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In Situ Measurement of Reaction Volume and Calculation of pH of Weak Acid Buffer Solutions Under High Pressure Stephen K. Min, Chaminda P. Samaranayake, and Sudhir K. Sastry* Department of Food, Agricultural, and Biological Engineering, The Ohio State University, 590 Woody Hayes Drive, Columbus, Ohio 43210, United States ABSTRACT: Direct measurements of reaction volume, so far, have been limited to atmospheric pressure. This study describes a method for in situ reaction volume measurements under pressure using a variable volume piezometer. Reaction volumes for protonic ionization of weak acid buffering agents (MES, citric acid, sulfanilic acid, and phosphoric acid) were measured in situ under pressure up to 400 MPa at 25 °C. The methodology involved initial separation of buffering agents within the piezometer using gelatin capsules. Under pressure, the volume of the reactants was measured at 25 °C, and the contents were heated to 40 °C to dissolve the gelatin and allow the reaction to occur, and cooled to 25 °C, where the volume of products was measured. Reaction volumes were used to calculate pH of the buffer solutions as a function of pressure. The results show that the measured reaction volumes as well as the calculated pH values generally quite agree with their respective theoretically predicted values up to 100 MPa. The results of this study highlight the need for a comprehensive theory to describe the pressure behavior of ionization reactions in realistic systems especially at higher pressures.
’ INTRODUCTION Weak acid buffer solutions can have pressure-dependent pH changes, due to pressure-dependent ionization equilibria. Although discussed in the literature since the late 1800s,1 current work in high pressure food processing, pharmaceutical science, geology, and marine science has renewed interest in pressure-dependent pH change. The pH affects biological and chemical systems; it influences microorganism and spore inactivation, spore germination, chemical reaction rates, Maillard browning, enzyme activity, protein gel formation, and protein denaturation.24 Since biological and biochemical systems are often studied in buffer solutions, understanding pressure-dependent pH is important to plan experiments and interpret results. Pressurized chemical systems follow LeChatelier’s theory, equilibrating at smaller volumes. Hypotheses state that increasing pressure increases dissociation of weak acids, as ionized products fill smaller volumes due to solvent electrostriction around resulting charged species.5 A consequence of pressuredependent weak acid dissociation is pressure-dependent pH. Planck1 presented a relation for pressure-dependence of the molal equilibrium constant, Ka, of a monobasic weak acid, HA
where ΔV, the reaction volume, is the difference between partial molar volumes of the products and reactants, (ΣiVs)products (ΣiVs)reactants, in an infinitely dilute solution. Integrating eq 3 at constant temperature, the pressure-dependence of pKa can be determined if the pressure-dependence of ΔV is known: Z Pi þ 1 1 pK aPi pK aPi þ 1 ¼ ΔV dP ð4Þ 2:303RT Pi
HA S Hþ þ A
ð1Þ
DpHm DpK a = DP DP
am, Hþ am, A am, HA
ð2Þ
The pKa values determined by the reaction volume data (eq 4) can be used to calculate pHm, which then can be converted to
ð3Þ
Received: November 18, 2010 Revised: March 17, 2011 Published: May 04, 2011
Ka ¼
Dln Ka ΔV ¼ RT DP T r 2011 American Chemical Society
From eq 2, the molal pKa can be related to molal pH (traditionally, pH is defined in terms of molar hydrogen ion activity6), pHm, with the activity coefficient, γ, and molal concentration ratio of the acid (HA) and its conjugate base (A) as γ mA ð5Þ pHm ¼ pK a þ log A þ log γHA mHA For dilute buffer solutions, at constant temperature, the molal pH change as a function of pressure can be approximated as follows (eq 6):7,8
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classical molar pH, pHM, by knowing the density at each pressure (eq 7).6 pHM ¼ pHm log F
ð7Þ
Different approaches have been used to predict equilibrium constants and pH change of weak acid buffer solutions under pressure. The use of thermodynamic and solute/solvent interaction theories to estimate reaction volume and equilibrium constants under pressure has been attempted by several authors.912 The differences in these approaches are summarized by Nakahara,13 and consensus on a correct, comprehensive approach has not been reached.14 Equilibrium constants, calculated using theoretical models, differ from experimental values by up to 15% to 300 MPa for ionization of weak electrolytes.7 Measurement of pH under pressure to 150 MPa using electrical potential measurement across a glass electrode has been reported;15,16 however, this method is limited by pressure tolerance of the electrodes. Electrical conductivity measurements have been used to estimate equilibrium constants of weak acid buffers.1719 High pressure spectrophotometric measurement of pH of buffers by measuring the absorption spectra of solutions containing pH sensitive indicators and fluorophores has been attempted.2024 The indicators have pressure dependent equilibria that are sometimes ignored; additionally, these sensors are calibrated with available conductivity or theoretical data, making them no more accurate than their calibration data. A pH sensor for in situ pH measurement over a wide range of pressure has recently been reported.25 The measured pH changes for buffer solutions were found to be less than predicted using inferred reaction volume data from the literature.26 Measurement of reaction volume at atmospheric pressure has been reported for a range of buffering agents;27 however, no literature is available reporting reaction volume measurement as a function of pressure. The objectives of this study were to (i) develop a method to measure reaction volume for protonic ionization of weak acid buffering agents in situ under pressure; (ii) measure reaction volumes for protonic ionization of 2-(Nmorpholino)ethanesulfonic acid (MES), citric acid, sulfanilic acid, and phosphoric acid from 0.1 to 400 MPa at 25 °C; and (iii) calculate pH of the above weak acid buffer solutions as a function of pressure.
’ EXPERIMENTAL APPARATUS AND PROCEDURE Pressure Generating System. A hydrostatic pressure system (26190, Harwood Engineering), rated to 1000 MPa and 150 °C, was used. The pressure transmitting medium was 50/50 propylene glycol/distilled, demineralized water. The cylindrical, jacketed pressure vessel had interior dimensions of 2.5 cm diameter and 15 cm depth; the vessel’s top closure housed electrically insulated copper and type K thermocouple wire feedthroughs, allowing electric signal and temperature measurement in the vessel. A temperature controlled propylene glycol bath recirculated through a jacket around the vessel, allowing control of sample temperature. Method Development. A previous approach to measure reaction volume at atmospheric pressure was described by Kitamura and Itoh.27 They separated known volumes of acid and base in a dilatometer, mixed the reactants, and measured the volume of the resulting product. A mixing dilatometer, similar to that of Kitamura and Itoh,27 could not be realized with the constraints of available pressure equipment. Therefore, a new
Figure 1. Temperature and reaction progression of bulk and capsule solutions under pressure. Left: intact capsules separating reactant solutions at 25 °C before heating. Middle: melting gelatin capsules at 40 °C. Right: mixed solution at 25 °C after heating.
method was developed for in situ measurement under pressure, using a variable volume piezometer. The piezometer, of cylindrical shape, was equipped with a movable copper piston at one end. When pressurized, piston movement in response to compression caused an impedance change in a coil wound around the piezometer. The impedance change was calibrated against volume changes of water as described below. A detailed piezometer description was previously reported by Min et al.28 Reactants were separated by sealing one reactant in three gelatin capsules, which were submerged within the other reactant, contained in the piezometer. The reactants were then pressurized to test pressure, and impedance, corresponding to reactant volume in the piezometer, was measured at 25 °C. The sample temperature was raised to 40 °C, allowing the capsules to melt and the reaction to start. The sample was then cooled, still at test pressure, and impedance was measured at 25 °C, corresponding to product volume in the piezometer. Figure 1 shows the temperature and reaction progression under pressure. A control experiment was performed in the same manner with gelatin and water to account for the volume change of background reactions. Differences between pre- and postheating impedance readings at 25 °C for the test (acid, base, gelatin) and control (water, gelatin) were used to calculate volume change with an experimentally determined calibration factor. Reaction volume measurements were made at different pressures, and pH was calculated from the reaction volume data. Calibration of the Piezometer. The purpose of calibration was to associate a volume change with impedance change due to piston movement at each pressure. Min et al.28 described an isothermal calibration procedure, which was herein modified for the reaction volume measurements. An isothermal calibration factor, (∂V/∂Z)T, can be defined as a product of (∂V/∂P)T and (∂P/∂Z)T. By knowing the pressure dependence of the volume and the impedance, the calibration factor, CF (cm3 Ω1), can be determined as DV ðDV =DPÞT CF ¼ ¼ ð8Þ DZ T ðDZ=DPÞT 6565
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The piezometer was filled with distilled, deionized water and pressurized; temperature was stabilized at 25 °C, and impedance was recorded. The National Institute of Standards and Technology (NIST)29 pressuredensity data for water and the known mass of water in the piezometer were used to calculate volume of water in the piezometer at each test pressure. The above calibration measurements were performed in triplicate, and typical values are shown in Table 1. According to Min et al.,28 the volume data were fitted to an exponential regression equation to correlate volume as a function of pressure. Similarly, as the volume is proportional to the impedance, the impedance data were also fitted to an exponential regression equation to correlate impedance as a function of pressure. The calibration factor was calculated (Table 1) at each test pressure according to eq 8 differentiating the regression equations. Reaction Volume Measurement. As previously described, reaction volumes for protonic ionization of weak acid buffering agents were measured by separating one reactant, the capsule solution, inside three gelatin capsules from the other reactant, the bulk solution, inside the piezometer. Table 2 shows the reactant designation, capsule or bulk solution, for each reaction studied. ACS grade weak acids were used as buffering agents. Aqueous stock solutions were prepared in distilled, demineralized water of (1) 0.603 M 2-(N-morpholino)ethanesulfonic acid (MES) (Fluka), (2) 0.572 M citric acid (Aldrich), (3) 0.053 M sulfanilic acid (Acros Organics), and (4) 0.058 M phosphoric acid (Aldrich). NaOH (Mallindckrodt) solutions of different concentrations were prepared for reactions with the buffering agents. The NaOH concentration for reaction with each weak acid buffering agent was determined by completing trial and error reactions at atmospheric pressure to yield the desired end pH. The pH of solutions at atmospheric pressure was measured with a glass electrode and pH meter (Fisher Allied, Accumet 810). USP grade, size 2 (0.37 mL) gelatin capsules were used to isolate the NaOH solutions from the buffering agent solutions. Preliminary testing, measuring no change of electrical conductivity and pH of the bulk solution before and after pressurization for 10 min, with each buffering agent/NaOH combination confirmed that gelatin successfully isolated the materials at all pressures at 25 °C and below for 10 min. Table 1. Typical Calibration Data Obtained from the Measurements with Water (25°C)
a
P (MPa)
V (cm3)
Zava (Ω)
CF (cm3 Ω1)
0.1
7.662
25.214
0.302
100 200
7.322 7.090
24.583 24.067
0.299 0.296
300
6.903
23.625
0.293
400
6.746
23.336
0.290
Standard deviation of the measurements 300 MPa),34 and existence of localized structural heterogeneities of liquid water35 could be responsible for the observed deviation of the measurements from the calculated results. Therefore, in reality, achieving infinite dilution at higher pressures (>100 MPa) may be practically not possible, consequently limiting the validity of the theoretical calculations based on infinite dilution to lower pressures. 6568
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Figure 3. Reaction volume for protonic ionization of citric acid as a function of pressure at 25 °C. Filled circles with solid line and open circles with dashed line show measured and calculated reaction volumes, respectively. Error bars represent standard deviation of the experimental measurements. Reaction volumes were calculated from the El’yanov and Hamann equation (eq 17).11
Figure 4. Reaction volume for protonic ionization of sulfanilic acid as a function of pressure at 25 °C. Sulfanilic acid was tested up to 200 MPa due to its poor solubility described in the text. Filled circles with solid line and open circles with dashed line show measured and calculated reaction volumes, respectively. Error bars represent standard deviation of the experimental measurements. Reaction volumes were calculated from the El’yanov and Hamann equation (eq 17).11
Calculated pH of the Buffer Solutions as a Function of Pressure. Figure 6 shows the classical molar pH, calculated
using eqs 14 and 16, as a function of pressure for the buffer solutions. The largest change is seen in phosphoric acid buffer dropping an average of 0.25 pH units per 100 MPa, while citric acid buffer lowers its pH by 0.13 units per 100 MPa. Sulfanilic acid buffer shows almost no pH sensitivity to pressure, whereas MES buffer increases its pH by 0.075 units per 100 MPa. The above results suggest that increasing ionization of phosphoric acid and citric acid as a function of pressure increases hydrogen ion concentration, promoting pH decrease, whereas MES and sulfanilic acid show relative pH stability under pressure. A quantitative expression for the pressure dependence of ionic equilibria was proposed by El’yanov and Hamann11 on the basis of the same data as in eq 17; the only inputs were reaction volume
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Figure 5. Reaction volume for protonic ionization of phosphoric acid as a function of pressure at 25 °C. Filled circles with solid line and open circles with dashed line show measured and calculated reaction volumes, respectively. Error bars represent standard deviation of the experimental measurements. Reaction volumes were calculated from the El’yanov and Hamann equation (eq 17).11
Figure 6. Calculated pH of weak acid buffer solutions as a function of pressure at 25 °C. MES, citric acid, sulfanilic acid, and phosphoric acid are depicted by diamonds, squares, triangles, and circles, respectively. Filled symbols represent pH calculated with the measured reaction volumes in situ under pressure in this study. Open symbols represent pH calculated using the El’yanov and Hamann equation (eq 18)11 with the reaction volumes measured under atmospheric pressure in this study (see the text for calculations).
at infinite dilution and molal equilibrium constant at atmospheric pressure: ! Ka P PΔVo ¼ ð18Þ log Ka o 2:303RTð1 þ bPÞ Equation 18 has since been applied to calculate pH of weak acid buffers under pressure with reaction volumes determined at atmospheric pressure.12 With the above equation (eq 18), the differences in molal pKa at incremental pressures can be calculated, and then those differences can be used to calculate pH as a function of pressure according to eqs 14 and 16. This particular calculation procedure was performed with the reaction volumes 6569
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Table 6. pH Change Calculated from This Study Compared with Previously Reported Values in the Pressure Range 0.1400 MPa (25°C) buffer MES
citric acid
sulfanilic acid
phosphoric acid
pH at 0.1 MPa a
(ΔpH)/100 MPa
5.3
0.075
4.0b
0.035
5.0b
0.06
5.0c
0.25
4.55a 4.0b
0.13 0.025
5.0b
0.03
7.0e
0.17
3.2a
0.005
3.23b
0.005
3.23d
0.02
6.9a
0.25
6.86b 7.2c
0.07 0.46
6.90d
0.34
7.0e
0.18
a
This study. b Samaranayake and Sastry.26 c Hayert et al.24 d El’yanov.7 e Quinlan and Reinhart.23
measured under atmospheric pressure in this study (Table 5), and the results are displayed in Figure 6. It can be seen that the calculated pH from the in situ reaction volume measurements in this study and that from the El’yanov and Hamann’s equation (eq 18)11 are the same up to 100 MPa for all the buffer solutions (up to 200 MPa for sulfanilic acid). However, beyond 100 MPa, the calculation procedure based on the El’yanov and Hamann’s equation (eq 18)11 predicts higher or lower pH values relative to those calculated from the in situ reaction volume measurements in this study. The differences in calculated pH at higher pressures (>100 MPa) relate to the pKa calculation, by the in situ reaction volume measurements versus by the El’yanov and Hamann’s equation (eq 18). Table 6 compares calculated pH from this study with previously reported data. Although some results of this study are comparable to the values reported in literature (e.g., sulfanilic acid data), none of the literature data are considered as “standard data” to verify the accuracy of the results of this study. The differences in results among studies in Table 6 indicate the methodological differences in pH determination under high pressure. It is important to note that all the reaction-volumebased pH calculation procedures, including this study, exclusively consider the protonic ionization reaction (eq 1) of buffering agents. However, in addition to the buffering agent, a buffer solution contains water and, possibly, many other dissolved substances (unknown), either present in distilled, demineralized water (e.g., dissolved CO2) or accompanied as impurities with the chemicals used for pH adjustment of the buffer. Upon pressurization, dissociation of water and ionization reactions of some dissolved substances involving protons can modify the theoretically expected pH of the buffer. Furthermore, water is considered as a homogeneous medium under pressure in developing reaction-volume-based theoretical relationships.14 However, in reality, localized structural heterogeneities of liquid water do exist even at 300 MPa35 influencing the movement of protons (and thereby pH) under high pressure. Stippl et al.14 have
reviewed the existing reaction-volume-based theoretical relationships and highlighted the importance of a comprehensive theory, which is yet to be developed, to describe the pressure behavior of ionization reactions in realistic systems. In situ pH measurement under high pressure (up to 784.6 MPa) with a hydrogen ion selective sensor shows that the measured pH changes for buffer solutions are generally less than predicted using inferred reaction volume data from the literature.26
’ CONCLUSIONS Using a variable volume piezometer, a method has been successfully developed for in situ reaction volume measurements under pressure. The method has also been validated by measuring reaction volumes under atmospheric pressure for protonic ionization of weak acid buffering agents and comparing with the respective values reported in literature. The measured reaction volumes are generally quite comparable to the calculated values by El’yanov and Hamann’s equation up to 100 MPa. Beyond this pressure, the measured reaction volumes start deviating from the respective calculated values, possibly indicating the limited validity of the theoretical calculations for realistic systems at higher pressures. The results of pH calculation of the buffer solutions by the measured reaction volumes and by El’yanov and Hamann’s equation follow a similar trend up to and beyond 100 MPa. For a buffer solution at the same pressure and temperature, various pH values reported among studies suggest that methodologies to measure pH in situ under pressure should continue to be developed until consensus for pH values under pressure exists. ’ AUTHOR INFORMATION Corresponding Author
*Phone: (614) 292-3508. Fax: (614) 292-9448. E-mail: sastry.2@ osu.edu.
’ ACKNOWLEDGMENT The authors would like to acknowledge research support provided by USDA-CSREES-NRICGP grant 2005-3550315365, by the Ohio Agricultural Research and Development Center (OARDC), by the Ohio State University and by the Center for Advanced Processing and Packaging Studies (CAPPS). The authors also would like to acknowledge Dr. V.M. Balasubramaniam for his support for this study. References to commercial products or trade names are made with understanding that no endorsement or discrimination by the Ohio State University is implied. ’ NOMENCLATURE a Chemical activity (mol kg1 or mol L1, depending if subscript is m or M) CF Calibration factor (cm3 Ω1) Molal equilibrium constant Ka P Pressure (Pa or MPa) R Universal gas constant (8.314 J K1 mol1) T Temperature (K) V Partial molar volume at infinite dilution (m3 3 mol1) V Volume (cm3 or m3) Z Impedance (Ω) ΔV Reaction volume at infinite dilution (m3 mol1) 6570
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Activity coefficient Density (kg m3)
’ SUBSCRIPTS av Average of replicates i Test pressure i iþ1 Test pressure i þ 1, incrementally higher than pressure i m Molal basis M Molar basis o At atmospheric pressure P Refers to pressurized condition s Species s T Constant temperature ’ REFERENCES (1) Planck, M. Ann. Phys. Chem. 1887, 2 (32), 462–500. (2) Rastogi, N. K.; Raghavarao, M. S.; Balasubramaniam, V. M.; Niranjan, K.; Knorr, D. Crit. Rev. Food Sci. Nutr. 2007, 47, 69–112. (3) Hendrickx, M.; Knorr, D. Ultra High Pressure Treatment of Foods; Plenum Publishing: New York, 2001. (4) Barbosa-Canovas, G. V.; Tapia, M.; Pilar Cano, M. Novel Food Processing Technologies; CRC Press: New York, 2005. (5) Hamann, S. D. Rev. Phys. Chem. Jpn. 1980, 50, 147–168. (6) McCarty, C. G.; Vitz, E. J. Chem. Educ. 2006, 83 (5), 752–757. (7) El’yanov, B. S. Aust. J. Chem. 1975, 28, 933–943. (8) Neumann, R. C.; Kauzmann, W.; Zipp, A. J. Phys. Chem. 1973, 77 (22), 2687–2691. (9) North, N. J. Phys. Chem. 1973, 77 (7), 931–934. (10) Owen, B. B.; Brinkley, S. Chem. Rev. 1941, 29, 461–474. (11) El’yanov, B. S.; Hamann, S. D. Aust. J. Chem. 1975, No. 28, 945–954. (12) Bruins, M. E.; Matser, A. M.; Janssen, A.; Boom, R. M. High Pressure Res. 2007, 27 (1), 101–107. (13) Nakahara, M. Rev. Phys. Chem. Jpn. 1974, 44 (2), 57–64. (14) Stippl, C. M.; Delado, A.; Becker, T. M. Eur. Food Res. Technol. 2005, 221, 151–156. (15) Disteche, A. Rev. Sci. Instrum. 1959, 30 (6), 474–478. (16) Crolet, J. L.; Bonis, M. R. Corrosion-NACE 1983, 39 (2), 39–46. (17) Hamann, S. D.; Strauss, W. Trans. Faraday Soc. 1955, 51, 1684–1690. (18) Lown, D. A.; Thirsk, H. R.; Wynne-Jones, L. Trans. Faraday Soc. 1970, 66, 51–73. (19) Kalinina, A. G.; Kryukov, P. A. International Corrosion Conference Series; National Association of Corrosion Engineers: Houston, TX, 1976; pp 158163. (20) Neumann, R. C.; Kauzmann, W.; Zipp, A. J. Phys. Chem. 1973, 77 (22), 2687–2691. (21) Tsuda, M.; Shirotani, I.; Minomura, S.; Teryama, Y. Bull. Chem. Soc. Jpn. 1976, 49 (11), 2952–2955. (22) Stippl, V. M.; Delgado, A.; Becker, T. M. Innovative Food Sci. Emerging Technol. 2004, 5, 285–292. (23) Quinlan, R. J.; Reinhart, G. D. Anal. Biochem. 2005, 341, 69–76. (24) Hayert, M.; Perrier-Cornet, J. M.; Gervais, P. J. Phys. Chem. A 1999, 103, 1785–1789. (25) Sastry, S. K.; Samaranayake, C. P. Apparatus and Method for Measurement of pH over a Wide Range of Pressure. U.S. Patent Application Number 60/971, 068. (26) Samaranayake, C. P.; Sastry, S. K. In-Situ Measurement of pH Under High Pressure. J. Phys. Chem. B 2010, 114, 13326–13332. (27) Kitamura, Y.; Itoh, T. J. Solution Chem. 1987, 16 (9), 715–725. (28) Min, S.; Sastry, S.; Balasubramaniam, V. M. High Pressure Res. 2009, 29 (2), 278–289. (29) NIST Chemistry WebBook, http://webbook.nist.gov/chemistry/, accessed Jan 2011.
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