Thermodynamics of 4-methylphenol dissociation in water at high temperature using UV-Vis spectroscopy

Article abstract of DOI:10.1016/S0021-9614(02)00203-3

The dissociation equilibrium of 4-methylphenol in aqueous solutions has been studied spectrophotometrically over the temperature range 298 to 448 K; at higher temperatures the anion decomposed appreciably. The solutions that were studied had different rat

Full text of DOI:10.1016/S0021-9614(02)00203-3

J. Chem. Thermodynamics 2002, 34, 1467–1479
doi:10.1016/S0021-9614(02)00203-3
Available online at http://www.idealibrary.com on
Thermodynamics of 4-methylphenol
dissociation in water at high temperature
using UV–Vis spectroscopy
Lucila P. Mꢀendez De Leo,
Unidad de Actividad Qu ꢀ{ mica, Comisi oꢀ n Nacional de Energ ꢀ{ a At oꢀ mica,
Av. Libertador 8250, 1429-Capital Federal, Argentina
Hugo L. Bianchi,b
Unidad de Actividad Qu ꢀ{ mica, Comisi oꢀ n Nacional de Energ ꢀ{ a At oꢀ mica,
Av. Libertador 8250, 1429-Capital Federal, Argentina
Escuela de Ciencia y Tecnolog ꢀ{ a, Univ. Nac. General San Mart ꢀ{ n,
Alem 3901, 1651 San Andr eꢀ s, Argentina
and Roberto J. Fernꢀandez-Prini,a,b
Unidad de Actividad Qu ꢀ{ mica, Comisi oꢀ n Nacional de Energ ꢀ{ a At oꢀ mica,
Av. Libertador 8250, 1429Capital Federal, Argentina
Instituto de Qu ꢀ{ mica F ꢀ{ sica de Materiales, Ambiente y Energ ꢀ{ a,
Facultad de Ciencias Exactas y Naturales, Universidad de
Buenos Aires, Ciudad Universitaria, Pabell oꢀ n II, 1428-Capital
Federal, Argentina
The dissociation equilibrium of 4-methylphenol in aqueous solutions has been studied
spectrophotometrically over the temperature range 298 to 448 K; at higher temperatures
the anion decomposed appreciably. The solutions that were studied had different ratios of
weakacid to conjugated base, and the ionic strength was varied with sodium trifluo-
ꢁ1
ꢁ1
romethane sulfonate between 0.0 mol ꢀ kg and 0.3 mol ꢀ kg . The overall analysis of
the optical absorption of the solutions in the range 250 to 380 nm was based on the
corresponding isocoulombic reaction. We report the values of the thermodynamic
quantities at 298.2 K for the two equilibria. The results also suggest that 4-methylphenol
may be used as an indicator to study equilibria of other weakaqueous electrolytes. Ó 2002
Elsevier Science Ltd. All rights reserved.
a
b
To whom correspondence should be addressed (E-mail: rfprini@cnea.gov.ar).
Members of the Carrera de Investigador Científico y T ꢀe cnico of CONICET (Argentina).
0021-9614/02/$ - see front matter
Ó 2002 Elsevier Science Ltd. All rights reserved.

1468
L. P. MØndez De Leo et al.
KEYWORDS: thermodynamics; 4-methylphenol; dissociation; equilibrium; high tem-
perature
1
. Introduction
There is a general lackof thermodynamic information about the properties of organic
ions and molecules in aqueous solutions at high temperature. The increasing demand of
such information in many fields of application, like geoscience, chemical technology,
biological processes at high temperature, waste disposal, and electric power generation, is
an important incentive to study the thermodynamic behavior of those solutes in water.
In particular, it is interesting to get more accurate information on the behavior of weak
organic acids and bases, substances which are omnipresent in the various fields of ap-
plication. Since at increasing temperature water becomes a better solvent for nonpolar
substances, while becoming a poorer solvent for ionic species, it is worth inquiring about
the properties of the molecules of neutral acids or bases and their conjugate ionic species
produced by protolytic equilibria. Some of these weakelectrolytes which have UV–Vis
absorption bands may also be of interest as indicators of the acid–base behavior of other
weaksolutes dissolved in water at high temperature.
In the present paper we report spectrophotometric measurements of the dissociation
constant of 4-methylphenol in water with and without added sodium trifluoromethane
sulfonate (NaTFMS) up to temperatures of 450 K, a temperature range over which this
conjugate (acid/base) system may be studied with no significant decomposition.
2
. Experimental
MATERIALS
The 4-methylphenol from ICN (0.99 + mass fraction purity) was purified by vacuum
sublimation into a borosilicate vessel at T ¼ 323 K. Purity of the 4-methylphenol sample
from ICN was monitored with GLC and n.m.r. analyses. The n.m.r. showed that the
reagent had a low content of another isomer with an estimated mole fraction smaller than
0
.1%, it was used without further purification. Liquid trifluoromethane sulfonic acid
(
HTFMS) from ICN and Alpha were used, samples of the acid dissolved in water were
analyzed by ionic chromatography and we could verify that they only contained the
TFMS anion and a small amount of sulfate ion. The sodium salt was prepared as de-
ð1Þ
scribed by Palmer and Drummond. To obtain the sodium salt of HTFMS the liquid was
neutralized with 50% (w/w) NaOH, solid NaTFMS precipitated and was filtered off.
Solutions were prepared by weighing the necessary amount of NaTFMS. Water was
distilled and then deionized with a Millipore water purification system. Dissolved oxygen
was removed by flowing argon through the solution while keeping the water reservoir at
3
23 K to reduce gas solubility.
Aqueous solutions of 4-methylphenol were titrated conductimetrically with NaOH in
an argon atmosphere using a Wayne Kerr 6425 high accuracy electronic conductivity
bridge and a thermostatted cell. The NaOH concentration was established by titrating the
solution with a standard potassium hydrogen phthalate solution. Titrations were done

Thermodynamics of 4-methylphenol dissociation in water
1469
employing a weight burette, the mass of NaOH solution used was corrected for buoyancy.
Reported concentrations of 4-methylphenol were checked spectrophotometrically at room
temperature.
Stocksolutions of 4-methylphenol, sodium hydroxide and NaTFMS were stored in
large airtight polyethylene bottles pressurized with argon. These stocksolutions were
used to prepare the mixtures by weight just before each measurement.
SPECTROSCOPIC MEASUREMENTS
The absorption spectra of the samples were obtained with an Oriel modular spectro-
photometer. The equipment consisted of a deuterium lamp, a monochromator of 125 mm
focal length having a holographic diffraction grating, it had two quartz beam splitters to
eliminate the effect of spikes of polarized light generated at the holographic grating, two
quartz optical fibers and a low-frequency chopper completed the experimental setup.
FIGURE 1. Experimental setup. SP: modular spectrophotometer; TRG1 and TRG2 triggers for
synchro; PM: photomultiplier attached to the synchronous detection system; DVM: HP multime-
ters; IL: inlet line; P: pump; C: cell; PT: pressure transducer; BK: backpressure valve; PID: two
chanel PID temperature controller (cf. text).

1470
L. P. MØndez De Leo et al.
A blockdiagram of the setup built with these components is depicted in figure 1. The
system operates as a double-beam spectrophotometer with a photomultiplier as detector
connected to a high resolution voltmeter (HP 34401A) triggered on phase with the
mechanical beam modulation. The optical fibers helped to isolate thermally the critical
parts of the photodetector separating them from the high temperature thermostatting
oven. The equipment was connected to a personal computer through a GPIB interface, the
computer controlled the auxiliary trigger signals and the monochromator wavelength, it
also stored the values of the absorbance of the solution, as well as the pressure and
temperature values.
Figure 2 shows the high pressure optical cell in detail. The cell was built from a single
nickel bar (Ni200), it had two sapphire windows and gold gaskets were used to seal them
to the cell body. Two perforated lids were screwed onto the ends of a stainless steel
cylindric container to hold in position the cell components during the measurements. Two
capillary nickel tubings were used to preheat the solutions and inject them into the cell,
their internal diameter was 0.7 mm and the outer diameter 1.56 mm; this type of tubing
allowed the fast thermal equilibration of the solutions.
The setup was used to study different mixtures of 4-methylphenol and NaOH in water.
The concentration of 4-methylphenol in the solutions was always around
ꢁ
4
ꢁ1
2
0
ꢀ 10 mol ꢀ kg , while the concentration of sodium hydroxide varied between
ꢁ1 ꢁ1
mol ꢀ kg and 0.03 mol ꢀ kg . NaTFMS was added to the mixtures to change the ionic
strengths of the solutions.
The UV–Vis absorption spectra of all the solutions at temperatures from 348 K to
4
48 K and pressures from 0.5 MPa to 5 MPa were obtained using the equipment described
above. At the beginning of each experiment hydrogen was bubbled through the solutions
for at least 15 min to maintain a reductive atmosphere, thus minimizing the riskof de-
composition by oxidation of the organic solute. To measure the optical absorption of the
FIGURE 2. High pressure cell. (A) Stainless steel container, (B) nickel body cell, (C) stainless
steel nut, (D) sapphire windows, (E) calibrated platinum thermometer, (F) gold gaskets.

Thermodynamics of 4-methylphenol dissociation in water
1471
samples water was first circulated to clean the system and the base line was then re-
corded. At first the solution was injected at high flow rate during 2 min to sweep the
3
ꢁ1
water that was in the system, then the flow rate was reduced to 0.2 cm ꢀ min and 3 min
elapsed before taking measurements to allow stabilization of the temperature in the cell
within Æ0:2 K.
The spectra of the solutions in the 250 to 400 nm wavelength range were recorded
every 5 nm; the complete spectrum was recorded in 3 min. The spectra of the solutions
were recorded twice to guarantee that the system was stable and the absence of any
chemical reaction which could affect the measurements.
The typical spectra of 4-methylphenol, the acid species, in pure water shows a single
UV peakat 280 nm over the experimental wavelength range. The conjugated anion shows
a peakat 295 nm (for T ¼ 298 K), a larger absorption band appears in the lower extreme
ð2Þ
Ã
of our experimental wavelength range; Jortner et al. reported for phenolate anion two
bands in the UV spectrum corresponding to a p ! p electronic transition which in all
probability is the same transition responsible for the 4-methylphenolate bands. The po-
sition of the peakof 4-methylphenol was not observed to change when the temperature
went from 298 K to 448 K, while that of the anion shifted 15 nm to the red.
The optical path of the cell was determined at room temperature using methylene blue
solutions, their optical absorption was measured first in quartz cells of standard path
length and then in the high pressure cell. These measurements were done at 665 nm,
which corresponds to the maximum of the absorption band of the dye. The final value of
the optical path in the high pressure cell was (2:05 Æ 0:08) cm. It was estimated that
thermal expansion of the nickel cell would change the cell path less than 0.2% over the
working temperature range, hence the change of path length with temperature was ne-
glected. The absorbance of solutions of methylene blue of different concentrations was
measured in the high pressure cell to checkthe linearity of the dependence of optical
absorption with concentration.
A Ruska dead weight balance was used to calibrate a Druck (PTX621) pressure
transducer up to 20 MPa. Drifts of the transducer were controlled by frequent checkof the
atmospheric pressure, in this way the pressure could be read better than 0.01 MPa. A
calibrated 100 X platinum resistance thermometer inserted into the body of the cell was
used to measure the temperature of the solutions in the ITS90 scale. This platinum re-
sistance thermometer was calibrated with a Hart Scientific thermometer, a 100 X standard
resistance, a high stability DC source and a high resolution DVM.
3
. Results
According to BeerÕs law the optical absorbance of a solution at any given wavelength (k)
may be expressed by
X
AðkÞ ¼
ꢀiðkÞcil;
ð1Þ
i
where c is the molar concentration of species i, ꢀ ðkÞ is its molar absorptivity at wave-
i
i
length k and l is the cell path length. The concentration of the acid and basic species of

1472
L. P. MØndez De Leo et al.
4
-methylphenol in the solutions, which were prepared by weight, were converted into
molarities calculating the density of each solution according to
P
1
000 þ
mkMk
k
q ¼ q0 1
P
;
ð2Þ
000 þ
m V ðIÞq
k
k
k
0
using published partial molar volumes for the compounds present in the solutions, that is
ð3Þ
ð4Þ
ð5Þ
ð6Þ
NaTFMS, 4-methylphenol, sodium 4-methylphenolate, and NaOH. The partial
molar volumes V
k
ðIÞ were those calculated for the binary solutions at the same ionic
strength I from the experimental data of the corresponding solute in water, i.e., neglecting
the mixing term. The partial molar volume of the 4-methylphenol was assumed inde-
pendent of the presence of other solutes in the solution. This is supported by the
ð4Þ
agreement between the values reported by Hn ꢁe dkovsk ꢀy et al. for aqueous solutions of
the pure 4-methylphenol, and the data calculated in our laboratory for the acid species
from measurements in mixtures of the acid and of its conjugated base . This procedure
ð7Þ
will give an error on the molal volumes of the mixtures lower than 0.4%.
The equilibrium for the acid dissociation of the 4-methylphenol can be represented by
ðIÞ
and the equilibrium constant for reaction (I) is given by
2
Ka ¼ Qac ;
ð3Þ
Æ
a
Æ
where Q is the concentration quotient, c is the mean activity coefficient of dissociated
acid and the activity coefficient of the neutral acid was taken as unity.
TABLE 1. Values of the spectra as function of temperature
T/K
4-Methylphenol
4-Methylphenolate
kmax/nm
e
kmax/nm
e
2
3
3
3
3
4
4
98.15
278
278
279
279
280
280
281
1671
1669
1668
1667
1666
1665
1664
295
297
299
301
304
306
308
2480
2604
2728
2852
2976
3100
3224
23.15
48.15
73.15
98.15
23.15
48.15

Thermodynamics of 4-methylphenol dissociation in water
1473
The spectra of the acid at different temperatures were obtained by measuring the
absorbance of solutions of 4-methylphenol without addition of sodium hydroxide. They
did not change with the ionic strength of the solution and depended weakly on the
temperature. The values of the molar absorptivity and of the wavelengths at the peak
maxima are reported in table 1 for the acid and the conjugated base at the average round
temperatures. For temperatures not greater than 348 K the spectra of the basic anion could
be obtained experimentally by additions of NaOH until the spectra did not vary with
further additions of NaOH. The total concentration of added NaOH never exceeded
ꢁ
1
0
.03 mol ꢀ kg to avoid corrosion of the optical cell metal surface and deterioration of the
sapphire windows. At temperatures of 373 K or above, this maximum concentration of
sodium hydroxide was not enough to transform all the acid into the basic anion. For
solutions in this temperature range, the molar absorptivity of the 4-methylphenolate ion
was calculated from the spectra of the partially neutralized solutions, as described below.
The values of kmax for the anion are also reported in table 1. In this case the molar ab-
sorptivity was much larger, as expected for a charged species.
FIGURE 3. Spectra of a typical set of mixtures at 374.6 K and 3.42 MPa with molar absorptivity
ꢁ
1
plotted against wavelength. The ionic strength was 0.106 mol ꢀ kg and the concentration of 4-
ꢁ4
ꢁ1
ꢁ1
methylphenol 2:08 ꢀ 10 mol ꢀ kg . The concentration of NaOH was: (ꢂ) 0 mol ꢀ kg ; (Ã)
ꢁ3
ꢁ1
ꢁ2
ꢁ1
ꢁ2
ꢁ1
2
:91 ꢀ 10 mol ꢀ kg ; (4) 1:01 ꢀ 10 mol ꢀ kg ; (5) 2:91 ꢀ 10 mol ꢀ kg . The curves were
calculated with the calculated Qiso. The bold line corresponds to the calculated spectrum of the
basic specie (cf. text).

1474
L. P. MØndez De Leo et al.
Figure 3 shows four spectra corresponding to solutions with different amounts of
NaOH at T ¼ 374:6 K and 3.42 MPa experiments. The change of the spectra as the
degree of dissociation increases is clearly shown in the figure. We considered that
the spectra of the solutions could be described as a linear combination of the spectra of
ꢁ
the 4-methylphenol (HA) and the 4-methyl phenolate (A ):
ꢀ
ðkÞ ¼ ꢀHAðkÞð1 ꢁ aÞ þ ꢀA
ꢁ
ðkÞa ¼ AðkÞ=ðlcÞ;
ð4Þ
where ꢀHA and ꢀAꢁ are the molar absorptivities of the acidic and the basic species
respectively, c is the total molar concentration of absorbing species and a is the degree
of dissociation defined by
ꢁ
ꢁ
a ¼ cðA Þ=c ¼ mðA Þ=m;
ð5Þ
where m is the total stoichiometric molality of 4-methylphenol and of its anion
ꢁ
ðm ¼ mðHAÞ þ mðA ÞÞ.
4
. Data treatment
The dissociation constant of weakacids depends on the temperature and pressure as well
as on the ionic strength of the medium. The spectra of 4-methylphenol solutions with
different sodium hydroxide content, but having the same temperature, pressure, and ionic
strength, were compared in order to calculate the dissociation constant of 4-methylphe-
nol.
The strategy followed to process the spectroscopic data consisted in an overall ad-
justment of the optical absorption recorded over the wavelength range extending from
2
50 nm to 380 nm. The adjustment was based on the stoichiometric concentrations of 4-
methylphenol and NaOH and on the measured optical absorbance which are related to the
degree of dissociation. Two small regions of the spectra around the isosbestic points (cf.
figure 3) were excluded from the analysis because there the difference between the ab-
sorption due to the acidic and the basic species was very small.
For calculation procedures it is convenient to express the equilibrium between 4-
methylphenol and its anion in terms of the isocoulombic reaction, which is obtained by
substracting the autoprotolysis of water from equilibrium (I). The isocoulombic equi-
librium is then represented by
ðIIÞ
In this way the equilibrium of 4-methylphenol has a simpler dependence of the
concentration ratio Qiso on the ionic strength, because

Thermodynamics of 4-methylphenol dissociation in water
1475
2
c ðNaAÞ
Æ
Æ
Kiso ¼ Qiso
;
ð6Þ
2
c ðNaOHÞ
where c ðNaXÞ is the mean activity coefficient of the electrolyte NaX. According to
Æ
ð8Þ
Pitzer, the expression for ln c ðNaXÞ in a mixture of three anions, up to terms linear in
Æ
concentration, is
ꢁ
ꢁ
ln c ðNaXÞ ¼ F þ mðTFMS ÞBðNaTFMSÞ þ mðA ÞBðNaAÞ
Æ
ꢁ
þ
þ mðOH ÞBðNaOHÞ þ mðNa ÞBðNaXÞ;
ð7Þ
where the quantity F is
c
þ
ꢁ
0
þ
ꢁ
0
F ¼ f þ mðNa ÞmðTFMS ÞB ðNaTFMSÞ þ mðNa ÞmðA ÞB ðNaAÞ
þ
ꢁ
0
þ mðNa ÞmðOH ÞB ðNaOHÞ:
Here BðMXÞ is the second virial coefficient, B ðMXÞ is its ionic strength derivative and f
ð8Þ
c
0
is
n
o
c
1=2
1=2
1=2
f ¼ ꢁAU I =ð1 þ bI Þ þ ð2=bÞ lnð1 þ bI Þ ;
ð9Þ
where A is the Debye–Huckel slope for the osmotic coefficient and b an universal
U
1=2
ꢁ1
parameter having the value of 1.2 kg ꢀ mol .
Consequently the logarithm of the mean activity coefficients ratio is
ln fc ðNaAÞ=c ðNaOHÞg ¼ fBðNaAÞ ꢁ BðNaOHÞgI;
ð10Þ
Æ
Æ
þ
because in our case the ionic strength I ¼ mðNa Þ. The value of Q in NaTFMS solu-
w
ð1;9Þ
tions, necessary to calculate Qiso, were obtained from the references.
First we have calculated the value of Qiso at each temperature, ionic strength and each
ꢁ
m and for the different values of the ratio {mðHAÞ=mðA Þ}. The temperature for the
different ratios was kept constant within 0.1 K and the ionic strength was constant within
5
%. Then the calculation procedure of Qiso started using a seed value for Qiso which for
all temperatures, was taken equal to the equilibrium concentration quotient for the dis-
sociation of 4-methylphenol at T ¼ 298 K. Using the mass and charge balance equations,
and the equilibrium for the water autoprotolysis, the concentrations of each of the species
i
m were calculated using
a
Qiso ¼
:
ð11Þ
ꢁ
mðOH Þð1 ꢁ aÞ
With this set of values and equation (5), ꢀðkÞ was calculated and compared with the
experimental values. The differences between the two quantities were minimized using a
nonlinear least-squares procedure which yielded values of DQiso for each iteration. It-
erations were repeated until the square root of the standard deviation of the calculated and
experimental ꢀðkÞ values was smaller than 0.01%.
Finally, the average value of ꢀAꢁ ðkÞ for a given T; I set was calculated using the
following equation:

1476
L. P. MØndez De Leo et al.
ꢀ
ꢁ
X
1
stot
ꢀsðkÞ ꢁ ꢀHAðkÞð1 ꢁ asÞ
as
ꢀ
Aꢁ ðkÞ ¼
;
ð12Þ
s
where the subscript s denotes the particular solution and stot is the number of solutions
studied, usually three or four. This calculation procedure yielded the values of Qiso for
different T; I which are reported in table 2.
5
. Discussion
To calculate the isocoulombic equilibrium constant at each temperature it is necessary to
use equation (6). The ln K ðTÞ may be expressed in terms of ln K ðT Þ and ln Q ðTÞ
iso
iso
r
iso
and the ratio of mean activity coefficients given in equation (10).
DHðTrÞ
ꢀ1
1
ꢁ
DCp
R
ꢂ
ꢀ ꢁ
T
Tr
ꢀ
1
T
1ꢁꢃ
ꢁ Tr
ln Q ðT; p; IÞ ¼ ln K ðT Þ þ
ꢁ T
þ
ln
þ Tr
iso
iso
r
R
Tr
DV
RT
ꢁ
ðp ꢁ p Þ ꢁ 2DBI;
ð13Þ
r
where T
r
¼ 298:15 K, is the reference temperature, DB ¼ BðNaAÞ ꢁ BðNaOHÞ and DC
p
,
the isobaric heat capacity of reaction, was assumed temperature independent. DV for
equilibrium (II) is given by
DV ¼ V 1ðNaAÞ þ V ðH2OÞ ꢁ V 1ðHAÞ ꢁ V 1ðNaOHÞ:
Ã
ð14Þ
TABLE 2. Experimental data
I=10 mol ꢀ kgꢁ1
ꢁ
3
log Qiso
T/K
p/MPa
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
98.15
98.15
43.40
42.50
48.40
73.63
73.28
74.60
99.42
99.89
21.88
18.49
23.10
48.01
69.26
65.04
0.101
0.102
1.423
4.723
1.517
3.302
4.733
3.424
4.764
3.440
3.306
4.826
3.607
4.574
4.923
4.831
0.628
3.66
3.43
3.07
3.20
3.09
2.89
2.51
2.60
2.35
2.31
2.17
2.27
2.17
2.14
2.02
2.03
108
5.77
34.3
106
3.36
33.2
106
33.2
106
10.4
35.4
106
10.4
33.8
106

Thermodynamics of 4-methylphenol dissociation in water
1477
ð5;4;6Þ 1
The partial molar volume of solute species
VðMXÞ and the molar volume of pure
ð10Þ
Ã
water V ðH
2
OÞ were calculated as a function of temperature using published data. The
four other thermodynamic properties appearing in equation (13) were used as adjustable
parameters in the fitting procedure.
The complete set of Qiso values were used to calculate the best values of ln K ðTrÞ,
iso
DHðT
r
Þ, DC
p
, and DB in equation (13). The values obtained are given in table 3, the
uncertainties correspond to the standard deviation of the fitted parameter on the global fit
of equation (13). In turn, these quantities were used to calculate ln Kiso and DH at dif-
ferent temperatures and ionic strengths; they are reported in table 4 as well as log Qiso and
log Q
a
, reported in table 5.
ð1;11Þ
Using the heat of ionization of water
we calculated from the value obtained for
D H, that the enthalpy of ionization D H of 4-methylphenol at T ¼ 298 K was
iso
a
ꢁ
1
(
25:6 Æ 6) kJ ꢀ mol . It is interesting to compare this value with the D H of 2-naphthol,
a
since the two acids are molecularly similar. The thermodynamic quantities characterizing
ð12;13Þ
the ionization of 2-naphthol have been determined in two studies,
at T ¼ 298 K
ꢁ
1
ꢁ1
Xiang and Johnston obtained 24.33 kJ ꢀ mol and Park et al. 21.68 kJ ꢀ mol . These
values are similar to that obtained in the present workfor 4-methylphenol, as expected
a
from the similarity of the molecular structures of the two acids. The values of D H for the
phenolic acids are much more endothermic than for other stronger organic acids; for
instance, for aqueous benzoic and acetic acid, Read has determined that D H at
a
T ¼ 298 K are )0.1 kJ ꢀ molꢁ and )0.8 kJ ꢀ mol , respectively.
1
ꢁ1
ð14Þ
These results agree
TABLE 3. Values of the thermodynamic quantities of equilibria (I) and (II) at T ¼ 298 K and
0
.1 MPa
Isoculombic reaction
Ionization reaction
log K
3:65 Æ 0:01
ꢁ30:25 Æ 6
57
ꢁ10:36 Æ 0:03
ꢁ
1
DH=ð kJ ꢀ mol
Þ
25:55 Æ 6
)174
–
=ðJ ꢀ K ꢀ molꢁ1Þ
ꢁ1
DC
p
DB=ðkg ꢀ molꢁ
1
Þ
0:56 Æ 0:9
Note. Reported uncertainties correspond to the standard deviation of the parameters obtained with the global
fit with equation (13).
TABLE 4. Calculated values of the thermodynamics propeties of isocoulombic reaction as function
of temperature at 1 MPa
DH=kJ ꢀ molꢁ
1
DV =cm ꢀ mol
3
ꢁ1
T/K
log Kiso
2
98.15
23.15
48.15
73.15
98.15
23.15
48.15
3.658
3.254
2.926
2.657
2.435
2.250
2.097
)30.25
)28.83
)27.40
)25.98
)24.55
)23.13
)21.70
)49.35
)31.31
)20.62
)15.77
)15.28
)17.65
)21.40
3
3
3
3
4
4

1478
L. P. MØndez De Leo et al.
TABLE 5. Calculated values from equation (13) at 1 MPa
T/K
log Qiso
log Q
a
I ¼ 0:00mol ꢀ kgꢁ
1
2
3
3
3
3
4
4
98.15
3.66
3.25
2.93
2.66
2.43
2.25
2.10
)10.34
)10.02
23.15
48.15
73.15
98.15
23.15
48.15
)9.79
)9.62
)9.49
)9.41
)9.36
I ¼ 0:05mol ꢀ kgꢁ
1
2
3
3
3
3
4
4
98.15
23.15
48.15
73.15
98.15
23.15
48.15
3.63
3.23
2.90
2.63
2.41
2.23
2.07
)10.19
)9.86
)9.62
)9.43
)9.29
)9.19
)9.11
I ¼ 0:10mol ꢀ kgꢁ
1
2
3
3
3
3
4
4
98.15
23.15
48.15
73.15
98.15
23.15
48.15
3.61
3.21
2.88
2.61
2.39
2.20
2.05
)10.16
)9.83
)9.59
)9.40
)9.25
)9.14
)9.06
TABLE 6. Coefficients for Q
w
on equation (A.1)
ꢁ
7
5
a
1
a
2
a
3
a
4
a
5
a
6
a
7
)17441.676
)106.34385
0.26464199
ꢁ1:1960741 ꢀ 10ꢁ
582.13046
a
a
a
a
a
a
a
8
1:4814262 ꢀ 10
ꢁ
9
4:7265749 ꢀ 10
)0.0157
10
11
12
13
14
4
13.004958
)0.014477684
7
)0.42858439
33.003030
6:2939366 ꢀ 10ꢁ
ꢁ
3
ꢁ4:1853938 ꢀ 10

Thermodynamics of 4-methylphenol dissociation in water
1479
with the general observation that the ionization of weakacids becomes more endothermic
as the strength of the acids decreases.
It is also valuable to compare the values of DC for the ionization reaction (I) of these
p
ꢁ
1
ꢁ1ð12Þ
same four weakacids at T ¼ 298 K, for 2-naphthol they are )189 J ꢀ K ꢀ mol
and
ꢁ
1
ꢁ1 ð13Þ
ꢁ1 ð14Þ
ꢁ1
ꢁ1
)
)
116 J ꢀ K ꢀ mol ,
for benzoic acid )200 J ꢀ K ꢀ mol
and for acetic acid
reported for water
ꢁ
1
ð1;11Þ
233 JꢀK ꢀ mol ; for 4-methylphenol, using the value of DC
p
ꢁ
1
ꢁ1
we obtained DC
p
ð298KÞ ¼ ꢁ174J ꢀ K ꢀ mol . All the values of the heat capacities of
ionization are very similar.
The authors are grateful to Dr. D.A. Palmer for helpful discussion of and the indication
about the calculation log Q . Partial support by CONICET (PIP 4208/1997), ANPCyT
w
(
PICT 6818), and Fundaci ꢀo n Balseiro is gratefully acknowledged.
Appendix A
The concentration ratio for the autoprotolysis equilibrium of water in NaTFMS was
ð1Þ
calculated as following Palmer and Drummond, but using the modified coefficients
ð9Þ
suggested by Palmer:
ꢁ
1
2
c
log Q ¼ a s þ a lnðsÞ þ a s þ a s þ a þ 2f = lnð10Þ
w
1
2
3
4
5
ꢁ
1
2
þ ½a6 þ a7s þ a8s þ a9ꢁsꢃꢁ þ a10/ꢁ
þ bða11 þ a12s þ a13ꢁ s þ a14ꢁ sÞðp ꢁ psatÞ;
1=2
2
1=2
ðA:1Þ
ꢁ
1
ð15Þ
where s is T/K, ꢁ is I=mol ꢀ kg , / is the osmotic coefficient of NaCl solution; b the
ð16Þ
isothermal compressibility of water
REFERENCES
and the coefficients a are reported in table 6.
i
1
2
3
4
5
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3. Park, S.; Kim, H.; Kim, K.; Lee, J.; Lho, D. Phys. Chem. Chem. Phys. 1999, 1, 1893–1898.
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9
1
1
1
1
1
1
1
(
Received 14 September 2001; in final form 10 June 2002)
WE-322