4788
Ind. Eng. Chem. Res. 1996, 35, 4788-4795
Spectroscopic Measurement of pH in Aqueous Sulfuric Acid and Ammonia from Sub- to Supercritical Conditions Tao Xiang and Keith P. Johnston* Department of Chemical Engineering, The University of Texas, Austin, Texas 78712
William T. Wofford and Earnest F. Gloyna Department of Civil Engineering, The University of Texas, Austin, Texas 78712
The pH of aqueous sulfuric acid and sulfuric acid-ammonia mixtures was measured using the optical indicator acridine at temperatures from 200 to 400 °C and pressures from 3500 (24.1) to 6000 psia (41.3 MPa). Because of large changes in the pKa of protonated acridine in supercritical water (SCW), the measurable pH range shifts from 2-4 at a density of 0.60 g/cm3 to 4.5-7 at a density of 0.24 g/cm3. At 3500 psia, the first dissociation constant (Ka1) of H2SO4 decreases sharply with increasing temperature above 350 °C, primarily due to a reduction in density and thus the solvation of the bisulfate and hydrogen ions. The acidity of H2SO4 relative to HCl increases with increasing temperature at constant pressure up to the critical point of pure water. Based on titrations of sulfuric acid solutions with ammonia, weak acid-weak base behavior is observed at 380 °C and 5000 psia (34.5 MPa). At these conditions the system H2SO4-NH4HSO4 may be used as a buffer to maintain pH in the range 3.5 ( 0.25. Introduction Knowledge of pH and the thermodynamic properties of acid-base reactions is crucial to understanding the thermochemistry and reaction chemistry of hydrothermal processes such as oxidation of organics (Gloyna and Li, 1993; Tester et al., 1993), metal corrosion, formation and precipitation of metal-hydroxy complexes and/or salts, catalysis, and hydrolysis (Klein et al., 1992). In steam power cycles at near critical conditions, dilute acid impurities are neutralized with bases such as ammonia to minimize corrosion (White et al., 1995). Ulmer and Barnes (Ulmer and Barnes, 1987) have compiled a list of buffers useful in high-temperature, high-pressure, aqueous solutions. The thermodynamic data needed for calibration of these buffers are limited to temperatures below 350 °C, with the exception of the HCl-Cl- buffer with an upper temperature limit of 800 °C (Ulmer and Barnes, 1987). Thus, the application of pH buffers to supercritical water (SCW) solutions is in its infancy. Hydrothermal pH sensors of ZrO2, palladium hydrides, and iridium oxides up to 300 °C have been reviewed (Bourcer et al., 1987). Recent advances in the development of several types of sensors for SCW solutions up to 600 °C have also been reviewed (Kriksunov and Macdonald, 1994). Yttria-stabilized zirconia (YSZ) and W/WO3 electrodes being developed by Macdonald and co-workers promise to provide a useful method for measuring pH in high-temperature oxidizing environments, such as those found in electric power generation and hydrothermal oxidation sytems. Important improvements have been made in developing reference electrodes to reduce uncertainty in the thermal liquid junction potential (Kriksunov and Macdonald, 1994). A complimentary technique for characterizing the acidity of aqueous solutions is to determine the acid-base ratio of an optical indicator from its UVvis absorption spectra (Hafeman et al., 1993; Huh et al., 1993). Recently, the dissociation constants for 2-naphthol, 2-naphthoic acid, s-collidine, and acridine have been determined up to 400 °C and 6000 psia (Xiang and Johnston, 1994, 1996; Ryan et al., 1996). The pHdependent absorption spectra of these compounds, in S0888-5885(96)00368-5 CCC: $12.00
conjunction with the measured dissociation constants, may be used to determine the pH of unknown solutions. For hydrothermal oxidation systems (also called SCW oxidation or SCWO), optical indicators may be used to characterize the pH behavior of feed solutions or their simulants in the absence of the oxidant. The objective of this work was to utilize the optical indicator acridine to measure the pH of aqueous sulfuric acid and an aqueous mixture of sulfuric acid and ammonia. At temperatures above 350 °C, where the second dissociation constant of sulfuric acid is negligible, the measured pH values were used to calculate the first dissociation constant (Ka1) of H2SO4 as a function of temperature and density. A modified Born model was used to extrapolate earlier Ka1 data from low temperature to SCW conditions, and these results are compared with the new data. Finally, titration curves for the addition of ammonia to sulfuric acid were measured up to 380 °C and 5000 psia (34.5 MPa). Pronounced differences in acid-base titration curves at ambient conditions and at supercritical water conditions are examined in terms of large changes in ion solvation due to a reduction in the dielectric constant. The results are relevant for understanding the neutralization of acids and for the preparation of buffer solutions in SCW. Experimental Section The water was deionized (Barnstead Nanopure II) and deoxygenated with nitrogen. Acridine (Aldrich) was purified by vacuum sublimation at approximately 180 °C. Reagent-grade 96.0 wt % sulfuric acid (Aldrich) was used to prepare a stock solution of 0.216 m (mol kg-1) H2SO4, and a commercial solution of 30.0% ammonium hydroxide-water (Mallinckrodt) was used to make a stock solution of 0.4465 m NH3. These solutions were used without further purification. The concentration of acridine in the feed solutions was fixed at approximately 10-4 m, which was the minimum concentration necessary in order to obtain accurate absorbance spectra at all experimental conditions. The concentration of sulfuric acid was varied between 5 × 10-4 and 10-2 m H2SO4, depending upon the tempera© 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4789
ture and the density of the experiment. All solutions containing acridine were prepared within 24 h of use and purged with nitrogen immediately before each experiment. UV-vis absorption spectra were obtained with the same experimental apparatus described previously (Bennett and Johnston, 1994; Xiang and Johnston, 1994). The stability of acridine in pure water at high temperatures and pressures was first tested in batch stainless steel reactors (Xiang and Johnston, 1994). Products were analyzed by gas chromatography, and no significant change in acridine concentration was observed during the 2 h test period at 400 °C and 5000 psia. The effect of H2SO4 on the stability of acridine was tested directly in the UV-vis absorbance cell. At temperatures between 300 and 400 °C and H2SO4 concentrations ranging from 10-3 to 10-2 m, the absorbance of acridine changed less than 2% in 5 min, which was considered satisfactory for use as an indicator. The absorbance cell was flushed with a fresh solution prior to obtaining each spectrum as an added precaution to minimize the effect of indicator decomposition. After flushing, the temperature of the cell was allowed to equilibrate for approximately 1 min before beginning the spectral scan. During a spectral scan, which lasted 20 s, temperature varied less than 1 °C and the pressure changed less than 0.6 bar. The baseline absorbance of pure water in the optical cell was measured at several temperatures during the course of each experiment and used to correct the solution spectra for changes in the absorbance properties of the sapphire windows. In general, the absorbance of sapphire in the wavelength range of interest (400-500 nm) increased uniformly with increasing temperature and also with the gradual corrosion of the window surface. Sapphire corrosion was found to be more severe in alkaline solutions (pH25 °C > 9) than in neutral or acidic solutions, necessitating more frequent baseline corrections and window replacement. Results and Discussion Measurement of pH in Aqueous Sulfuric Acid. The pH-dependent absorption spectra of acridine can be used to measure the pH of aqueous solutions. Consider the reversible reaction between the organic base acridine and the hydrogen ion:
B + H+ ) BH+
(1)
The equilibrium constant, Ka for the protonation of a base is defined in terms of the activities of the products and reactants as -1,
Ka-1 )
Kb aBH+ ) Kw aBaH+
(2)
From eq 2 it is evident that Ka-1 is a relative property relating the basicity of acridine to that of water (Ryan et al., 1996). Using the standard definitions, pH ) -log aH+ and a ) γm where γ is the activity coefficient, eq 2 can be rewritten as
pH ) log Ka-1 - log
γ(mBH+ mB
(3)
where γ( is the mean activity coefficient of ions and mBH+ and mB are the molal concentrations of the acidic and basic forms of acridine, respectively. The total
Figure 1. Effect of sulfuric acid concentration on the absorbance spectra of acridine at 380 °C and 6000 psia. The symbols are shown only to identify the pH in the legend.
absorbance of acridine at a given wavelength, λ, is a linear combination of the absorbance of the acidic and basic species. For a fixed path length,
λ[B]0 ) λa[BH+] + λb[B]
(4)
where [B]0 is the initial molar concentration of acridine, [BH+] and [B] are the molar concentrations of the acidic and basic species, and λa, λb, and λ are the extinction coefficients of the pure acidic species (low pH limit), the pure basic species (high pH limit), and the solution mixture, respectively. Notice that, unlike λa and λb, the value of λ is a function of pH because the distribution of BH+ and B within the solution mixture is a function of pH. The total concentration of acridine and sulfuric acid varied between 10-4 and 10-2 m. For these dilute solutions, the relationship between molarity and molality is given by
[B]0 ≈ Fm0B
(5)
where F is the density of water and mB0 is the initial molal concentration of acridine. The same relationship holds for both the acidic and basic species. Thus, eq 4 becomes
λmB0 ) λamBH+ + λbmB
(6)
where mBH+ and mB are the molal concentrations of the acidic and basic species of acridine, respectively. Figure 1 shows the absorbance spectra of acridine at 380 °C and 6000 psia in several different solutions of sulfuric acid. In order to compare the spectra of solutions with small differences in acridine concentration, the absorbance values were normalized to a concentration of 10 -4 M and multiplied by the factor F0/F, where F0 is 1 g cm-3 and F is the experimental water density. The purpose of the second factor was to compensate for the change in indicator concentration within the optical cell due to changes in water density. The large differences between λa and λb at wavelengths between 400 and 500 nm make this an ideal range for measuring mBH+ and mB. From the material balance we have
mB0 ) mBH+ + mB Substituting eq 7 into eq 6 and rearranging gives
(7)
4790 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
mBH+ λ - λb ) a mB - λ
(8)
λ
Finally, substituting eq 8 into eq 3 and integrating from 400 to 500 nm yields the result:
(
pH ) log Ka-1 - log γ(
500λ
- λb
λ
λ
∫400 a -
dλ
)
(9)
At a given temperature, the integrated values of λa and λb are constants which were found to be independent of pressure over the range of experimental conditions. In this work, solutions with pH25 °C ) 1.5 and ) 9.2 were used to determine the values of λa and λb, respectively. For a dilute solution, the mean activity coefficient, γ(, may be considered independent of the relative compositions of the mixture and dependent only on the total ionic strength, I. The value of I at experimental conditions was on the order of 10-3 m, which was considered sufficiently dilute to calculate γ( using Pitzer’s formulation of the Debye-Hu¨ckel equation, neglecting the composition-dependent terms (Pitzer, 1991).
ln γ( ) -|zMzX|Aφ
(
Figure 2. Effect of temperature on the absorbance spectra of acridine in a solution of sulfuric acid at 3500 psia. The symbols are shown only to identify the temperature in the legend.
I1/2 + 1.6667 ln(1 + (1 + 1.2I1/2)
)
1.2I1/2) (10) where
I)
∑mizi2 ) 2(mHSO 1
1 2
Aφ )
(
-
4
+ mH+ + mBH+)
)( )
1 2πN0Fw 3 1000
1/2
e2 kT
2/3
and N0 is Avogadro’s number, and the standard state for γ( is defined at infinite dilution. Values for acridine up to 400 °C and 6000 psia have been determined previously from the reaction between acridine and hydrochloric acid (Ryan et al., 1996). In order to measure Ka-1, it was necessary to use literature data for the ionization constant, Ka, of hydrochloric acid (Frantz and Marshall, 1984). The uncertainty in log Ka when calculated from the correlation given by Frantz and Marshall was approximately (0.2 log units at 400 °C and 0.6 g cm-3. The dielectric constant, , was calculated from the equation given by Uematsu and Frank (Uematsu and Franck, 1980), and the water density, F, was obtained from the steam tables (Haar et al., 1984). With values for Ka-1 as a function of temperature and pressure, the pH of a solution containing acridine can be calculated from eq 9 by using the integrated UV-vis spectra. Figure 2 shows typical absorbance spectra for acridine in solutions of sulfuric acid (pH25 °C ) 2.75) as a function of temperature at 3500 psia. The decrease in absorbance with increasing temperature at constant pressure indicates that acridine becomes less protonated at high temperatures. This results from the exothermic nature of the two reactions of interest: (1) the ionization of sulfuric acid and (2) the isocoulombic reaction of acridine with H+. As temperature increases, the equilibria of the two reactions shift in the direction which lowers the
Figure 3. Effect of pressure on the absorbance spectra of acridine in a solution of sulfuric acid at 380 °C. The symbols are shown only to identify the pressures in the legend.
concentration of the protonated form of acridine. The shift is greater for sulfuric acid, since this reaction is ionogenic. Figure 3 shows the spectra of acridine as a function of pressure at 380 °C. Acridine becomes less protonated with decreasing pressure. The reason for this behavior stems from the changes occurring in the solvent properties of water. At near-critical and supercritical temperatures, the density and dielectric constant () of water are strong functions of pressure. A reduction in pressure results in a large decrease in density and . At 380 °C, Ka-1 will increase with decreasing pressure because the BH+ ion has a much smaller charge per volume than H+ and is therefore favored by the smaller dielectric constant (Ryan et al., 1996). However, Figure 3 shows that acridine becomes less protonated with decreasing pressure at 380 °C, suggesting that the effect of pressure on Ka-1 is overshadowed by the effect of pressure on the dissociation constants (Ka1 and Ka2) of sulfuric acid. Since is a measure of solvent polarity and, indirectly, hydrogen-bonding strength, the ionic products generated by the dissociation of sulfuric acid will be more difficult to solvate following a large reduction in the of water. Thus, the dissociation reaction equilibrium will shift in favor of the neutral reactant, H2SO4. The resulting decrease in H+ concentration is why acridine becomes less protonated with decreasing pressure at 380 °C even though Ka-1 actually increases. At high temperatures, especially above the critical point of water, Ka2 is much smaller than Ka1 (Oscarson et al., 1988), so that the decrease in absorbance of acridine results mainly from the decrease in Ka1. A quantitative description of the changes in Ka1 of
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4791
Ka1 )
Figure 4. Effect of temperature on the pH of sulfuric acid solutions measured with acridine. All data were measured at 3500 psia except for the data at 400 °C, which were measured at 4000 psia.
γ(2mHSO4-mH+
(12)
mH2SO4
where, for dilute solutions, the activity of water is defined to equal unity and the activity coefficients of the individual ions have been replaced with the mean ionic activity coefficient. The activity of water defined equal to unity is the convention most commonly taken for expressing the dissociation constant (Frantz and Marshall, 1984). In some studies an alternative equilibrium constant has been defined by representing the activity of water by its concentration or density (Franck, 1956; Quist and Marshall, 1968; Wofford et al., 1995). However, the changes in the value of Ka1 resulting from the addition of an explicit density term in the denominator of eq 12 are small compared to the changes in Ka1 which occur due to variations in dielectric constant. Assuming that the second dissociation reaction can be neglected at temperatures g350 °C, we have from the charge balance
mHSO4- ) mH+ + mBH+
(13)
and from the material balance
mH2SO40 ) mH2SO4 + mHSO4-
(14)
where mH2SO40 is the initial molal concentration of H2SO4. Substituting eqs 13 and 14 into eq 12 yields the following expression for Ka1: Figure 5. Effect of density on the pH of a 7.8 × 10-3 m H2SO4 solution.
sulfuric acid as a function of temperature and pressure (or density) will be given later. Figure 4 shows the change in pH as a function of temperature at 3500 psia in solutions of 7.8 × 10-3 and 5.4 × 10-4 m H2SO4. The concentration of acridine was 10-4 m, and the values of pH were calculated according to eqs 9 and 10. The pH measurements shown in Figure 4 support the previous discussion regarding the effects of temperature on the dissociation of sulfuric acid. Figure 5 illustrates the change in pH with density for a 7.8 × 10-3 m H2SO4 solution. At subcritical temperatures, the change in pH with density is small. Above 350 °C the pH of the sulfuric acid solution becomes strongly dependent on density as a result of the large changes in the dielectric constant and the subsequent effects on the solvation of the ionic species HSO4- and H+. Measurement of the First Dissociation Constant of Sulfuric Acid in SCW. The first dissociation constant (Ka1) of sulfuric acid may be calculated from the pH values measured using acridine at temperatures where the assumption Ka1 . Ka2 . Kw is valid. Above 350 °C, the magnitude of the second dissociation constant (Ka2) is small, on the order of 10-7 (Oscarson et al., 1988), and the first dissociation reaction may be considered the only source of hydrogen ions. The dissociation behavior of sulfuric acid in SCW can be described by the reaction:
H2SO4 + H2O ) H3O+ + HSO4For eq 11, Ka1 is defined as
(11)
Ka1 )
(mH+2 + mH+mBH+)γ(2
(15)
(mH2SO40 - mH+ - mBH+)
Ka1 can then be calculated from eqs 10 and 15 from the known value of mH2SO40 and the values of mH+ and mBH+ determined from the UV-vis spectra of acridine. Experimental conditions and calculated values of pH and Ka1 are summarized in Table 1. The measured values of log Ka1 for the first dissociation constant of sulfuric acid at 3500 psia are plotted in Figure 6 for temperatures of 350, 380, and 400 °C. In addition, reference data are shown for log Ka1 measured between 150 and 320 °C along the saturation curve by Oscarson and co-workers (Oscarson et al., 1988). The light dashed line is based on the equation given by Oscarson and co-workers for the best fit to their experimental data between 150 and 320 °C. The heavy dashed line was calculated at 3500 psia from an equation derived in our previous work using the Born model of ion solvation (Xiang and Johnston, 1994)
ln Ka1 ) -
(
(
) )
∂ ln Ka1 ∆G°(T0,F0) ∆G°(T,F) )+ RT RT0 ∂(1/T)
)
( )(
×
F0
1 83549 1 1 1 1 1 + (16) T T0 T 0 R* R* H+ HSO4-
where Τ and F are the experimental temperature and water density, the reference temperature, T0, is 298.15 K, the reference density, F0, is 1 g cm-3, ) (T,F), and 0 ) 0(T,F0). Due to the difficulty in estimating the radius of the solvated proton, R* H+, and because of the large uncertainty in measurement of ln Ka1 at room temperature for such a strong acid, the terms -∆G°/ RT0, (∂ ln Ka1/∂(1/T))F0, and (1/R*H+ +1/R* HSO4-) in eq 16
4792 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 Table 1. Representative Experimental Conditions and Calculated Values of pH, γ(, and pKa1 of Sulfuric Acid ([H2SO4]0 ) 0.012 97 mol/kg) T/°C
P/psia
F/(g cm-3)
log Ka-1 a
pH (eq 14)
γ( (eq 20)
pKa1 (eq 19)
350 380 380 400 400 400 400
3500 3500 6000 4000 4500 5000 6000
0.622 0.399 0.600 0.243 0.396 0.468 0.533
3.06 3.67 2.99 4.99 3.62 3.29 3.08
2.61 3.08 2.69 4.91 3.32 2.81 2.61
0.531 0.381 0.509 0.423 0.442 0.373 0.384
3.75 4.97 3.95 7.55 5.30 4.47 4.02
a
Ref.: [Ryan, 1996, #400].
Figure 7. log Ka1 of H2SO4 versus log(density) for 350, 380, and 400 °C.
Figure 6. Comparison of experimentally determined values for log Ka1 of H2SO4 with literature data (Oscarson et al., 1988) and models (Oscarson et al., 1988; Xiang and Johnston, 1994) as a function of inverse temperature. Experimental values for log Ka of HCl (Mesmer et al., 1988) are also shown for comparison.
were obtained from the best fit of the data measured by Oscarson and co-workers between 150 and 320 °C. The resulting values for -∆G°/RT0, (∂ ln Ka1/∂(1/T))F0, -1 -1 and (1/R* H+ + 1/R* HSO4+) were 2.8, 1350 K , and 1.2 Å , respectively. The dielectric constant, , was calculated from the equation given by Uematsu and Frank (Uematsu and Franck, 1980), and the water density, F, was obtained from the steam tables (Haar et al., 1984). The chief advantage of using the Born model for ion solvation in hydrothermal systems lies in its simplicity. However, the Born equation neglects the effects of microheterogeneous solvation (Tanger and Pitzer, 1989; Gupta and Johnston, 1994), dielectric saturation, and solvent compressibility (Wood et al., 1994). For this reason, it was necessary to treat R* as an empirical parameter in order to achieve an accurate representation of the experimental data. The van’t Hoff isobar, [∂(ln K)/∂(1/T)]P ) -∆H°/R, is an exact expression relating the effect of temperature on the equilibrium constant to the enthalpy change of reaction. The isobaric decrease in log Ka1 with temperature indicates that this dissociation reaction is exothermic. Above 320 °C, the decrease in log Ka1 occurs at a much faster rate. Similar behavior has been observed for other dissociation reactions (Mesmer et al., 1988; Xiang and Johnston, 1994). The log Ka for the dissociation of HCl (Mesmer et al., 1988), plotted as a light solid line in Figure 6 for a pressure of 3500 psia, is one example. At subcritical temperatures, HCl is a stronger acid than H2SO4. However, at supercritical conditions, the acidities of HCl and H2SO4 are very similar. The ion solvation energy has a large impact on Ka1 because two ions are produced from the dissociation reaction (eq 11). With increasing temperature and decreasing density, the dielectric constant of water
drops from a value of ∼78 at 25 °C to a value of less than 10 at temperatures above 400 °C. The large reduction in makes the solvation of ionic products much less favorable. An important observation, illustrated in Figure 6, is that the modified Born model of ion-solvation energy (eq 16) gives a reasonable extrapolation of the low-temperature data of Oscarson and co-workers to higher temperatures. Even though the low-temperature log Ka1 values vary over only 3 orders of magnitude, log Ka1 can be predicted over 6 more orders of magnitude with the model. In Figure 7, log Ka1 is shown to have an almost linear dependence on log F over the temperature range from 350 to 400 °C. At 400 °C, the equilibrium constant from conductivity measurements (Quist et al., 1965) is about 1.5 orders of magnitude larger than the spectroscopically determined value. It is difficult to determine which value is more accurate. An advantage of the spectroscopic technique is that concentration measurement is relatively straightforward and does not depend upon any knowledge of ion transport. It is necessary to fit three constants, including the dissociation constant, to determine Ka1 from conductivity measurements at finite concentration. One of the challenges of this approach is that the mechanism of static and dynamic hydration and ion transport in supercritical water is much less well understood than in ambient water, although computer simulation can provide insight into these phenomena (Balbuena et al., 1996). The spectroscopic technique, to date, depends upon calibration of the indicator with an independent technique. In our case, HCl dissociation data from the conductivity measurements of Frantz and Marshall (Frantz and Marshall, 1984) were used for calibration. These data were considered more accurate at densities below 0.6 g cm-3 than those of earlier work (Franck, 1956). The experimentally measured first dissociation constant of sulfuric acid is compared with those of HCl and water in Figure 8. As temperature is increased, sulfuric acid loses acid strength more rapidly than water and more slowly than HCl. From ambient temperature to the critical temperature the logarithms of the relative acidities are highly linear in 1/T. A constant enthalpy change is often observed for isocoulombic reactions (Mesmer et al., 1991). At supercritical temperatures, the density decreases with an isobaric increase in temperature. In this region, log(Ka1/Kw) decreases about 5%. Because the Born radii of the Cl- and HSO4- ions
Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4793 Table 2. Equilibrium Constants at 5000 psia for Sulfuric Acid, Ammonia, and Water T/°C
log Ka1
log Ka2
log Ka(NH4+)
log Kw
25 200 380
∞ 0.512 -3.97
-1.488 -4.413 -8.680
-9.772 -6.335 -4.370
-13.870 -11.117 -12.142
In order to interpret the experimental results shown in Figure 9, we have calculated the expected pH values for the system of H2SO4 and NH3 by solving the following system of equations using Newton’s iteration method: Figure 8. Relative acidity of sulfuric acid versus water and sulfuric acid versus HCl at constant pressure.
Ka1mH2SO4 - γ(2mH+mHSO4- ) 0
(17)
Ka2mHSO4- - γ(mH+mSO4-2 ) 0
(18)
KamNH4+ - mH+mNH3 ) 0
(19)
Kw - γ(2mH+mOH- ) 0
(20)
mNH30 ) mNH3 + mNH4+
(21)
mH2SO40 ) mH2SO4 + mHSO4- + mSO4-2
(22)
mHSO4- + 2mSO4-2 + mOH- ) mH+ + mNH4+ (23) Figure 9. Titration of 7.0 × 10-3 m H2SO4 with NH3. Experimental pH values are compared with calculated values (eqs 1723) at 25, 200, and 380 °C and a pressure of 5000 psia.
are similar, it is not obvious a priori which way the equilibrium will shift with density. For example, ion solvation can be influenced by hydration numbers and local hydrogen bonding effects in addition to simple Born solvation. The relative acidity of HCl versus H2O, HCl + OH) H2O + Cl-, was studied by molecular dynamics free energy perturbation computer simulation (Balbuena et al., 1996). It was found that the Helmholtz free energy of reaction is essentially constant along the saturation curve and along a supercritical isochore at 0.29 g/cm3 and that the entropy change is very small. The same behavior is observed for H2SO4 versus H2O in Figure 8. Along the saturation curve, ∆A is 25.5 ( 2 kcal mol-1, and the entropy change is very small. For the relative acidity of H2SO4 versus HCl, ∆A was 4 ( 3 kcal mol-1. Titration of Sulfuric Acid with Ammonia in SCW. While the acid strength of sulfuric acid decreases with increasing temperature, ammonium, NH4+, on the other hand, becomes a strong acid at high temperatures (Mesmer et al., 1988). The similar acidities of H2SO4 and NH4+ at elevated temperatures suggest that a system consisting of H2SO4 and NH4HSO4 will be a good pH buffer for SCW solutions. The advantage of having NH4HSO4 as the conjugate base rather than NaHSO4, for example, is that the equilibrium between NH3 and NH4+ also buffers the solution. Figure 9 shows the titration data for the reaction of sulfuric acid with ammonia at 25, 200, and 380 °C. At 25 °C, measurements were made in a quartz cuvette and pH values were measured by a pH electrode. The two remaining curves were obtained in the UV-vis cell at a constant pressure of 5000 psia. The initial concentration of sulfuric acid was 6.98 × 10-3 m, and the concentration of acridine was 10-4 m.
As an approximation, γ( was calculated from Pitzer’s extended Debye-Hu¨ckel model (eq 10) for each reaction, where the ionic strength is
1 I ) (mHSO4- + 4mSO4-2 + mOH- + mH+ + mNH4+) (24) 2 The data used for the first dissociation constant of sulfuric acid, Ka1, came from our experimental results, as described above. We were unable to find any data in the literature for Ka2 of sulfuric acid at temperatures above 320 °C. Therefore, the value of Ka2 at 380 °C was estimated from the equation given by Oscarson (Oscarson et al., 1988). The dissociation constant of water, Kw, and the dissociation constant of NH4+, Ka ()Kw/Kb), were calculated from the equations given by Mesmer (Mesmer et al., 1988). The calculated pH values, represented by the curves in Figure 9, are in reasonable agreement with our experimental results. At 380 °C, the change in curvature at low NH3 concentrations may be due to larger experimental uncertainties in this region. Some of the differences between the measured and calculated values can be attributed to uncertainties in the equilibrium constants: Ka1, Ka2, Kw, and Kb. The values of the equilibrium constants used in developing the pH curves in Figure 9 are listed in Table 2. At 25 °C, the titration curve in Figure 9 is representative of that obtained for the titration of a strong diprotic acid with a strong base. The pH increases very little with addition of ammonia until both of the hydrogens in sulfuric acid are completely neutralized, at which point further addition of ammonia causes the solution pH to increase rapidly. The titration curve at 380 °C reflects the change in H2SO4 from a strong acid to a weak acid (Ka1 ∼ 10-4) and NH3 from a strong base to a weak base (Kb ∼ 10-8) (Mesmer et al., 1988). In this case the pH change at the equivalence points is much less dramatic than in the titration at 25 °C. At 380 °C, the equilibrium constant for the reaction between HSO4- and NH3 is relatively small. Therefore,
4794 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996
shifts from 2-4 at a density of 0.60 g/cm3 to 4.5-7 at a density of 0.24 g/cm3. The first dissociation constant (Ka1) of sulfuric acid exhibits exothermic behavior for all temperatures studied. The rate of decrease of Ka1 with temperature is accelerated at temperatures above 320 °C where losses in water density reduce the solvation of the ionic products. At high temperatures, log Ka1 exhibits linear dependence on log F in the temperature range 350-400 °C. As most reported dissociation constants of acids were measured at temperatures below 320 °C, caution must be exercised when using correlations based on low-temperature measurements to extrapolate to high temperatures. In contrast, extrapolations to high temperatures using the modified Born model can give more reasonable results. Based on titrations of sulfuric acid solutions with ammonia, weak acid-weak base behavior is observed at 380 °C and 5000 psia, unlike the strong acid-base behavior at ambient conditions. At these conditions the system H2SO4-NH4HSO4 may be used as a buffer to maintain pH in the range 3.5 ( 0.25. These types of measurements of acidbase reactions in supercritical water will be highly beneficial for understanding oxidation and hydrolysis reactions, corrosion, catalysis, and solubility behavior as all of these phenomena are often highly dependent upon pH. Figure 10. Titration of 7.0 × 10-3 m H2SO4 with NH3. Concentrations are calculated (eqs 17-23) as a function of NH3 added at 380 °C and 5000 psia.
only the first neutralization reaction occurs to any extent, as evidenced by the increase in pH at the point where 1 equiv of ammonia (mNH30/mH2SO40 ) 1) is added. Beyond the first equivalence point most of the buffering capacity, in the form of H2SO4, has been depleted and the pH becomes more sensitive to further additions of NH3. Based on the titration data shown in Figure 9, the system consisting of H2SO4 and NH4HSO4 at 380 °C and 5000 psia can buffer pH at 3.5 ( 0.25. Figure 10 shows the calculated concentrations (eqs 17-23) of all components as a function of NH3 added. Initially, the addition of NH3 to the sulfuric acid solution results in a large production of HSO4- and NH4+ from the first neutralization reaction between H2SO4 and NH3. At the first equivalence point, the solution can be considered to consist primarily of H2SO4 and NH4HSO4. After the first equivalence point the concentrations of NH4+ and HSO4- increase only slightly with further addition of NH3 because the first neutralization of H2SO4 is almost complete. Very little of HSO4- reacts with NH3 to form SO42- because HSO4- is a very weak acid at 380 °C and NH3 is not a strong enough base to cause deprotonation. As a result, the concentration of SO42-, though increasing slowly, remains several orders of magnitude smaller than the other component concentrations. After the second equivalence point (mNH30/ mH2SO40 ) 2), further addition of NH3 serves only to increase its own concentration and has little effect on the concentrations of the other components. Here, the solution consists primarily of NH4HSO4 and NH3. Conclusions After calibrating acridine with a reference acid, HCl, for which the dissociation constant is known from independent measurements, it may be used successfully to measure the pH of unknown solutions. Because of large changes in the pKa of protonated acridine in supercritical water (SCW), the measurable pH range
Acknowledgment We gratefully acknowledge support from the U.S. Army for a University Research Initiative Grant (30374CH-URI) and an AASERT Grant (DAAH 04-93-6-0363) and the Separations Research Program at The University of Texas, a consortium of over 30 companies. Literature Cited Balbuena, P. B.; Johnston, K. P.; Rossky, P. J. Molecular Dynamics Simulation of Electrolyte Solutions in Ambient and Supercritical Water: II. Relative Acidity of HCl. J. Phys. Chem. 1996, 100, 2716-2722. Balbuena, P.; Johnston, K. P.; Rossky, P. J. 1996, in preparation. Bennett, G. E.; Johnston, K. P. UV-visible Absorbance Spectrocopy of Organic Probes in Supercritical Water. J. Phys. Chem. 1994, 98, 441. Bourcer, W. L.; Ulmer, G. C.; Barnes, H. L. Hydrothermal pH Sensors of ZrO2, Pd Hydride, and Ir Oxides. In Hydrothermal Experimental Techniques; Ulmer, G. C., Barnes, H. L., Eds.; Wiley-Interscience: New York, 1987. Franck, E. U. Z. Phys. Chem. (Frankfurt) 1956, 8, 107. Frantz, J. D.; Marshall, W. L. Electrical Conductances and Ionization Constants of Salts, Acids, and Bases in Supercritical Aqueous Fluids: I. Hydrochloric Acid from 100 to 700 °C and at Pressures to 4000 bars. Am. J. Sci. 1984, 284, 651-667. Gloyna, E. F.; Li, L. Supercritical Water Oxidation: An Engineering Update. Waste Manage. 1993, 13, 379-394. Gupta, R. B.; Johnston, K. P. Ion Hydration in Supercritical Water. Ind. Eng. Chem. Res. 1994, 33, 2819. Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRC Steam Tables; Hemisphere: Washington, DC, 1984. Hafeman, D. G.; Grawford, K. L.; Bousse, L. J. Fundamental Thermochromic Properties of Buffered pH Indicator Solutions and the Formulation of “Athermochromic” Systems. J. Phys. Chem. 1993, 97, 3058-3066. Huh, Y.; Lee, J.-G.; Mepaiil, D. C.; Kim, K. Measurement of pH at Elevated Temperatures Using the Optical Indicator Acridine. J. Solution Chem. 1993, 22, 651-661. Klein, M. T.; Metha, Y. G.; Tory, L. A. Decoupling Substituent and Solvent Effects during Hydrolysis of Substituted Anisoles in Supercritical Water. Ind. Eng. Chem. Res. 1992, 31, 182187. Kriksunov, L. B.; Macdonald, D. D. Advances in Measuring Chemistry Parameters in High Temperature Aqueous Systems. In Physical Chemistry of Aqueous Systems: Meeting the Needs
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Fundamental Research. In Emerging Technologies in Hazardous Waste Management III; Tedder, D. W., Pohland, F. G., Eds.; American Chemical Society: Washington, DC, 1993; pp 3576. Uematsu, M.; Franck, E. U. Static Dielectric Constant of Water and Steam. J. Phys. Chem. Data 1980, 9, 1291. Ulmer, G. C.; Barnes, H. L. Hydrothermal Experimental Techniques; Wiley-Interscience: New York, 1987. White, H. J.; Sengers, J. V.; Neumann, D. B.; Bellows, J. C. Physical Chemistry of Aqueous Systems; Begell House: New York, 1995. Wofford, W.; Dell’Orco, P.; Gloyna, E. Solubility of Potassium Hydroxide and Potassium Phosphate in Supercritical Water. J. Chem. Eng. Data 1995, 40, 968-973. Wood, R. H.; Carter, R.; Quint, J.; Majer, V.; Thompson, P.; Boccio, J. Aqueous electrolytes at high temperatures: comparison of experiment with simulation and continuum models. J. Chem. Thermodyn. 1994, 26, 225-249. Xiang, T.; Johnston, K. P. Acid-Base Behavior of Organic Compounds in Supercritical Water. J. Phys. Chem. 1994, 98, 79157922. Xiang, T.; Johnston, K. P. Acid-Base Behavior in Supercritical Water: β-Naphthoic Acid-Ammonia Equilibrium. J. Solution Chem. 1996, in press.
Received for review June 28, 1996 Revised manuscript received September 19, 1996 Accepted September 19, 1996X IE960368Y
X Abstract published in Advance ACS Abstracts, November 1, 1996.
