Article pubs.acs.org/IECR
Solubility of Oxygen in Organic Solvents and Calculation of the Hansen Solubility Parameters of Oxygen Takashi Sato, Yuzo Hamada, Masaru Sumikawa, Sadao Araki, and Hideki Yamamoto* Department of Chemical, Energy and Environmental Engineering, Faculty of Environmental and Urban Engineering, Kansai University, 3-3-35 Yamate-cho, Suita-shi, Osaka 564-8680, Japan ABSTRACT: The solubility of oxygen in 21 pure organic solvents was measured at 298.2 K and 101.33 kPa using the static method. The Hansen solubility parameters (HSPs) of oxygen were determined from the measured solubilities in the pure solvents. The HSPs of oxygen were δd = 6.7 MPa1/2, δp = 0.0 MPa1/2, and δh = 3.8 MPa1/2, where d, p, and h stand for dispersion forces, dipole interaction, and hydrogen bonding, respectively. A linear relationship between the log of the gas solubility (log xG) in pure solvents and the difference between the HSP values of oxygen and the pure solvents was obtained with a high correlation coefficient of 0.944. In addition, the solubilities of oxygen in mixed solvents were measured, and these were compared with the oxygen gas solubility calculated from the HSPs of oxygen.
1. INTRODUCTION
2. HANSEN SOLUBILITY PARAMETER The solubility parameter δt (MPa1/2) used in this study is defined as8
The solubility of oxygen in organic solvents is an important property for the development of chemical plants and the quality control of solvents in many industries, such as the petroleum, food, and semiconductor industries. For example, molecular oxygen in hydrocarbon feed stocks plays a key role in fouling and corrosion of refinery units.1 Dissolved oxygen also contributes to shortening of the shelf life of refinery fuel products owing to deposit and sediment formation. The solubilities of gases in alcohols have attracted particular attention in connection with the mechanism of general anesthesia.2 In the liquid-phase oxidation of toluene, the oxygen partial pressure in the industrial reactors must be controlled at a very low concentration for safety.3 Hence, the solubility of oxygen is essential information for the design and optimization of this gas−liquid oxidation reactor, especially the solubility data under reaction pressure and temperature. The Hansen solubility parameters (HSPs) have recently attracted attention as physical properties for the solubility in various solvents. The relationship between the HSPs and solubility has been reported, such as for C60 fullerene4 and an asphaltene5 in various solvents. HSPs have been reported not only for organic solvents but also for many other substances, such as polymers6 and inorganic nanoparticles.7 However, there are few reports on the HSPs of gases, and a method for calculating the HSPs of gases has not been established. Furthermore, to the best of our knowledge, the relationship between gas solubility and the HSPs has not been reported. In this work, the solubility of oxygen in pure organic solvents was measured at 298.2 K and 101.33 kPa with the static method. We propose a new method for calculating the HSPs of gases, and the HSPs of oxygen were calculated using this method. In addition, the solubility of oxygen in mixed solvents was measured, and the results were compared with the calculated value from the HSPs. The purpose of this work is to report the relationship between the solubility of oxygen in some solvents and the HSPs. © 2014 American Chemical Society
δt = (E /V )1/2
(1) 3
where E (J) is the liquid cohesion energy and V (cm /mol) is the molar volume. Hansen divided the cohesion energy E (J) of the Hildebrand solubility parameter into three terms, dispersion interactions Ed (J), dipole interactions Ep (J), and hydrogenbonding interactions Eh (J), which can be expressed by9 E = Ed + Ep + E h δd = (Ed /V )1/2 ,
(2)
δp = (Ep/V )1/2 ,
δ h = (E h /V )1/2 (3)
δt 2 = δd 2 + δp2 + δ h 2
(4)
where δd (MPa1/2), δp (MPa1/2), and δh (MPa1/2) are the dispersion force, the dipole interaction force factor, and the hydrogen-bonding force factor of the HSP, respectively. Quantitative solubility can be represented by Ra (MPa1/2), which is the distance between the HSPs of two substances in the three-dimensional (3D)-HSP diagram: R a = [4(δd1 − δd2)2 + (δp1 − δp2)2 + (δ h1 − δ h2)2 ]1/2 (5)
A small Ra for a solute and solvent indicates that the solute will have high solubility in the solvent because the interaction forces acting between solute molecules and between solvent molecules are similar. Conversely, a large Ra value indicates that the solute will have low solubility in the solvent. Received: Revised: Accepted: Published: 19331
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Figure 1. Schematic diagram of experimental apparatus for gas solubility measurement.
solvent is a good solvent. When RED is >1, it is a poor solvent. Thus, the RED number can be used as an indicator of solubility. The solubility and Ra value are correlated because the RED number and the solubility are correlated. The HSPs of oxygen were calculated from the solubility of oxygen in the organic solvents. The detailed procedure for the calculation method of the HSP of oxygen is as follows. First, the oxygen solubilities (mole fraction) in organic solvents with known HSPs are measured. After we assumed the HSP values of oxygen, Ra was calculated from the HSP values of oxygen and the solvents. The correlation coefficient between Ra and the logarithmic solubility was calculated. Finally, the HSPs of oxygen were determined to obtain the largest correlation coefficient. The correlation coefficient was calculated using the following equation:
The HSPs of the pure organic solvents were obtained from the Hansen database.9 The solubility parameters of a mixed solvent can be calculated by the following equation: δi = ϕ1δi1 + ϕ2δi2
(6)
where ϕ is the volume fraction of each of the mixed solvents and the subscripts 1 and 2 represent components 1 and 2, respectively. The subscript i represents d, p, or h (i.e., δi represents the dispersion interaction, dipole interaction, or hydrogen-bonding interaction factors). Generally, the HSP values are calculated by the molecular group contribution method10 and/or the Hansen solubility sphere.4 However, the HSPs of oxygen are unable to be calculated by the group contribution method. The values have not been reported in the literature, and a calculation method for the HSP of gases is not available. In this work, the HSP values for gases are calculated using the relationship between the solubility and the difference of the HSP values of each component. The HSP values of oxygen were determined from the solubility in several pure solvents and the solvent’s HSP values. Hansen reported that the relative energy difference (RED) number and the solubility of C60 fullerene were correlated.11 The RED number is expressed as
RED = R a /R 0
n
R=
∑i = 1 (xi − x*)(yi − y*) n
n
[∑i = 1 (xi − x*)2 ][∑i = 1 (yi − y*)2 ]
(8)
where x and y are data groups 1 and 2 and where x* and y* are arithmetic averages of x and y.
3. EXPERIMENTAL SECTION 3.1. Materials. Oxygen gas (Taiyo Nippon Sanso Co., Tokyo, Japan, purity of >99.999 vol %) was used without further purification. The organic solvents used in this work were manufactured by Wako Pure Chemical Industries, Ltd. Methanol, ethanol, 1-propanol, 2-propanol, acetone, N,Ndimethylacetamide, and N,N-dimethylformamide were reagent
(7)
where R0 (MPa1/2) is the radius of the Hansen solubility sphere in the 3D-HSP diagram. When the RED number is ≤1, the 19332
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(L) is defined as the ratio of the volume of gas (VG) absorbed to the volume of the absorbing liquid (VL), that is,
grade. 1-Butanol, 2-butanol, 1-pentanol, 1-hexanol, ethylene glycol, propylene glycol, pentane, hexane, heptane, octane, cyclohexane, benzene, toluene, and dichloromethane were Wako special grade. All of the solvents were degassed by distillation for 90 min before gas dissolution. 3.2. Experimental Apparatus. A schematic diagram of the experimental apparatus used for the gas solubility measurements is shown in Figure 1. The apparatus is based on the static method,12−14 and it was possible to calculate the gas solubility by measuring the volume of gas dissolved in degassed solvent. This apparatus consisted of a degassing flask, a low-temperature circulating bath (Tokyo Rikakikai Co., Ltd., CA-1112), a vacuum pump (ULVAC Kiko Inc., G-100D), a stainless steel gas pump, a glass equilibrium cell, a Druck precision pressure indicator (GE Sensing & Inspection Technologies and GE Optimization and Control, DPI-150), a low-temperature circulator (Tokyo Rikakikai Co., Ltd., CTP-1000), and a constant temperature bath. The pipe arrangement, stainless steel tube, ferrule, and valve were manufactured by Swedgelok. The equilibrium cell was made of Pyrex glass. The volume of the equilibrium cell was about 200 cm3. It was attached by greaseless valves to enable it to be removed from the apparatus while maintaining the vacuum. By 1 mm in a vertical direction with one rotation, the inner volume of the gas pump changed 803.8 mm3. The dissolved gas in the solvents was degassed by reduced-pressure distillation under total reflux for 90 min using a degassing flask and condenser. The density of the solvents was measured by a portable density meter (Anton Paar, DMA35N). The accuracy of the temperature measurements around the equilibrium cell in the constant temperature bath full of water was ±0.02 K. The temperature was measured by precision thermometers (Automatic Systems Laboratories, F201). 3.3. Experimental Procedure. The solvent in the degassing flask was degassed by distillation for 90 min under total reflux. The solvents were degassed by opening valve V3 at regular intervals under pressure from a vacuum pump. The degassed solvent was moved from the degassing flask to the equilibrium cell through the pipe arrangement. Valves VA and VB were closed. The equilibrium cell was removed from the apparatus, and the weight of solvent in the equilibrium cell was measured. The equilibrium cell was then reattached to apparatus, and it was maintained at 298.2 K in a thermostat bath. After the vapor pressure of the solvent was measured, oxygen gas was introduced into the gas pump and pipe arrangement at 101.33 kPa. The gas was introduced into the equilibrium cell by opening valve V6, and gas dissolution started. When dissolving gas in solvent, valves VA, V5, and V9 were closed and valves VB, V7, and V8 were opened. The total pressure was maintained at 101.33 kPa by changing the volume of the gas pump. The process of dissolving the gas by opening valve V6 was repeated at regular intervals. The operation of opening valve V6 was repeated is because solvent in the equilibrium cell prevented it from flowing out to the gas pump side. It was considered that the solution had reached equilibrium when the pressure drop by opening V6 was ≤0.013 kPa. The composition of the mixed solvents was determined by gas chromatograph (Shimadzu GC-17A). 3.4. Calculation of the Gas Solubility. The gas solubilities are expressed in terms of the Ostwald coefficient because the experimental apparatus is able to measure the volume of dissolved gas in the solvent. The Ostwald coefficient
L = VG/VL
(9)
The molar volume of solvent before gas dissolution (VS) was calculated from the mass (mSA) and density (ρSA) of the solvent before gas dissolution:
VS = mS A /ρS A
(10)
In the same way, the molar volume of the solvent after gas dissolution (VS2) was calculated from the mass (mSB) and density (ρSB) of the solvent after gas dissolution:
VS2 = mS B /ρS B
(11)
The volume of gas in the gas pump before and after gas dissolution (V1A and V1B, respectively) can be expressed as V1 A = V1P1 A /P
(12)
V1B = [V1 A − (π /4)D2(hA − hB)/P]P1B/P
(13)
(P2B)
The partial pressure of the gas at equilibrium was calculated from the equilibrium pressure P2 and vapor pressure of the solvent (PS − P0): P2 B = P2 − (PS − P0)
The volume of gas in the equilibrium cell expressed as V2 B = (V0 − VS2)P2 B/P
(14)
(V2B)
can be (15)
The volume of dissolved gas in the solvent was calculated from eqs 12−15: VG = (V1 A − V1B − V2 B)P /P2 B
(16)
The Ostwald coefficient was converted to a mole fraction by the following equation: xG = (RT /PVLL + 1)−1
(17)
where R, T, P, and VL are the gas constant, temperature, standard pressure, and molar volume of the solvent before gas dissolution, respectively. 3.5. Measurement Accuracy. The standard uncertainty of the mole fraction of oxygen was calculated to confirm the accuracy of the measured value of the gas solubility. The standard uncertainty was calculated by15 n
u(xi) =
∑i = 1 (Xi ,m − Xi)2 (n − 1)
(18)
where Xi is a series of observed value, Xi is arithmetic average of Xi, and n − 1 is the degree of freedom. Equation 18 is used when standard uncertainty is calculated by experimental standard deviation. Experimental standard deviation estimated from frequency is evaluated by duplicate measurements.
4. RESULTS AND DISCUSSION 4.1. Solubility of Oxygen in Pure Organic Solvents. The solubility of oxygen in the 21 pure organic solvents was measured at 298.2 K and 101.33 kPa. The solubilities of oxygen and the standard uncertainties are shown in Table 1. The solubility values are the average of three measurements. The standard uncertainty was calculated using the measured 19333
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The HSPs of oxygen were calculated in such a way that the correlation coefficient of log xG (logarithm of oxygen solubility in the pure organic solvents) and Ra (3D-HSP distance between oxygen and solvents) was the highest. The log xG and Ra values are shown in Figure 2. The correlation coefficient between the
Table 1. Solubility of Oxygen in Pure Organic Solvents at 298.2 K and 101.3 kPa and Standard Uncertainty of the Measured Values solvent methanol ethanol 1-propanol 2-propanol 1-butanol 2-butanol 1-pentanol 1-hexanol ethylene glycol propylene glycol pentane hexane heptane octane cyclohexane benzene toluene dichloromethane acetone N,N-dimethylformamide N,N-dimethylacetamide
solubility of oxygen, xG standard uncertainty, u 4.15 × 10−4 5.71 × 10−4 6.76 × 10−4 7.78 × 10−4 7.76 × 10−4 8.34 × 10−4 8.76 × 10−4 9.60 × 10−4 7.23 × 10−5 1.86 × 10−4 2.65 × 10−3 2.25 × 10−3 2.19 × 10−3 2.17× 10−3 1.28 × 10−3 8.20 × 10−4 9.81 × 10−4 7.09 × 10−4 8.71 × 10−4 3.89 × 10−4 4.82 × 10−4
5.77 × 10−6 2.73 × 10−5 2.73 × 10−5 5.33 × 10−5 1.66 × 10−5 7.26 × 10−6 1.35 × 10−5 1.86 × 10−5 5.03 × 10−6 7.77 × 10−6 7.22 × 10−5 6.66 × 10−5 4.73 × 10−5 2.19 × 10−5 4.41 × 10−5 6.67 × 10−6 6.67 × 10−6 4.33 × 10−5 1.76 × 10−5 3.33× 10−6 3.54 × 10−6
Figure 2. Relationship of the distance between the HSPs of oxygen and solvents and the solubility of oxygen in the pure organic solvents.
logarithmic solubility of oxygen in the solvents and the Ra value calculated using the HSP values of oxygen and the solvents was 0.944. This indicates a good correlation between the HSP values and the solubility of oxygen. The HSPs of oxygen were determined to be δd = 6.7 MPa1/2, δp = 0.0 MPa1/2, δh = 3.8 MPa1/2, and δt = 7.7 MPa1/2. The δd solubility parameter is the dispersion interaction. The δd parameter of oxygen is smaller than that of the solvents because oxygen has weak dispersion interactions. The δp parameter of oxygen was 0.0 MPa1/2 because oxygen does not have a dipole. Even though oxygen has no hydrogen atoms, the δh parameter of oxygen was 3.8 MPa1/2 because it is suggested that the oxygen molecules form hydrogen bonds with other molecules. Hansen reported that the δh parameters are not zero for some substances with no hydrogen bonding.9 4.3. Calculation of Oxygen Solubility in Organic Solvents. The oxygen solubility in the pure organic solvents was calculated using the HSPs of oxygen. From Figure 2, the relationship between Ra and log xG for oxygen is
solubility of oxygen. In general, the solubility of oxygen increased with increasing alkyl chain length for alcohols, while it decreased with increasing alkyl chain length for alkanes. Conversely, the solubility of oxygen in N,N-dimethylformamide was less than in N,N-dimethylacetamide. 4.2. Calculation of the HSPs of Oxygen. The HSPs of oxygen were calculated using the measured oxygen solubilities in the 21 pure organic solvents. The logarithm of the oxygen solubility and the HSPs of the solvents are shown in Table 2. Table 2. Solubility of Oxygen in Pure Organic Solvents and HSPs of the Organic Solvents solvent
log xG
δd [MPa1/2]
δp [MPa1/2]
δh [MPa1/2]
methanol ethanol 1-propanol 2-propanol 1-butanol 2-butanol 1-pentanol 1-hexanol ethylene glycol propylene glycol pentane hexane heptane octane cyclohexane benzene toluene dichloromethane acetone N,N-dimethylformamide N,N-dimethylacetamide
−3.38 −3.24 −3.17 −3.11 −3.11 −3.08 −3.06 −3.02 −4.14 −3.73 −2.58 −2.65 −2.66 −2.66 −2.89 −3.09 −3.01 −3.15 −3.06 −3.41 −3.31
14.7 15.8 16.0 15.8 16.0 15.8 15.9 15.9 17.0 16.8 14.5 14.9 15.3 15.5 16.8 18.4 18.0 17.0 15.5 17.4 16.8
12.3 8.8 6.8 6.1 5.7 5.7 5.9 5.8 11.0 10.4 0.0 0.0 0.0 0.0 0.0 0.0 1.4 7.3 10.4 13.7 11.5
22.3 19.4 17.4 16.4 15.8 14.5 13.9 12.5 26.0 21.3 0.0 0.0 0.0 0.0 0.2 2.0 2.0 7.1 7.0 11.3 9.4
log xG = (− 8.89 × 10−2)R a − 1.10
(19)
The measured solubility of oxygen and the solubility calculated using the HSPs for the 21 solvents are shown in Table 3. The average difference between the measured and calculated values was 2.18%, and the maximum deviation was 4.57%. For alkane solvents, the average difference between the measured and calculated values was 1.37%, indicating that the calculated results are good. For alcohol solvents, the average difference between the measured and calculated values was 2.17%. The differences between the measured and calculated values of oxygen gas solubility in methanol, ethanol, and ethylene glycol were 4.57%, 3.96%, and 4.20%, respectively. This suggested that solvents with high δh values tend to have the largest differences between the measured and calculated values. The group contribution method for estimating the gas solubility was used for the various solvents. Group parameters for each group are required to estimate the physical properties using the group contribution method. The group parameters for the solubility of oxygen have been reported in a few group contribution methods, such as the universal quasichemical 19334
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Table 3. Calculated and Measured Solubilities of Oxygen in Pure Organic Solvents log xG solvent
observed
calculated
deviation [%]
methanol ethanol 1-propanol 2-propanol 1-butanol 2-butanol 1-pentanol 1-hexanol ethylene glycol propylene glycol pentane hexane heptane octane cyclohexane benzene toluene dichloromethane acetone N,N-dimethylformamide N,N-dimethylacetamide
−3.38 −3.24 −3.17 −3.11 −3.11 −3.08 −3.06 −3.02 −4.14 −3.73 −2.58 −2.65 −2.66 −2.66 −2.89 −3.06 −3.09 −3.01 −3.15 −3.31 −3.41
−3.54 −3.37 −3.24 −3.14 −3.13 −3.05 −3.04 −2.98 −3.97 −3.65 −2.53 −2.60 −2.66 −2.70 −2.92 −2.94 −3.19 −3.12 −3.06 −3.23 −3.46
4.57 3.96 2.12 1.08 0.74 1.09 0.59 1.18 4.20 2.12 1.96 2.00 0.17 1.35 1.04 3.93 3.21 3.66 2.69 2.67 1.48
Figure 4. Calculated and measured solubilities of oxygen in the ethanol−hexane mixed solvent system at 298.2 K and 101.3 kPa: (○) observed value and (●) calculated value.
functional group activity coefficient method and the analytical solution of groups method. In contrast, HSP values have been reported for more than 1200 substances. Thus, estimation using HSP values has advantages over using the group contribution method because of its wide application to many solvents. 4.4. Solubility of Oxygen in Mixed Solvents. The solubility of oxygen in mixed solvents was measured at 298.2 K and 101.33 kPa. Ethanol−cyclohexane, ethanol−hexane, ethanol−2-propanol, 2-propanol−cyclohexane, 2-propanol− hexane, and hexane−cyclohexane were chosen as mixed solvents in this work. The measured and calculated solubilities in the mixed solvents are shown in Figures 3−8. For the ethanol−cyclohexane, ethanol−hexane, 2-propanol−cyclohexane, and 2-propanol−hexane mixed solvent systems, the solubility of oxygen in the mixed solvent was higher than the ideal solubility. Ideal solubility is the gas solubility in mixed solvent estimated from the gas solubility in pure solvents. This phenomenon has also been observed for the solubility of
Figure 5. Calculated and measured solubilities of oxygen in the ethanol−2-propanol mixed solvent system at 298.2 K and 101.3 kPa: (○) observed value and (●) calculated value.
Figure 6. Calculated and observed solubilities of oxygen in the 2propanol−cyclohexane mixed solvent system at 298.2 K and 101.3 kPa: (○) observed value and (●) calculated value.
nitrogen in cyclohexane−benzene, cyclohexane−1-hexane, cyclohexane−CCl4, and benzene−CCl4 mixed solvent systems.16 For the ethanol−2-propanol and hexane−cyclohexane systems, the oxygen solubilities were close to the ideal solubility of oxygen in the mixed solvents. This is considered to be because the interaction forces of the two solvents in the mixed solvents are similar. The solubility of oxygen in the mixed solvents was calculated using the HSPs of oxygen and the solvents. The HSPs of the mixed solvents were calculated using eq 6. The Ra values were
Figure 3. Calculated and measured solubilities of oxygen in the ethanol−cyclohexane mixed solvent system at 298.2 K and 101.3 kPa: (○) observed value and (●) calculated value. 19335
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investigation is required to determine the correlation between the HSPs and solubility for gases other than oxygen.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■ Figure 7. Calculated and measured solubilities of oxygen in the 2propanol−hexane mixed solvent system at 298.2 K and 101.3 kPa: (○) observed value and (●) calculated value.
NOMENCLATURE D = diameter of gas pump, cm E = cohesive energy, J/mol h = scale markings of gas pump, cm L = Ostwald coefficient m = mass of solvent, g P = pressure, kPa Ra = solubility parameter, MPa1/2 R0 = radius of Hansen solubility sphere, MPa1/2 RED = relative energy difference u = standard uncertainty V = molar volume, cm3/mol x = mole fraction X = input quantity δ = solubility parameter, MPa1/2 ε = reproducibility π = circular constant ρ = density, g cm−3 σ = deviation φ = volume fraction
Subscripts Figure 8. Calculated and observed solubilities of oxygen in the hexane−cyclohexane mixed solvent system at 298.2 K and 101.3 kPa: (○) observed value and (●) calculated value.
determined using the HSPs of the mixed solvents and oxygen. The solubility of oxygen in the mixed solvents was calculated by substituting Ra into eq 19. The solubilities of oxygen calculated using the HSPs are shown in Figures 3−8. The average difference between the measured and calculated values was 2.34% for the ethanol−cyclohexane system, 4.43% for the ethanol−hexane system, 2.54% for the ethanol−2-propanol system, 1.62% for the 2-propanol−cyclohexane system, 4.40% for the 2-propanol−hexane system, and 0.94% for the hexane− cyclohexane system. For the ethanol−cyclohexane, ethanol− hexane, 2-propanol−cyclohexane, and 2-propanol−hexane systems, the solubility of oxygen calculated using the HSPs was higher than the ideal solubility as well as the measured value. In addition, the calculated solubilities were close to the ideal solubility as well as the measured values for the hexane− cyclohexane and ethanol−2-propanol systems. This is because the HSPs of the solvents in the mixed solvent were similar.
■
A = before gas dissolution ave = average B = after gas dissolution d = dispersion interaction G = gas h = hydrogen-bonding interaction i = component lit. = literature value max = maximum min = minimum obs = measured value p = dipole interaction S = solvent
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5. CONCLUSION The solubility of oxygen in 21 pure organic solvents was measured at 298.2 K and 101.33 kPa. The HSPs of oxygen were calculated from the oxygen solubility in the pure organic solvents. The HSPs of oxygen were δd = 6.7 MPa1/2, δp = 0.0 MPa1/2, δh = 3.8 MPa1/2, and δt = 7.7 MPa1/2. A new calculation method for the HSPs of gases is proposed. It is based on the relationship between oxygen solubility and the HSPs. Further 19336
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