → H 2SO4 + 2H+ + 2e−

(1.2)

+

−

2H + 2e → H 2

While this process, similar to normal water electrolysis, also requires water for the reaction, the increased efficiency, for example, by requiring less energy (in theory 0.158 V), makes the HyS process more advantageous. The Westinghouse Corporation, who initially developed the HyS process, used SO2 dissolved in sulfuric acid as feed to the electrolyzer step.3 In their research they showed that the amount of SO2 dissolved in the acid influences the electrolyzer’s performance. There are different views in the literature on the optimum H2SO4 concentration for the thermal to electrical conversion, initially 50 wt %5 and more recently 65 wt % was suggested.6 Solubility data is available for liquid SO2 in a number of solutions including H2SO4.7 Although literature does provide some experimental data on SO2 solubility in an H2SO4 solution, it is either limited to low concentrations of H2SO4 (< 30 wt %)8−10 or concentrated H2SO4 (> 65 wt %)11−14 at low pressures (< 300 kPa). In view of the limited information available on the SO 2 solubility at intermediate H 2 SO 4 concentrations, specifically at elevated pressures, it was decided to experimentally determine the SO2 solubility in 50 wt % H2SO4 as a function of both temperature (30 °C to 80 °C) and pressure (100 kPa to 1000 kPa).

2. EXPERIMENTAL SECTION 2.1. Materials. Analytical grade 98 % sulfuric acid (CJ Chemicals, South Africa) was used and a batch solution of 50 wt % was prepared by diluting the 98 wt % H2SO4 with DI water (milli-pore). SO2 gas (Afrox, South Africa) was used as Received: March 11, 2013 Accepted: November 18, 2013

(1.3) © XXXX American Chemical Society

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dx.doi.org/10.1021/je4002366 | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Figure 1. Setup for the SO2 solubility measurements in 50 wt % H2SO4.

reached. SO2 gas from A2 was then supplied to B2. At this stage the measured initial pressure (Pi) in B3 was significantly smaller (100 Pa) than the saturation pressure of the liquid used. Nonetheless, these partial pressures were included in all calculations. The partial pressure of SO2 (pSO2) was calculated as

received. A sampling cylinder (1 gal, 304SS) was used to contain the SO2. 2.2. Methods. 2.2.1. System Setup and Calibration. The basic experimental setup (Figure 1) was adopted from Zhang et al.14 with modifications made to facilitate the high pressure applications. The experimental setup mainly included a gas stainless steel vessel B2 (102.60 cm3) containing only SO2 gas and a solubility cell B3 (111.08 cm3), containing the acid, which consisted of a glass-lined stainless steel housing. Accurate UT10 pressure transducers (PI1 and PI2, WIKA SA) were used to measure the pressure in both B2 and B3. The temperature was measured using K type thermocouples (TI1 to TI5) connected to PID controllers (WIKA SA). The two vessels were heated using a water bath (B1, Labotec SA, 14L capacity), while heating tape (A1, Hi-Tech elements, SA) was used to heat the piping from the sampling cylinder to the gas vessel. The separate volumes (B2 and B3) were calibrated using a water displacement method. Additional volume calibration experiments were carried out in which vessel B2 was pressurized and allowed to expand into B3 by opening V3. The equilibrium pressure calculated using the water calibrated volumes of B2 and B3 were in accordance with experimental values with an error < 0.4 %. Pressure tests were performed by pressurizing the system to 15 000 kPa with N2 for 2 h followed by system flushing at 15 000 kPa for 10 min. A pressure drop of less than 2 Pa over 2 h was accepted as successful. The sampling cylinder was heated using heating tape to obtain the elevated pressures required for the study. The temperature of the sampling cylinder (A2) was kept at least 5 °C below the operating temperature of the water bath (B1) to avoid SO2 condensation. 2.2.2. Calculations. Exactly 70.00 (uncertainty u(V) = 0.05 mL) of either the milli-Q water or acid was added to B3. The system was vacuumed (GEC Machines LTD, BC2 212) after the desired temperature in both vessels (B2 and B3) had been

PSO2 = (P − P i)

(2.1)

where P is the measured pressure in bar and converted to kPa. Subsequently, the amount of SO2 in both chambers was calculated using eq 2.2: nSO2 =

pso V 2

zSO2RT

(2.2)

in which the compressibility factor (zSO2) of SO2 (2.3) was calculated using the second order Virial equation of state where nS2 is the moles of SO2 (g), V is the volume in cm3, R is the universal gas constant in J·K·mol−1, and T is the temperature (K). Experimental values for the second virial coefficient (B) of −4.040·10−4 and −3.328·10−4 m3·mol−1 were used for 30 °C and 50 °C, respectively, while an interpolated value of −2.715· 10−4 m3·mol−1 was used for the 80 °C experiments.15 Since the initial pressure in B3 was relatively low for all temperatures tested, the total pressure was used in the Virial equation. zSO2 = 1 +

BP RT

(2.3)

After opening V3, the system pressure equilibrated in typically 500 min. The amount of adsorbed SO2 was calculated according to

B



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in which neq was again calculated using eq 2.2 and eq 2.3, in which V now equals the sum of the volume of the two chambers and P is the equilibrium pressure. The change in volume of the liquid due to the dissolution of the SO2 gas was assumed to be negligible. This assumption was validated by the correlation found between the solubility data obtained for the pure water experiments and data obtained from literature (see section 2.3.1). Valve V3 was subsequently closed and additional SO2 was supplied to chamber B2 from A2, while maintaining chamber B3 as is. The experimental cycle was now repeated and absorption data were obtained for increasing equilibrium pressures. The absorption liquid was replaced for each temperature studied. To facilitate comparison with literature, the absorption data points (nabs) were converted to mol−1·g for the water experiments and to a g/g basis for the sulfuric acid experiments using densities of 0.9998 g/mL and 1.3951 g/mL for water and 50 wt % sulfuric acid, respectively (experimentally determined). The Henry coefficient (H) was determined from the initial slope of the solubility plot while the heat of solution (ΔHs/kJ· mol−1) was obtained from a van’t Hoff plot (eq 2.5) based on the approach proposed by Zhang et al.14

Figure 2. SO2 solubility in water at 40 °C.

ΔHs (2.5) RT 2.3. Results and Discussion. 2.3.1. SO2 Solubility in Water at 40 °C. Table 1 shows the data obtained for the SO2

with the data obtained by Shaw et al.16 This confirms that the experimental setup proposed in this study was adequate in determining the SO2 solubility in pure water. From these results it was assumed that the values obtained for the SO2 solubility in 50 wt % H2SO4 had a similar repeatability and accuracy. 2.3.2. SO2 Solubility in 50 wt % H2SO4. To determine the time required to reach equilibrium pressure, pressure decay experiments were conducted. In Figure 3 the results of such a

ln H = ln as −

Table 1. Solubility Data (S) for SO2 (g) per Kilogram of Water Obtained at 40 °Ca run 1

run 2

PSO2

solubility

PSO2

solubility

kPa

mol SO2/kg H2O

kPa

mol SO2/kg H2O

37.1 62.1 87.1 93.1 110.6 123.0 132.5 149.9 183.6

0.18 0.35 0.50 0.65 0.79 0.92 1.08 1.26 1.44

44.7 55.9 77.2

0.17 0.34 0.52

a

Standard uncertainties u are u(PSO2) = 2 kPa, u(S) = 0.1 S, u(T) = 0.1 °C (level of confidence = 0.95).

solubility in water. To determine the internal repeatability of the solubility measurements, the SO2 solubility experiments in water were repeated twice, first at 0 to 200 kPa (run 1) and second at 40 to 80 kPa (run 2). To further elucidate the data presented in Table 1, the solubility of SO2 was plotted as a function of pressure as shown in Figure 2. To illustrate the validity of the data the solubility data obtained by Shaw et al.16 over the pressure range of 0 kPa to 200 kPa at 40 °C was added to Figure 2. It is clear from Figure 2 that the solubility of SO2 in water increases proportionally with an increase in the partial pressure of the SO2 gas. This linear dependence between solubility and pressure has also been observed at other acid concentrations9,17−20 when maintaining a constant temperature. A 95% confidence level was obtained for both the regression intercepts and slopes when the data presented in this study is compared

Figure 3. Pressure decay as a function of time, 50 wt % H2SO4 at 30 °C.

pressure decay experiment is shown where the change in the SO2 pressure as a function of time was plotted at a single initial pressure measurement at 30 °C for both the SO2 (B2) and H2SO4 (B3) compartments. Only the first two pressure values for SO2 and H2SO4 were not equal as V3 had not yet been opened at that time. However, as soon as SO2 entered B3, the two pressure values became superimposed due to the fast pressure equilibration. On the basis of the starting conditions C



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Table 2. Solubility Data (S) for SO2(g) in 100 g of 50 wt % H2SO4 Solution at Various Temperatures and Pressuresa 30 °C

a

50 °C

80 °C

PSO2

solubility

PSO2

solubility

PSO2

solubility

kPa

g SO2/100 g H2SO4

kPa

g SO2/100 g H2SO4

kPa

g SO2/100 g H2SO4

18.8 33.6 46.8 59.9 69.9 82.5 88.8 97.7 112.5 125.2 142.6 154.6 170.2 184.2 196.1 206.5 217.3 226.4 240.1 247.0 257.9 265.3 270.0 276.6 280.5 282.4 288.5 292.5 299.0 304.6 310.1 316.4 323.1 326.9 330.7 338.9 342.9 346.6 349.2 351.4 353.0 357.9 362.8 365.4 365.8

0.55 1.02 1.49 1.91 2.29 2.69 3.03 3.34 3.82 4.33 4.91 5.31 5.84 6.27 6.67 7.08 7.43 7.77 8.19 8.52 8.90 9.14 9.37 9.55 9.74 9.79 9.99 10.1 10.3 10.5 10.7 11.1 11.2 11.4 11.5 11.9 12.1 12.2 12.4 12.5 12.6 12.8 12.9 12.9 13.1

49.4 82.0 108.9 136.1 159.2 186.1 220.0 246.1 279.1 308.0 337.4 381.8 418.3 450.8 492.8 522.2 542.3 553.2 572.2 582.1 593.6 599.2 607.6 617.6

0.46 0.86 1.19 1.46 1.68 1.95 2.37 2.74 3.28 3.79 4.30 5.01 5.62 6.17 6.73 7.25 7.54 7.79 8.02 8.26 8.45 8.63 8.82 8.91

96.50 141.9 192.6 258.2 386.0 478.6 602.6 682.0 736.8 816.3 890.4 935.1 956.7 1005 1027

0.11 0.19 0.41 0.76 1.17 1.68 2.30 2.90 3.50 4.18 4.92 5.62 6.31 7.06 7.80

Standard uncertainties u are u(PSO2) = 2 kPa, u(S) = 0.1 S, u(T) = 0.1 °C (level of confidence = 0.95).

for the specific run presented in Figure 3 (t = 0, P(B2) = 209.7 kPa, and P(B3) = 2.5 kPa), the total amount of SO2 gas present in B2 (before the solubility measurements started) was calculated as 1.113 g. From the first measurement, the obtained equilibrium pressure (P = 17.2 kPa) was used to calculate the first solubility point of SO2, which was 0.686 g of SO2 per 100 g of H2SO4. A similar decrease in pressure over time graphs were obtained for all the experiments conducted in this study. Phase equilibrium was assumed when the pressure remained constant,

which in all our experiments occurred before 500 min. Hence all equilibrium data was collected at, or after, 500 min. The data of the experimental solubility measurements obtained at equilibrium at numerous pressures of SO2 (PSO2) for 30 °C, 50 °C, and 80 °C in 50 wt % H2SO4 is presented in Table2. To visualize the trends obtained, the data from Table 2 is presented in Figure 4 showing the solubility as a function of both pressure and temperature. According to Figure 4, it is clear that the solubility of SO2 increased with increasing SO2 pressure irrespective of the temperature. The experimental D



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they were only able at low pressures to model the SO2 solubility by adapting Henrys Law. According to literature it is easier to describe SO2−H2SO4−H2O systems below 22 wt % H2SO4 where the ionization of SO2 is observed.10 Above 22 wt %, the SO2 dissolved in the acid remains in its molecular form,21 which further complicates the description of the SO2 system.7,22, Since modeling using Henry’s Law is not suitable at higher pressures (> 250 kPa), further work would be required to derive a model for the solubility data obtained, which however falls beyond the scope of this paper. The deviation from linearity was confirmed by Gorensek et al.17 who used a mixed solvent electrolyte model from OLI System, Inc. to predict the solubility of SO2 in a wide range of temperatures, pressures, and acid concentrations, obtaining an exponential dependence between the solubility and the pressure. In general, slightly lower solubilities were obtained experimentally compared to the modeled values of Gorensek et al.17 especially at temperatures above 50 °C. The deviation of the modeled data from the experimental data confirms the observation made by Hayduk et al.,13 which states that it is difficult to theoretically predict the solubility behavior of SO2 in such a complex systems. From the experimental data obtained it is clear that the most favorable conditions for solubility were attained at SO2 gas pressures of 365.8 kPa and 30 °C reaching 13.11 g of SO2 per 100 g of H2SO4. This solubility is in the same order of magnitude as the solubility measured by Hayduk et al.13 in 97 wt % H2SO4, in which a maximum SO2 solubility of 8.48 g of SO2 per 100 g of H2SO4 at 25 °C and 250 kPa was attained. From the linear sections of the experimental data, the Henry law constant was determined for each temperature tested in this study. By plotting ln H as a function of 1/T (Figure 5), the heat of solution was obtained from the slope in the (ΔHs/R) term. It is clear from Figure 5 that a linear dependence of ln H on 1/ T for 50 wt % H2SO4 was attained for the three temperatures tested between 30 °C and 80 °C.

Figure 4. SO2 solubility as a function of temperature and pressure in 50 wt % H2SO4.

solubility at 30 °C (◇ in Figure 4) increased almost linearly with increasing pressure confirming the adherence to Henry’s law with a slight deviation above 250 kPa. The linearity in this pressure range has also been observed by other authors using a variety of acid concentrations and temperatures.8,10,14 For example, when studying the solubility of SO2 in 97 wt % sulfuric acid under higher pressures at 25 °C, Hayduk et al.,13 who used nitrogen gas to increase the total pressure while diluting the SO2 pressure, found that an increase in pressure does promote the solubility of SO2, which seems reasonable considering the increased SO2 activity with increasing SO2 pressure. Initially the solubility at 50 °C (γ) followed a similar trend to the initial trend observed at 30 °C with a linear region up to approximately 250 kPa, followed by another albeit slightly steeper slope above 250 kPa. It is also clear that the solubility decreased as the temperature increased from 30 °C to 50 °C, that is, although a SO2 pressure of almost double was reached for the measurements done at 50 °C, the solubility is clearly lower when compared to the solubility obtained at 30 °C. That implies that in order to dissolve 1.4 g of SO2 per 100 g of H2SO4 at 30 °C a pressure of only 46.8 kPa was required, whereas a pressure of 136.1 kPa was needed when the temperature was increased to 50 °C. When Hunger et al.9 evaluated the solubility of SO2 gas in 2 M (≈20 wt %) H2SO4 solution at 25 °C and 50 °C, they observed a similar trend; that is, that the solubility decreased with increasing temperature. This was also confirmed by Zhang et al.14 who obtained a decrease in the SO2 solubility with increasing temperature when working in an 79.01 wt % H2SO4 environment. The solubility data shown for 80 °C has no clear linear pressure region (obeying Henry’s law) as had been the case for 30 °C and 50 °C. The deviation from Henry’s law at 80 °C can probably be ascribed to the nonideality of the SO2−H2SO4− H2O system at higher temperatures. When using concentrations above 65.71 wt % H2SO4, Zhang et al.14 did observe a linear pressure dependence of the solubility at low pressures, which however deviated from linearity above 100 kPa. Similarly

Figure 5. A plot of ln H as a function of temperature for 50 wt % H2SO4. E



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The heat of solution obtained from the slope in Figure 5, was −36 kJ·mol−1 (uncertainty u(ΔH) = 5 kJ·mol−1) This value corresponds well with the value determined by Langenberg et al.23 who found that the heat of solution, when dissolving SO2 in a cold (−83 °C to −32 °C) thin film of 41 wt % H2SO4, was −36.4 kJ·mol−1. These values however differ to the heat of solution determined by Zhang et al.14 who calculated a heat of solution of −20.95 kJ·mol−1 in 95.51 wt % H2SO4 over a temperature range of 25 °C to 120 °C. 2.3.3. SO2 Diffusion in 50 wt % H2SO4. The time dependent data, an example of which was shown in Figure 3, were used to determine the observed diffusion coefficient (D/m2·s−1). Since the liquid phase was not stirred, the penetration theory of diffusion in a stagnant fluid was applied,24 where the flux of SO2 (JSO2/mol·m−2·s−1) in the sulfuric acid solution can be described as Figure 6. Absorption of SO2 as a function of √t, for the estimation of the apparent diffusion coefficient.

D (c int − co) π

JSO = 2

(2.6)

where cint and co represent the concentration (m3·mol−1) at the interface and bulk, respectively, at time 0. The total amount of SO2 adsorbed in the liquid can be obtained by integrating eq 2.6 and multiplying with the liquid−gas interfacial (S/m2) to arrive at D (c int − co) t S π

nSO2 =

It was experimentally observed that the pressure shortly after opening valve V3 showed some fluctuations which typically stabilized after about 1 min. The data given in Figure 6 was obtained after 1 min, confirming the linear trend given by eq 2.7. From the slope, the observed diffusion coefficient can be obtained and a value of 3.7·10−7 m2·s−1 (uncertainty u(D) = 0.5·10−7 cm2·s−1) was found. The values did not change significantly with varying partial pressures of the SO2 (loading of the sulfuric acid). These observed values are significantly larger than those predicted when using the Wilke−Chang equation.25 It is noteworthy that the diffusion of SO2 in water (2.5·10−8 to 2.3·10−9 m2·s−1)26,27 is significantly lower than the calculated apparent diffusion rate of SO2 in 50 wt % H2SO4 (3.6·10−7 m2· s−1). This high diffusion rate however confirms the observation made in Figure 3, where equilibrium was reached after only 300 min. When SO2 dissolves in water, it dissociates among others to form the species HSO−3 (reaction 1 and 2), a conversion which is so fast in water that it is regarded as instantaneous.10

(2.7)

Therefore, when the penetration theory is applicable, which is only for relative short times, the amount of SO2 that is absorbed in the liquid is proportional to the square root of t. As previously discussed, the amount of SO2 absorbed can be calculated using eq 2.2. Apart from the data given in Figure 3, three other runs were examined dynamically at 30 °C, the data of which is presented in Table 3, with a graphic presentation given in Figure 6. The runs were obtained at different partial pressures of SO2, in which each run was conducted using increasing pressures of SO2. Table 3. Dissolution of SO2 as a Function of Time in Different SO2 Loaded 50 wt % H2SO4 Solutions at 30 °Ca 1.485b

1.931b

3.024b

3.824b

time

nabs

time

nabs

time

nabs

time

nabs

min

×10−4

min

×10−4

min

×10−4

min

×10−4

3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0

2.65 4.08 5.50 6.87 8.18 9.55 10.9 12 13.1 14.3 15.3 16.4

3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

6.8 8.17 9.48 10.7 11.9 13 13.9 15.2

4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0

4.66 5.57 6.42 7.39 8.19 8.99 9.79 10.3 10.5 11.3 12.7 13.4 14.1

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

5.09 6.45 8.11 9.59 11.4 12.7 14 15.3 16.6 18

SO2 (g) ⇌ SO2 (aq)

(2.8)

SO2 (aq) + H 2O ⇌ H+ + HSO3−

(2.9)

However in an acid environment at 50 wt % H2SO4, the SO2 as previously stated will remain largely in the molecular form,28 and it can be assumed that the dissolved SO2 is equal to the soluble SO2, a finding that was confirmed by Zhang et al.14 It is therefore likely that the difference in the diffusion rates of SO2 observed is related to the difference in the type of sulfur species found in water versus a high H2SO4 acid environment. In both aqueous as well as 50 wt % H2SO4 environment, hydrogen bonding will occur between water molecules and the HSO−3 or SO2 species in water or 50 wt % H2SO4, respectively. Since an ionic species forms stronger and more hydrogen bonds than a non-charged species, the ionic SO2 found in water has a significantly larger effective diameter than the molecular SO2 found in 50 wt % H2SO4. According to the Einstein− Stokes equation larger species have a slower diffusion rate in a liquid than smaller species, which would help explain the apparent diffusion rates observed in our study.

a

Standard uncertainties u are u(t) = 0.05 min, u(S) = 0.1 S, u(nabs) = 0.1 nabs, u(T) = 0.1 °C (level of confidence = 0.95). bUnit: g of SO2/ 100 g of 50 wt % H2SO4 solution. F



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(11) Miles, F. D.; Fenton, J. The solubility of sulphur dioxide in sulfuric acid. J. Chem Soc. Trans. 1920, 117, 59−61. (12) Miles, F. D.; Carson, T. The solubility of sulphur dioxide in fuming sulphuric acid. Ind. Eng. Chem. Res. 1998, 37, 1167−1172. (13) Hayduk, W.; Asanti, H.; Storck, B. C. Solubility of sulfur dioxide in aqueous sulfuric acid solutions. J. Chem. Eng. Data 1998, 33, 506− 509. (14) Zhang, Q.; Wang, H.; Dalla Lanna, I. G.; Chuang, K. T. Solubility of sulfur dioxide in sulfuric acid of high concentration. Ind. Eng. Chem. Res. 1998, 37, 1167−1172. (15) Kang, T. L.; Hirth, L. J.; Kobe, K. A.; McKetta, J. J. Pressure− volume−temperature properties of sulfur dioxide. J. Chem. Eng. Data 1961, 6, 220−226. (16) Shaw, C. A.; Romero, M. A.; Elder, R. H.; Ewan, B. C. R.; Allen, R. W. K. Measurements of the solubility of sulphur dioxide in water for the sulphur family of thermochemical cycles. Int. J. Hydrogen Energy 2011, DOI: 10.1016/j.ihydene.2011.01.105. (17) Gorensek, M. B.; Staser, J. A.; Stanford, T. G.; Weidner, J. W. A thermodynamic analysis of the SO2/H2SO4 system in SO2-depolarized electrolysis. Int. J. Hydrogen Energy 2009, 34, 9089−6095. (18) Siddiqi, M. A.; Krissmann, J.; Peters-Gerth, P.; Lucas, M.; Lucas, K. Spectroscopic measurement of the (vapour+liquid) equilibria of (sulfur dioxde + water). J. Chem. Thermodyn. 1996, 28, 685−700. (19) Krichevsky, I. R.; Kasarnovsky, J. S. Thermodynamic calculations of solubilities of nitrogen and hydrogen in water at high pressures. J. Am. Chem. Soc. 1935, 57, 2168−2171. (20) Govindarao, V. M. H.; Gopalakrishna, K. V. Solubilities of sulfur dioxide at low partial pressures in dilute sulfuric acid solutions. Ind. Eng. Chem. Res. 1993, 32, 2111−2117. (21) Gold, V.; Tye, F. L. The state of sulphur dioxide dissolved in sulphuric acid. J. Chem. Soc. 1950, 571, 2932−2934. (22) van Berkum, J. G.; Diepen, G. A. M. Phase Equilibria in SO2+H2O: the sulfur dioxide gas hydrate, two liquid phases, and the gas phase in the temperature range 273 to 400 K and at pressures up to 400 MPa. J. Chem. Thermodynamics 1979, 11, 317−334. (23) Langeberg, S.; Proksch, V.; Schurath, U. Solubilities and diffusion of trace gases in cold sulfuric acid films. Atmos. Environ. 1998, 32, 3129−3137. (24) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 2nd ed.; University Press: Cambridge, UK, 1997; p 32. (25) Miyabe, K.; Isogai, R. Estimation of molecular diffusivity in liquid phase systems by the Wilke-Chang equation. J. Chromatgr. A 2011, 1218, 6639−6645. (26) Koliadima, A.; Kapolos, J.; Farmakis, L. Diffusion coefficients of SO2 in water and partition coefficients of SO2 in water−air interface at different temperatures and pH values. Instr. Sci, Technol. 2009, 37, 274−283. (27) Lealst, D. G. Diffusion coefficient of aqueous sulfur dioxide at 25°. J. Chem. Eng. Data 1984, 29, 281−282. (28) Gold, V.; Tye, F. L. The state of sulphur dioxide dissolved in sulphuric acid. J. Chem. Soc. 1950, 571, 2932−2934.

3. CONCLUSION In this study the solubility of SO2 in 50 wt % H2SO4 was experimentally measured as a function of the pressure of SO2 at 30 °C, 50 °C, and 80 °C. It was shown that the solubility of SO2 increased with increasing pressure while it decreased with increasing temperature. These results were in agreement with results obtained previously via modeling. According to these trends the highest solubility of 13.11 g of SO2 per 100 g of H2SO4 was obtained at 30 °C and a pressure of 365.8 kPa. From the ln H vs 1/T plot, a heat of solution of 36 kJ·mol−1 (uncertainty u(ΔH) = 5 kJ·mol−1) was calculated. Subsequently the diffusion of SO2 into the H2SO4 was calculated using the penetration theory of diffusion in a stagnant fluid. From the nabs vs √t plots a repeatable straight line was obtained. From the slope a diffusion coefficient of 3.7 · 10−7 m2·s−1 (uncertainty u(D) = 0.5·10−7 m2·s−1) was calculated, which was independent of the partial pressure of the SO2.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +27 18 285 2461. Fax: +27 18 299 2350. E-mail: [email protected]. Address: Private Bag X6001, Potchefstroom 2520, South Africa. Funding

We would like to thank the Chemical Resource Beneficiation (CRB) Focus Area at the North West University for providing the facilities to conduct this study and HySA infrastructure for the funding of this study. Notes

The authors declare no competing financial interest.

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REFERENCES

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SO2 Solubility in 50 wt % H2SO4 at Elevated Temperatures and

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