J . Phys. Chem. 1994, 98, 7915-7922
7915
Acid-Base Behavior of Organic Compounds in Supercritical Water Tao Xiang and Keith P. Johnston' Department of Chemical Engineering, University of Texas, Austin, Texas 78712
Received: March 16, 1994'
The equilibrium constant KBHAfor a reaction between a n organic acid (@-naphthol) and a base (OH- ion) has been measured for the first time in supercritical water (SCW) u p to 400 O C and 470 bar, by using UV-vis spectroscopy. Solvatochromic shifts for the @-naphtholateanion are used to determine the extent of hydrogen bonding with water and ion pairing with the series of cations Na+, K+, and Cs+. The ionization constant for @-naphthol,Ka, is determined from KBHAand previous measurements of the ionization constant for pure water, K,. All of the results are consistent with the Born model. A t constant temperature, density effects a r e much larger for Kathan KBHA, since the latter reaction is iso-Coulombic. A t constant water density, KBHA is exothermic due to the stronger acidity of 2-naphthol versus water, whereas Ka is endothermic due to the energy required for ionization. However, the behavior becomes much more complex a t constant pressure, due to large negative values of partial molar enthalpies, entropies, and volumes of ions a t high temperatures, which a r e a result of the large isothermal compressibility and volume expansivity of the solvent.
Introduction Interest in SCW phenomena is spreading from the fields of geochemistry and power cycle technology to other processes including hydrothermal oxidation of organic wastes (also called supercritical water oxidation).l-3 Although Bronsted acid-base chemistry plays a central role in aqueous chemistry, it is not very well understood in supercritical water (SCW) media. A better knowledge of acidity in SCW is vital in order to understand key aspects of these technologies including reaction mechanisms, corrosion,4 and the phase behavior of electrolytes. The present understanding of acidity is based on measurements of the ionization constant K , of inorganic acids and bases from electrochemical potentials at subcritical conditions up to 300 OC and from conductivity measurements up to 800 O C and 4 kbar.5 Conductivity measurements of Kahave been made a t supercritical conditions for twoacids, H2Oand HCl. To our knowledge, organic acids have not been studied in SCW. Furthermore, the equilibrium constant for the reaction of an acid and base, KBHA,has not been measured. Our objectives are to develop an apparatus to measure KBHA quantitatively with UV-vis spectroscopy for the reaction of an organic acid, @-naphthol,and a base, KOH, and to understand the temperature, pressure, and density effects on both KBHAand Ka with a Born model, in terms of the charge per volume of the various reacting species. This is the first step in our ultimate goal to develop a series of stable acid-base indicators for SCW which may be used to determine pH over a wide range of acidity. Thermodynamic properties in supercritical solutions are complicated by the large free volume and isothermal compressibility.6 Consequently, electrostriction of water about ions is pronounced, as is evident in the large negative values of partial molar volumes, enthalpies, and entropies.5 Computer simulation7J and molecular thermodynamic models9J0of ion solvation indicate that the structure of water molecules in the first shell about an ion resembles that in ambient water despite all of the thermal energy. Recently, a chemical reaction has been simulated in SCW, the S Nsubstitution ~ reaction, C1- CH3Cl = ClCH3 Cl-." It was shown that the free energy barrier in SCW is more like the barrier in ambient water than that in a polar organic solvent such as dimethylformamide (e = 37). The electrostriction of water about an ion may be described by the Born model with a modified radius.gJ0 This type of model
+
e Abstract
published in Advance ACS Abstracrs, July 1, 1994.
+
will be used to analyze our data for the reaction of @-naphthol and OH-. By studying KBHAversus temperature at constant density, we will characterize the energetics in a well-defined manner. This approach will circumvent contributions due to unusually large magnitudes of partial molar enthalpies, which complicate the behavior at constant pressure. Furthermore, we will contrast the well-behaved effects of density on KBHAat constant temperature with the complex effects of pressure. Although conductivity data have provided most of the present insight into acid-base interactions in SCW, there are some limitations in this technique. Only a few different types of ions may be present, and there must be a change in charge upon reaction. The conductivity technique is well-suited for the ionization of a molecule into a single cation and anion in neutral water. It is not appropriate for reactionssuch as the oneof interest here, H A + OH- = H2O A-, since it is difficult to measure small concentrations of A- when the concentration of OH- is much larger. Furthermore, because the mechanism of ion solvation is complex at SCW condition^,^ the accuracy in determining ion concentrations from ion conductivities is somewhat limited.I2 Therefore, it is beneficial to develop complementary techniques. In-situ studies of molecular interactions and reactions in SCW are rare. Whereas a few spectroscopic studies have considered pure supercritical waterl3-14 (SCW) (Tc= 374 OC, Pc = 221 bar, pc = 0.321 g/cm3) and inorganic SCW solutions,15J6 studies of organic solutes in SCW are just beginning. Recently reported spectral shifts in the *--A* band of benzophenone and the n--A* band of acetone provide insight into the solvent strength of water, the clustering of water about an organic solute, and hydrogen bonding.17 For example, at 380 O C hydrogen bonding between water and acetone is well-established at 0 . 5 and ~ ~changes little with an increase in density. Density effects on hydrogen bonding have also been studied in inert supercritical fluids by FTIR spectroscopy.18 Only a few other in-situ techniques have been used to study reversible reactions in SCW. Electrochemical techniques have been used to measure the hydration of hydroquinone from the diffusion coefficient and the redox potential for the benzoquinone/hydroquinonecouple and the 1211- couple.19~20 Clearly, there is a need for further in-situ investigation. A number of challenges are addressed to perform quantitative UV-vis spectroscopy of organic solutes in SCW solutions. We chose to study @-naphthol,based on our finding that it is stable in alkaline SCW solutions for minutes. The photophysical
+
0022-3654/94/2098-79 15%04.50/0 0 1994 American Chemical Society
7916
Xiang and Johnston
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994
properties of &naphthol have been studied in supercritical C02 containing water as a cosolvent, but proton transfer was not observed.21 Perhaps the greatest challenge is to measure peak areas quantitatively and very quickly, before the sometimes severe corrosion of the sapphire windows reduces transmission. A stopped-flow apparatus with a 200-pL cell has been designed whichallowsa solution tobereplenishedin 30s. Thecellcontained disposable sapphire windows, which were sealed without introducing crevices that would otherwise trap impurities and lead to long mixing times. Another complication in studying Bronstead acid-base behavior in SCW is ion pairing at low p . Both the peak areas and solvatochromic shifts in the band for the &naphtholate anion will be examined to characterize ion pairing for three counterions: Na+, K+, and Cs+.
Theory We begin with the reaction of an organic acid (HA), in this case &naphthol, with an inorganic base, KOH, in water: HA
+ KOH = KA + H,O
+ OH- = A- + H 2 0
(2)
and the equilibrium constant for this acid-base reaction may be defined as KBHA=
mA-/mHAmOH-
(3)
where the infinite dilution activity coefficient of each species is defined as unity and the mole fraction of water is essentially unity. Notice that this reaction is iso-Coulombic. In contrast, two charges are generated in the ionization reaction of an acid given by H A = H+
+ A-
t
HzO
Actual p
AGYT. Po)
+ n20 Reference p o Figure 1. Thermodynamic cycle for density effect on reaction of HA + HA
+
A'
OH-.
molecules, and (3) bulk water where the ions do not effect the water structure. A lattice fluid hydrogen-bonding model has been developed for region 2 to describe the hydrogen bonding of water molecules to the inner-sphere water.1° The electrostatic contribution to the ion solvation may be represented by the Born equation
(9) where 7 is a constant equal to 83 549 A K, Z i is the ionic charge, and R* represents the effective electrostatic radius of the spherical cavity in the dielectric continuum. In order to calculate KBHA,we consider two thermochemical steps: first, changing temperature from TO(298.15 K) to T a t a constant standard-state density po chosen as 1 g/cm3 and then changing the density from po to p a t constant temperature. At constant PO, we will assume that the relationship between log KBHAand 1/T is linear. The resulting equation a t constant po is
(10)
To calculate the change in AG with density, we use the cycle in Figure 1 with the result AG( T,p) = AGO( T,po) + AGA- + AGH,O - AGHA - AGOH(11)
(6)
AG( T,p) = AGO( T,po) + AGA- - AGO,-
(7)
As in eq 3, the mole fraction of water is essentially unity. Notice that subtraction of eq 6 from eq 4 yields eq 2, such that KBHA= Ka/Kw
OH-
A'
Because thesolvation energies for the neutral molecules &naphthol and H 2 0are relatively small compared to those for the ions, we assume that AGm and AGH~omay be cancelled to yield
the ionization equilibrium constant is often expressed as2, Kw = mH+moH-
+
+
(5)
For the ionization of water
H,O = H+ + OH-
OH
(4)
Therefore, the effect of density (and likewise the dielectric constant) on these two types of reactions may be expected to be quite different. The equilibrium constant for the ionization of an acid may be written as
K, = mH+mA-/mHA
t
(1)
If KOH and KA are completelydissociated in water, eq 1 becomes HA
AGYT, p 1 HA
(12)
Substitution of eq 10 and the Born equation into eq 12 yields the result
In KBHA= --AGO RT =
(8)
Therefore, KBHAdescribes the acidity of an organic acid H A relative to that of water. Whereas t may have a large effect on Ka and K,, it may be expected to have a small effect on this relative property KBHA,again because this reaction is isoCoulombic. The effect of density on the three above types of acid-base reactions may be understood with ion solvation models.9J0~23-24 The water molecules may be separated into three regions: (1) an inner sphere where the water molecules have direct contact with the ion, (2) an outer sphere where there is no direct contact with the ion, but where the solvent structure is influenced by the charge on the ions as well as hydrogen bonding between water
where t = t(T,p) and eo = eo(T,po). The equilibrium constant is found from the expression log KBHA= -AG0/2.303RT. Additional thermodynamic properties are given by the usual relationships AVO = - R T ( I ~ ~ K / B P ) ~ , A=IRP P ( a 1 n K I C ~ T ) ~ , and TASO = AIP - AGO.
Experimental Section Materials and Tests of Stability in SCW. The water was distilled, deionized (Barnstead Nanopure 11), and deoxygenated
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7917
Organic Compounds in Supercritical Water
j o o c o o o o o o
t
400,
00
h
1
i
2.0 U
-t
1.5
E0 c
v
g 1.0
1no D
2oo
O
C
0
m
e0 v)
n
,001
0.5
a
i
0.0
0
100
300 400 Temperature(C) 200
500
Figure 2. Temperatures and pressures studied experimentally.
with nitrogen. @-Naphtholwas purified by vacuum sublimation a t about 150 OC. The stability of @-naphtholin pure water was tested in batch stainless steel reactors, which consisted of a Swagelock I/& tee. The solutions first were purged with nitrogen for 30 min. Thereactors weresealedat room temperature in a nitrogen atmosphere and were immersed in a constanttemperature (400 "C) sand bath for 2 h. The products were analyzed by gas chromatography. @-Naphtholwas stable in pure water for at least 2 h at 400 OC and 5000 psi. The effect of KOH on the stability was tested directly in the UV-vis cell. At a temperature below 350 OC and a concentration of KOH from 0 to 0.01 M, @-naphthol(and P-naphtholate) is reasonably stable for a t least for 30 min, since the absorption changes less than 2%. For temperatures above 350 OC and a KOH concentration above 0.01 M, theabsorbanceofP-naphthol (or @-naphtholate)changes about 2-5% in 10 min. The change is due in part to the formation of pits in the sapphire windows; however, there may have been some reactions of the organics. Spectroscopic Measurements. Experimental work with supercritical water requires a number of safety precautions; shielding is extremely important. UV-vis absorption spectra were obtained with a Cary (Varian) 2290 spectrophotometer which was interfaced to an IBM PC computer in a recently described new apparatus.I7 The main differences are that integrated spectral areas are needed in the present study, and the previous study was done in neutral water, where corrosion is very minor. The reference beam was masked with the same aperture as the sample. Because of changes in transmission due to corrosion of sapphire, the base line of pure water was measured often, especially a t high T. The typical time to fully change solutions in the cell was about 10 min. A single spectrum was recorded in about 3 min, after allowing temperature to equilibrate for about 2 min. It was necessary to purge the solutions with nitrogen for a t least for 30 min to remove oxygen. The temperature of the preheater was usually about 50 OC below the temperature of the experiment to minimize thermal stress on the windows, which could lead to cracks. Figure 2 shows the temperature and pressure coordinates at which spectra of @-naphtholwere taken. For each experiment point, at least five different concentrations of KOH were used. The typical concentrations for @-naphtholwere 4 X IW to le3 M depending on the density of the experiment. In order to minimize the error, the typical concentrations of KOH werevaried from 0 to 0.018 M depending upon &HA. At a given temperature, the spectra were measured sequentially in the order of increasing pressure. The pressure was controlled electronically with Beckman Model 100 A HPLC pump and was measured to within f 1% with a Heise 7 10A digital pressuregauge. During a spectral scan, the pressure varied less than 0.6 bar.
280
300 320 340 360 380 Wavelength( nm) Figure 3. Absorbance spectra for @-naphtholin acid form in pure water.
sa,
+50C
-.-1OOC
-
+150C
+zooc
.p! 2 . 5
E'0
-2250C
+350C
. .
: . . .
2.0 1
c
v
a, 0
c m
g
1.5
: 1
1.0
P
a0.50
0.0
280
310 340 370 Wavelength(nm)
400
Figure 4. Absorbance spectra for 8-naphthol in 0.009 m KOH solution (acidic form: 326.7 nm; basic form: ,A, shifts from 345 to 370 nm).
Results and Discussion Analysis of Spectra. Typical spectra for @-naphthol in the acidic form in pure water are shown in Figure 3. At 25 "C,pKa = 9.63, so that ionization can be neglected in neutral water. There is no evidence of a peak for the basic form, which would be found at longer w a ~ e l e n g t hat , ~ any ~ of the conditions studied. Two Gaussian curves were fit to the spectra above 300 nm, and the longer wavelength peak was assigned to the pure acid. The A,, (326.7 f 0.02 nm) for this pure acid peak does not change with the temperature from 25 to 400 OC. The peak width at halfmaximum changes with temperature but does change significantly with pressure. Beers law plots were prepared for this peak for various temperatures, and it was found that R > 0.99. The uncertainty in the acid peak area is always less than 5% and is usually less than 1-2%. The absorption spectra for @-naphtholare in Figure 4 for a given KOH concentration. The A, for the longer wavelength T-T* @-naphtholateanion peak26927 shifts from 345 to 370 nm as temperature increases. Two Gaussian peaks are fit to the spectra to represent the acidic and basic forms as follows:
For a fixed T , B and v,&, are constant as stated above. The Gaussian parameters A:,,, A:ax, Bb, and ,:v were fit to the spectra, with R > 0.999 and x2 < 0.01. Up to 380 O C , the concentration of base is determined from the difference between the total concentration and the accuratelycalibrated concentration of the acid. Above 380 OC, the strong absorbance of the peak below 280 nm interferes with the acid peak, but not the base
Xiang and Johnston
7918 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 831
1
'
'
'
'
'
'
'
'
'
'
'
'
'
'
0 Na'
'
50
I
4
looa'
1506
-
200A
0
i
250@A 300
79
350
I
78
0.2
.
~
' a
'
-3.0
400C
A "
"
0.4
"
"
"
0.6
Density(g.cm
"
- 3,
0.8
'
'
" 1 .o
Figure 5. Maximum r-w* absorption energy for sodium, potassium, and cesium &naphtholate in water versus density at various temperatures.
peak. Thus, we determined the concentration of base from the area of the base peak, which was calibrated to the known acid concentration at 350 OC. This approach is reasonable since Bb changes little with temperature in this range. Solvation of &Naphtholate Anion in SCW. Spectra were measured for alkali 6-naphtholates with various cations in order to examine ion pairing, since E,,, is known to shift with the degree of ion ~ a i r i n g . ~In~Figure . ~ ~ 5, the maximum energy E,, is plotted versus water density for the various cations. For a given density above 0.5 g ~ m - the ~ , change in E,, with cation is within the experimental uncertainty. Ion pairing is minimal in this region. The blue shift in E,,, for the free anion with increasing density is due to the different hydrogen bond acceptor strengths of the ground and excited states. The ground-state anion is stabilized by hydrogen bonds with water to a greater extent than the excited state. In the excited state, the electron density is more delocalized and less charge density is available on the oxygen atom for hydrogen bonding. The blue shift may be used to make an estimate of the hydrogen bond energy in the ground state. Based on Emax of the 6-naphtholate anion in methanol and DMF, Legros et a1.2* estimated that the hydrogen-bonding energy is about 5-7 kcal/ mol at room temperature for methanol. To make a crude estimate of the hydrogen bonding in water, we assume the relationship between E,, and hydrogen bond energy is similar for methanol and water. We also neglect any intramolecular thermochromic shift. As shown in Figure 5, E,,, and thus the hydrogen bond energy between the O-naphtholate anion and water decreases when the density is decreased along the saturation curve. From 1 to 0.5 g cm-3, E,, undergoes a red shift of about 4 kcal/mol, indicating two-thirds of the hydrogen bonds are destroyed, which is consistent with results for hydrogen bonding between water and acetone." When the density of water is below 0.5 g ~ m - E~ ,, for Avaries modestly among the various counterions indicating ion pairing. In contact ion pairs, the electric field due to the cation perturbs the molecular energy levels of the anions.26.27 The favorable electrostatic interaction is stronger for the ground state than theexcited state, since theelectrondensity ismoredelocalized in the excited state. Therefore, the absorption bands of contact ion pairs are shifted to higher energy with respect to those of free ions or solvent-separated ion pairs.27 As expected, this blue shift increases as the charge per volume of the cation increases from K+ to Na+. The larger E,,, for Cs+ than K+was not expected and may bedue to theexperimental uncertainty. With increasing density, the hydrogen bonding between the P-naphtholate anion
-2.5
-2.0
-1.5
i
:
-1.0
log( m e r 1 Figure 6. Ratio of HA and A- concentrations versus moH- for the determination of KBW. 4.0
--
1 " " " " " " " ' l
3.0
m
25
-8 2.0
0.6 0.8 1 .o Density(g.cm3 Figure 7. Density effect on KBW for the reaction of &naphthol (HA) + OH- at various temperatures (solid line: model given in eq 13). 0.2
0.4
and water becomes stronger (blue shift), while the concentration of ion pairs decreases (red shift). Thus, ion pairing and hydrogen bonding shift E,, in opposite directions. Over the conditions studied, E,, always shifts to the blue with an increase in density, except for one data point for sodium&naphtholate at 0.25 g/cm3. For this point, the unusually large value of E,,, indicates strong interactions with the Na+ ion. The prevalence of contact ion pairs may be expected at this condition, since e is only 3.5. Acid-Base Equilibrium to 400 OC. For each experiment, the reaction was equilibrated at constant temperature and pressure, such that AG was a minimum. Spectra were obtained for a series of KOH concentrations in order to determine KBHA.Equation 3 may be rearranged to provide a linear relationship for data reduction:
(2)
log - = -log KBHA- log moH-
(15)
A typical plot is presented in Figure 6,where the lines were drawn with a slope of -1 according to eq 15. Given the challenges in high-pressure and -temperature spectroscopy in corrosive solutions, the results are quite satisfactory. The value of KBHAis obtained from theline (with slope = -1) for mHA = mA-,according to the relationship
log KBHA = -log mOH-
(16)
The uncertainty in K B increases ~ at high temperatures as the density decreases, due to the possibilities of ion pairing and solubility limitations of KOH. In Figure 7, log KBHAis plotted against the bulk density of water for different temperatures from ambient to supercritical
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7919
Organic Compounds in Supercritical Water
TABLE 1: Temperature Effects on KBHAand K. at Constant Density versus Constant Pressure
In KBHA(low r ) In K B H A(high 7‘) In Ka (low 7‘) In Ka (high r )
-
-
+
+
+ + -
3.2,
, , ,
,
,
,
,
,
,
.
,
,
,
,
’
,
, ,
,
,
,
,
,
.
,
,
, .
,
,
-
+ +-
conditions. For low temperatures, only a narrow p range could be studied, since liquid water is relatively incompressible. For subcritical temperatures, the lowest density at each temperature is near the saturation curve. At constant density, KBHA decreases with temperature, indicating exothermic behavior (see Table 1). At temperatures approaching T,,the density range becomes considerably larger. Here there is a noticeable decrease in log KBHAwith density at constant temperature. Experimental results for the temperature dependence of KBHA are shown in Figure 8 for a constant pressure of 345 bar. Other aspects of the figure will be discussed after presenting the model. Over most of the temperature range this acid-base reaction is exothermic (at a constant pressure of 345 bar); however, it becomes endothermic a t the highest temperatures (see Table 1 ) . At high temperatures, the results are complicated by the large decrease in p with an increase in T. The nearly linear relationship of log KBHAwith 1/T over the temperature range from 25 to 300 OC indicates ACO, is small over this temperature range, as is the case for other iso-Coulombic reaction^.^ To understand the density effect on KBHA, we apply the model in eq 13. Only the Born term depends upon density. The Born radius was chosen carefully since it has a large effect on the free energy. For the OH- ion, we included the water of hydration in the Born radius, since it is strongly hydrated. The value Of R * ~ H is 2.58 A.9 For the 8-naphtholate anion, which is much less solvated, we did not include water in RA-and used a value of 3.71 The van? Hoff equation was used to regress 8 In KBHA/ a( 1 / T) in the linear region of the isobaric log KBHAvs 1 / T data a t 345 bar below 300 OC. The dielectric constant E was calculated from the equation given by Uematsu and Frank,29and the water density was calculated with an equation from the steam tables.30 The prediction of the model for the density dependence is in good agreement with the data (Figure 7). At high density where t is high, the term (l/e - l / t o ) approaches zero, and log KBHA varies little with density. According to the Born model, this density effect is small since the reaction is “iso-Coulombic” and would go to zero for two ions with identical Born radii. As the density is lowered, e decreases and the Born term becomes significant. The larger naphtholate anion which has a smaller charge per volume is favored with this decrease in e, as is apparent in eq 13. A modest density dependence on log KBHAbecomes noticeable. The predictions below a density of about 0.4-0.5g/cm3 are shown only to illustrate the Born term; clearly, ion pairing which is not considered will also have a large influence. For the iso-Coulombic reaction of HCl + OH-,5 density has a smaller effect on KBHA than for @-naphthol. This observation is easily explained by the smaller change in charge per volume between OH- and C1- than for OH- and the naphtholate anion (see eq 13). The model is used to calculate the isochoric and isobaric temperaturedependence of KBHAin Figure 8. Consider an isobar a t 250 bar starting at low temperature. As the temperature is increased, KBHA decreases and then increases abruptly near the critical temperature. The isobars below this “V-shaped” curve are also at supercritical pressures. Above the critical pressure, the curvature in the isobars decreases as the pressure increases. This complex behavior may be explained more effectively after first examining the isochores. The low-density isochores are shown only for the vapor phase and terminate at the phase boundary, whereas the isochore a t p = 1 is entirely in the one-phase region. The isochores are
A
2.4
I
m
s -8 1.6 /-500,#:.,
;,’
250bar
- - .345
,
,
..... ... ...... 1000 0 exp.dala(345bar)
- - -p=0.2
:, _ _ . , _ ,&_ ,
,
.........
,
pa.6 P=0.8
-p=1
0.8 1.5
2.0 2.5 lOOOIT(1 IK) Fipre8. Comparison of temperature effects on K B H Aat constant pressure versus at constant density (lines are from model given in eq 13).
relatively linear and exhibit exothermic behavior. The exothermic behavior is expected, since &naphthol is a stronger acid than water, and similarly the OH- ion is a stronger base than the naphtholate anion. The simpler behavior for isochores relative to isobars is observed for numerous other properties of nonelectrolytes and electrolytes in supercritical fluids. The simpler temperature dependence a t constant density is general and reflects the effect of maintaining a constant spatial relationship between molecules while allowing temperature to change. Similarly, the properties which influence solvent strength, such as the cohesive energy density, polarizability per volume, and t, are related much more directly to the density than to the pressure. The change in slope of log KBHAvs 1 / T at constant pressure may be understood in terms of the following thermodynamic relationship:
AHO/RP = (a In KIaT), = (a In KIaT), - PCU(a In K l a p ) ,
(17)
wherea is thevolumeexpansivity (-l/p)(ap/dT)p. Thereversible reaction between 2-hydroxypyridine and 2-pyridone has been analyzed with this relati~nship.~’At lower temperatures, the isothermal compressibility and volume expansivity are relatively small, and the second term may be neglected. Here, the reaction is exothermic for KBHA as is the case for the isochores (see Table 1). However, at higher temperatures, the volume expansivity becomes large and the second term becomes dominant. Because a In K/ap is relatively constant, the shape of the isotherms at high temperature follows thevolume expansivity. The isobars become endothermic a t high temperatures, since a In K / a p is negative and the volume expansivity is positive. Again, the decrease in K with an increase in p is due to the greater stabilization of the smaller OH- ion relative to the naphtholate anion as a increases. The calculated results for the thermodynamic quantities, AHo, ASo,and AVO, are shown in Figures 9-1 1 . At infinite dilution the change in volume may be written as
The partial molar volume of a given species i is given by the thermodynamic relationship
Xiang and Johnston
7920 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 150
TABLE 2 parameter (I
3-
-
100
b C
d
0
E
4
50
&
e-
5 0
-50
0
200
600
400
800
t(C) Figure 9. Change in enthalpy for the reaction of 8-naphthol + OH- in water according to the model in eq 13.
t-
250bar ---ti00
c
-r 0
E
2ool
Parameters for K. of &Naphthol in Eq 21 value parameter value -4.186 -2.822
e
lo3 6.24s x 105 -8.35s x 107 X
f g
7.170 3.153 x 103 9.54 x 104
interactions are relatively strong, which is a primary reason that the term in brackets and thus AVD are positive. The loss of electrostriction about the OH- ion exceeds the gain in electrostriction due to the formation of A-. Thus, AVO and AHO are positive. Furthermore, the solution is disordered upon reaction because of the net loss in electrostriction. The magnitude of each of these properties becomes large in regions where the compressibility of the solvent becomes large." For the reaction of HCl with OH-, the change in electrostriction between the OH- and C1- ions is smaller than in our case; therefore AVO is smaller. IonizationReactionConstantofB-Naphtbol,KO.The ionization constant K. for an organic acid HA may be calculated from KBHA with eq 8 by using known values of K,. The equation of Marshall and Frank2*J2was used for Kw: log K = a
+ b/ T + c/ p + d/ + k log p
(2 1)
where
i
k=e+f/T+g/p We will also use this equation to correlate K, for @-naphthol.This simple function may easily be differentiated to obtain a variety of thermodynamic properties.5J3J4 The results are
AHo = -2.303R[(b
+ 2c/T + 3 d / p ) + (f+ 2g/T) log p ] - R p k a (22)
ASo = 2.303R[(a - 2 c / p - 2 d / p ) + (e - 2 g / p ) log p ] - R T k a (23) 1100
'
'
'
'
'
'
'
'
'
AVO = -RTkp
'
-250bar
.......5OObar
(24)
Theparametersineq21 for theKaofj3-naphthol wereobtained by nonlinear regression and are given in Table 2. The results are -800..... 4000bar shown in Figure 12 for a variety of isotherms. Using these parameters, thecalculated pK. of &naphthol at 25 'C and 1 atm is 9.6, which is in good agreement with the reported pK,, 9.63. For each temperature, K,, increases monotonically with density. "E 5000 i The stabilities of the ions increase relative to &naphthol as the I ! density and c increase. At each density, Ka increases with 200 temperature, exhibiting endothermic behavior. 2oo/ / / In Figure 13, K, is plotted as a function 1 / T both at constant : / pressure and at constant density. The isobar at 250 bar is closest .&. r. r.................... .. . . .. . . . . . . . . . . . : to the critical pressure (221 bar). All points above and to the left - 1 0 0 /of this isobar are also at supercritical pressures. At constant 0 200 400 600 800 density, K, increases with temperature, exhibiting endothermic t(C) behavior. The energy to break the 0-H bond for this relatively Figure 11. Change in volume for the reaction of 8-naphthol + OH- in weakacid is greater than that released by solvation of the resulting water according to the model in eq 13. ions. The slopes do not change significantly from 0.4 to 1 g/cm3. Similar results have been observed for K. of H20 and HCl.S where j3 is the isothermal compressibility. At infinite dilution, The isochoric slopes of KOversus 1/ T a t constant density follow two factors are present: j3, which is a property of the pure solvent, the strengths of the various acids. The isochoric slopes for the and aP/ani, which describes the solute-solvent intermolecular strongest acid HCl are positive, indicating exothermic behavior. forces. Substitution of eq 19 into eq 18 yields For the weakest acid water, K, is endothermic. The endothermic slope for KOof j3-naphthol falls between the endothermic slope for H 2 0 and the exothermic slope for HCl. As for K B H ~the , slopes of the a In K,/a( 1/ T ) isobars exhibit complex behavior incontrast with the simpleisochores. However, the curvature is concave downward, opposite to that for &A. The property j3,a pure solvent property, is always positive. The Again the results may be explained with eq 17. At high sign in AVO dependsuponthedP/an,factors which areal1 negative, temperatures the second term is dominant, and again a In Kf ap since the solute-solvent forces are attractive. The OH--H20
-
.
1 OOObar
L
5 5 1
1/ I'
,0
0
/
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7921
Organic Compounds in Supercritical Water
A
-1000
- l 1 ,o O, 1/ ;
-13.0 0.3
,
,
,
,
,
,
0.7 0.9 Den8 it y (g c m3)
0.5
.
,
,
,
I
E n'
1
Y
1
......... ,
-3000 0
1.1
Figure 12. Density effect on K. for the dissociation of &naphthol in
water at various temperatures (data points: determinedfrom experimental KBHAand eq 21 for Kw; solid line: nonlinear regression according to eq 21).
iI
-4kbar
,
0.2,
200
,
,
/
, I , ,'; ; ,
400
600
,
,
,
800
t(C) Figure 14. Change in volume for the dissociation of @-naphtholin water
according to eq 24. number of solvent molecules contract about an ion, the solution becomes more ordered. Here si is more negative for the ions than HA. Therefore ASois also negative. Finally, the increase in the number of attractive solute-solvent interactions also causes AHo to be negative.31 For the iso-Coulombic reaction of H A and OH-, thechangesin AVO, ASo,and A P areconsiderably smaller, because of a significant degree of cancellation that results from having one ion on each side of the equation.
Conclusions
- 1l 2
i;d .
i
or likewise as (see eq 19)
AVO = vpn[aP/an,,
+ aP/anA-- aP/anHA]
(26)
The aP/an factors are more negative (more attractive) for the ions than HA; consequently AVO is negative. When a large
Quantitative measurements of K B H A were made successfully with the new stopped flow UV-vis apparatus. Key experimental advancements were the use of disposable windows and the short time required to replace the solutions. This spectroscopic technique complements ion conductivity measurements. IsoCoulombic reactions may be studied, and it is not necessary to know mechanisms for ion conductivity in SCW to determine equilibrium constants. All of the results are consistent with the Born model illustrating the importance of the charge per radius on each ion. For the reaction of @naphthol with OH-, density has little effect on K B H A at low temperatures where the Born term described by l / c is small. However, at high temperature where the Born term becomes significant, the naphtholate anion is favored as density is lowered isothermally, since it has a smaller charge per Born radius. Because solvation is more directly dependent on density than pressure, temperature derivatives at constant density provide greater insight into the fundamental chemistry than those at constant pressure. At constant density, the reaction of H A and OH- is exothermic due to the stronger acidity of &naphthol versus water and the stronger basicity of OH- versus the naphtholate anion. In contrast, Ka exhibits endothermic behavior, since the energy needed to break the O-oH bond for this relatively weak acid is greater than that released by solvation of the resulting ions. Furthermore, a much larger density effect is observed for Ka, since the degree of charge changes upon reaction. At constant pressure, the explanation is much more complex a t high temperatures due to the large negative partial molar properties of the ions. The sign of AHo changes for both reactions. There are two related explanations for the change at high temperatures: (1) The volume expansivity becomes large so that the density effect on K becomes important, and (2) the partial molar enthalpies of the ions become large negative values. In either case, the same key interactions govern the behavior. For KBHA,the change to endothermic behavior is due to the larger electrostriction of water about OH- than the naphtholate anion. For the same reason, AVO and ASo are positive. For K,,the change to exothermic behavior is due to the electrostriction resulting from ionization. Likewise, A V ' and ASoare negative.
7922
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994
Furthermore, the magnitudes of these properties are larger for the ionization reaction, since the charge changes upon reaction. With the assumption that the Born radius for OH- includes water of hydration and that of the naphtholate ion does not, the model is in good agreement with the experimental data. However, additional work is needed to better understand how specificforces such as hydrogen bonding influence ion solvation, as is being done with computer s i m u l a t i ~ n . ~ ~Density S ~ ~ ~ and temperature effects on hydrogen bonding are of interest and can be studied by FTIR spectroscopy, as has been done in SF6.I8 At densities below the critical density, our results are complicated by ion pairing, which can be further understood with e~perimentall~ and computer simulations studies.
Acknowledgment. We gratefully acknowledge support from the U S . Army for a University Research InitiativeGrant (30374CH-URI) and the Separations Research Program at the University of Texas, a consortium of over 30 companies. We appreciate helpful discussions with E. U. Franck and acknowledge Durrell Haynes for designing the spectroscopic cell. References and Notes (1) Shaw, R. W.; Brill, T. B.; Clifford, A. A.; Eckert, C. A.; Franck, E.
U.Chem. Eng. News 1991,69, 26. (2) Tester, J. W.; Holgate, H. R.; Armellini, F. J.; Webley,P. A.; Killilea, W. R.; Hong, G. T.; Barnes, H. E. 1993, 518, 35. (3) Sealock, L. J.; Elliott, D. C.; Baker, E. G.; Butner, R. S. fnd. Eng. Chem. Res. 1993, 32, 1535. (4) Huang, S.;Daehling, K.; Carlson, T. E.; Taylor, P.; Wai, C.; Propp, J. ACS Symp. Ser. 1989, No. 406, 276. ( 5 ) Mesmer, R. E.; Marshall, W. L.; Palmer, D. A,; Simonson, J. M.; Holmes, H. F. J . Solution Chem. 1988, 17, 699. (6) Sengers, J. M. H. L. In Supercritical Fluid Technology; Ely, J., Bruno, T. J., Eds.; CRC Press: Boca Raton, FL, 1991; p 1. (7) Cochran, H. D.; Cummings, P. T.; Karaborni,S. FluidPhuse Equilib. 1992, 71, 1. (8) Cui, S.T.; Harris, J. G. Chem. Eng. Sci., in press. (9) Tanger, J. C.; Pitzer, K. S. J . Phys. Chem. 1989, 93, 4941.
Xiang and Johnston (10) Gupta, R. B.; Johnston, K. P., submitted to Ind. Eng. Chem. Res. (1 1) Balbuena, P. B.; Johnston, K. P.; Rossky, P. J. J . Am. Chem. Soc. 1994, 116,2689. (12) Franck, E.U., personal communication. (13) Buback, M.; Crerar, D.; Koplitz, L. M. In Hydrothermal Experimental Techniques; Ulmer, G., Barnes, H., Eds.;Wiley: New York, 1987. (14) Postorino, P.;Tromp, R. H.; Ricci, M.-A.;Soper, A. K.; Neilson,G. W. Nature 1993, 366, 668. (15) Spohn, P. D.; Brill, T. B. J . Phys. Chem. 1989, 93,6224. (16) Marshall, W. L.; Begun, G. M. J . Chem. SOC.Faraday Tram. 2 1989,85, 1963. (17) Bennett, G. E.; Johnston, K. P. J. Phys. Chem. 1994, 98, 441. (18) Kazarian,S.G.;Gupta,R.B.;Clarke,M.J.;Johnston,K. P.;Poliakoff, M. J. Am. Chem.Soc. 1993,115, 11099. (19) Flarsheim, W. M.; Tsou,Y. M.; Trachtenberg, I.; Johnston, K. P.; Bard, A. J. J . Phys. Chem. 1986, 90, 3857. (20) Flarsheim, W. M.; Bard, A. J.; Johnston, K. P. J . Phys. Chem. 1989, 93. 4234. (21) Tomakso, D. L.; Knutson, B. L.; Pouillot, F.; Liotta, C. L.; Eckert, C. A. J. Phys. Chem. 1993, 97, 11823. (22) Marshall, W. L.; Franck, E. U. J . Phys. Chem. Ref: Dafu 1981,10, 295. (23) Oscarson, J. L.;Gillespie, S. E.; Christensen, J. J.; Izatt, R. M.; Brown, P. R. J. Solution Chem. 1988, 17, 1988. (24) Oscarson, J. L.; Izatt, R. M.; Brown, P. R.; Pawlak, 2.;Gillepie, S. E.; Christensen, J. J. J. Solution Chem. 1988, 17, 841. (25) Boyer, R.; Deckey, G.; Marzzacco, C.; Mulvaney, M.; Schwab, C.; Halpern, A. M. J. Chem. Edduc. 1985, 62, 630. (26) Vandereecken, P.; Soumillion, J. P.; Auweraer, M. V. D.; Schryver, F. C. D. Chem. Phys. Lett. 1987,136, 441. (27) Soumllion, J. P.; Vandereecken, P.; Auweraer, M. V. D.; Schryver, F. C. D.; Schanck, A. J . Am. Chem. SOC.1989,111, 2217. (28) Legros, B.; Vandereecken, P.; Soumillion, J. P. J . Phys. Chem. 1991, 95, 4752. (29) Uematsu, M.; Franck, E.U. J . Phys. Chem. Ref. Data 1980,9,1291. (30) Haar, L.; Gallagher, J. S.; Kell, G. S.NESINRC Steam Tables; Hemisphere: Washington, DC, 1984. (31) Peck, D. G.; Mehta, A. J.; Johnston, K. P. J . Phys. Chem. 1989,93, 4297. (32) Marshall, W. L. J . Phys. Chem. 1970, 74, 346. (33) Gates, J. A.; Wood, R. H.; Qulnt, J. R. J . Phys. Chem. 1982, 86, 4948. (34) Mesmer, R. E.; Palmer, D. A.; Simonson, J. M. Ion Association at
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