C 2006) Journal of Solution Chemistry, Vol. 35, No. 4, April 2006 ( DOI: 10.1007/s10953-005-9014-9
Pressure Dependence of the Acid/Base Equilibrium of Methyl Orange in Aqueous Solutions to 1000 bar at 20◦ C O. M. Suleimenov1 and Jean-Franc¸ois Boily2,∗ Received August 13, 2005; accepted October 18, 2005 Published Online: April 14, 2006 The pressure dependence of the acid/base equilibrium of methyl orange in aqueous solution was measured at 20 ◦ C in the 1–1000 bar range with a newly designed flowthrough spectrophotometric cell. Combined chemometric and thermodynamic analyses of the UV-Vis spectrophotometric data were used to extract the dissociation constants as well as the changes in molar volume and isothermal compressibility of methyl orange as a function of pressure. The results show that increasing the pressure promotes the deprotonation of methyl orange, with pK values ranging from 3.505 at 1 bar to 3.445 ± 0.002 at 1000 bar. Increasing the pressure also yields small negative changes in the molar volume ranging from –6.9 cm3 ·mol−1 at 1 bar to −1.7 cm3 ·mol−1 at 1000 bar. The isothermal compressibility of methyl orange in this pressure range was estimated using the second derivative of second- and third-order polynomial fits to the constants, and resulted in a constant value of –48.4 × 10−4 cm3 ·mol−1 ·bar−1 in the former case, but increasing values from –107 × 10−4 cm3 ·mol−1 ·bar−1 at 1 bar to 3.43 × 10−4 cm3 ·mol−1 ·bar−1 at 1000 bar in the latter case. Molar absorption coefficients for the protonated and deprotonated species were also shown to be only slightly effected by pressure changes and can be used to predict accurately the absorption spectra of methyl orange as a function of pressure. KEY WORDS: Methyl orange, pressure, equilbria, UV-Vis spectrophotometry.
INTRODUCTION The uses of methyl orange are widespread for a large number research and industrial applications. Protonation-induced changes in the electronic spectra are perhaps the most noteworthy attributes of methyl orange, making this compound 1 Institute
of Mineralogy and Petrology, Swiss Federal Institute of Technology (ETH), Zurich, Zurich, Switzerland. 2 Pacific Northwest National Laboratory, P.O. Box 999, Richland 99352, Washington; e-mail:
[email protected]. 541 C 2006 Springer Science+Business Media, Inc. 0095-9782/06/0400-0541/0
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one of the most well-known and frequently used pH indicators. Its acid–base properties have, as a result, been studied at room temperature and pressure in different media, including various water/organic solvent mixtures. In a recent study, these properties were also investigated as a function of temperature and revealed endothermic protonation reactions with the nitrogen centers of this molecule.(1) Gauss–Lorentz fitting parameters were also reported that enable the molar absorption coefficients of the methyl orange aqueous species to be reproduced in the 10–90 ◦ C range. The effects of pressure on the acidity and the spectrophotometric attributes of methyl orange remain, however, unknown and are essential, for instance, for in situ spectrophotometric determinations of pH in mildly acidic pressurized aqueous systems. In this study we report the acid–base properties of methyl orange as a function of pressure using a novel flow-through spectrophotometric titanium cell design(2) capable of measurements up to 400 ◦ C and 1000 bar. Characteristic features of the new cell include a new window design, compact size, small volume and reliability of performance. More details can be found in Suleimenov.(2) Preliminary measurements at elevated temperatures, however, showed that methyl orange decomposed appreciably even at temperatures as low as 50 ◦ C, most likely due to interactions with the titanium components of the cell. The experiments presented in this study were, as a result, carried out in the 1–1000 bar range at 20 ◦ C, where methyl orange is stable in the aqueous phase. The thermodynamic properties of methyl orange in this pressure range are extracted from these data using a combination of chemometric and thermodynamic analyses.
MATERIALS AND METHODS A stock solution of 50 mmol·kg−1 methyl orange was prepared from the sodium salt and standardized potentiometrically. A 10 mmol·kg−1 stock solution of perchloric acid was prepared from the concentrated acid (70%, Aldrich) and standardized against dried trizma base (Aldrich) using methyl orange as the indicator. Solutions containing a 1.0:0.0, 0.5:0.5, and 0.0:1.0 mixtures of the protonated and deprotonated methyl orange species at 20 ◦ C and 1 bar were pumped into the spectrophotometric cell and exposed to pressures in the 1–1000 bar range. The spectrophotometric cell used for this study was a recently developed design by Suleimenov(2) consisting of a titanium flow-through cell using mushroom-type sapphire windows sealed with elastic graphite Grafoil (GrafTeck International Ltd., Wilmington). Pressure was generated with a 10 cm3 spindle press (SITECSieber Engineering AG, 2 kbar maximum pressure) through titanium capillary tubes to the desired level and was measured in situ with a strain gauge pressure transducer (WIKA, 1 to 1000 bar) calibrated against a Heisepressure gauge (absolute 1–1250 bar). The UV-Vis spectra measurements were carried out with
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a Cary50 UV-VIS spectrophotometer in the 275–575 nm range at an interval of 1 nm with a 1 s measurement for each point. RESULTS AND DISCUSSION The spectra of the solution at ca. 0.5:0.5 protonated:deprotonated methyl orange species at 20 ◦ C are shown in Fig. 1a for pressures in the 1–1000 bar range. Those of the fully protonated and deprotonated species are shown in Fig. 1b. Increasing the pressures induces significant changes in the absorption spectra of the ca. 0.5:0.5 protonated:deprotonated mixture, as highlighted in the difference spectra of Fig. 2. These differences are clear indications of changes in the proton affinity of the methyl orange species induced by pressure. Absorbance values of the fully protonated and deprotonated species as a function of pressure exhibited smaller changes due to pressure changes (Fig. 1b) and are in agreement with the values obtained from Boily and Seward(2) at 1 bar. Given the low concentrations of methyl orange, the water density values tabulated in Wagner and Kruse(3) were used to predict the molarity of the methyl orange species as a function of pressure. Changes in the spectra of the ca. 0.5:0.5 protonated:deprotonated methyl orange species solution were first analyzed with the factor indication function of Malinowski(4) to determine the number of chromophoric species: IND =
RSD(k) (n − k)2
(1)
where n is the number of solutions and k is the tentative number of chemically significant factors. The value of RSD(k) was obtained from the values of incremental numbers of linearly independent factors obtained from a Singular Value Decomposition,(5) whereby the absorbance matrix A is represented by A = Um×k Sk×k VTn×k
(2)
where the subscript ‘m’ is the number of wavelengths, ‘n’ the number of experimental solutions and the size of the orthogonal vectors of U are reported in the vector S. The matrix V contains the information for each solution composition. The resulting IND function, shown in Fig. 3, shows that the pressure-induced changes in the spectra can be accounted for solely by two aqueous-phase species, i.e., where IND reaches a minimum. These two species realistically correspond to the protonated and deprotonated species. It is thus noteworthy to mention that previously proposed tautomeric/isomeric equilibria between various protonated N bases(6–8) cannot be significantly perturbed through changes in pressure at low solution acidity. Methyl orange dimers can also be excluded in these solutions, as was demonstrated in a previous study.(1) The results of the SVD of A were also used to extract the thermodynamic properties of the methyl orange species. All vectors with k > 2 are discarded
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ε / mol-1·cm-1·dm3
35000 100 bars
30000 25000 20000 15000 10000 5000 0
300
350
400
450
500
550
600
λ / nm (a) 60000 1000 bars Z+-
ε / mol-1·cm-1·dm3
50000 100 bars
40000
30000
A-
20000
10000
0
300
350
400
450
500
550
600
λ / nm (b) Fig. 1. Apparent molar absorption coefficient (absorbance data normalized for the methyl orange molarity) in the 100–1000 bar range. Arrows indicate changes with increased pressure. Methyl orange molality=15 µmol·kg−1 . (a) Values for ca. 0.5:0.5 deprotonated:protonated methyl orange solution; (b) values for the fully protonated (Z+− ) and fully deprotonated species (A− ).
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4000 1000 bars
∆ε / mol-1·cm-1·dm3
3000
2000
1000 200 bars
0
-1000
300
350
400
450 λ / nm
500
550
600
Fig. 2. Difference spectra relative to the apparent molar absorption coefficients at 100 bar.
x 10
-5
5
4
IND
3
2
1
0
1
2
3
4
5
6
k Fig. 3. Values of the factor indication function, Eq. (1), as a function of the number of linearly independent factors (chromophoric species).
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as they correspond to chemically insignificant variations that may otherwise be realistically ascribed to random noise and errors resulting from solution preparations and manipulations, representing less than 1% of the raw absorption data. The thermodynamic properties of methyl orange were therefore extracted with the equation T A mod = Um×2 S2×2 Vn×2 = ε A− [A− ] + ε Z +− [Z+− ]
(3)
where ε is the molar absorption coefficient for the singly protonated methyl orange zwitterions Z+− and its conjugate base A− . Values for the concentrations were obtained by solving for deprotonation reaction of methyl orange Z+− H+ + A−
(4)
with the associated molal-scale thermodynamic equilibrium constant K and for the dissociation of water, with pressure-dependent values taken from Marshall and Franck.(9) Activity coefficients (γ ) for each species i are obtained from the extended Debye–H¨uckel equation: log10 γi = −
AI 1/2 + bI 1 + B a˚ I 1/2
(5)
˚ for H+ and 4 A ˚ for the N base of methyl where a˚ is the ion-size parameter (9 A orange), I is the ionic strength and the pressure-dependent values of A, B and b are taken from Helgeson et al.(10) The activity coefficient for the zwitterion Z+− is also assumed to be equal to 1. The fit was optimized by minimizing the χ 2 of the function |Amod − Um×2 S2×2 VTn×2 | and the associated standard deviation was obtained by the method of the parabolic expansion of the χ 2 surface.(11) All fits were of high quality, yielding reduced χ 2 values close to unity. The best-fitting values of K are reported in Table I along with their standard deviations and are also shown in Fig. 4. The results show a pressure-induced increase in the acidity of methyl orange in the pressure range of 1–1000 bar of about 0.055 log10 K units. These corresponding Gibbs energy values were fitted as a function of pressure with various analytical expressions. The two best functions were second- and third-order polynomials such that
and
G ◦ = a + bp + cp 2
(6)
G ◦ = a+bp +cp 2 +dp 3
(7)
−2
where p is the pressure (N·m ) and the a, b, c and d are adjustable parameters cooptimized in the least-square sense. The third-order polynomial equation provides the best fit to the data, as shown in Fig. 4, but it should be emphasized that the form of the equation has important repercussions on the calculated molar volume changes and the isothermal compressibility. The analytical derivative of
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Table I. Pressure Dependence of the Thermodynamic Properties for the Dissociation of Methyl Orange log10 Ka ± 3σ
p (bars) 1 100 200 300 400 500 600 700 800 900 1000
−3.505d ± 0.002 −3.493 ± 0.002 −3.485 ± 0.002 −3.476 ± 0.002 −3.470 ± 0.002 −3.464 ± 0.002 −3.460 ± 0.002 −3.455 ± 0.002 −3.452 ± 0.002 −3.448 ± 0.002 −3.445 ± 0.002
V◦,b
κ ◦ ×10−4b
V◦,c
κ ◦ ×10−4c
−5.9 −5.3 −4.8 −4.3 −3.8 −3.3 −2.7 −2.2 −1.7 −1.2 −0.7
−48.4
−6.9 −5.9 −4.9 −4.2 −3.5 −2.9 −2.5 −2.1 −1.9 −1.7 −1.7
−107 −96.4 −85.3 −74.2 −63.1 −52.0 −40.9 −29.8 −18.7 −7.65 3.43
a Equilibrium
constant for the dissociation reaction of Eq. (4) and associated standard deviations. b Change in molar volume (cm3 ·mol−1 ) and compressibility (cm3 ·mol−1 ·bar−1 ) derived from second-order equation (1). c Change in molar volume derived from the third-order equation. d Taken from Boily and Seward (reference 1).
3.51
3.50
-log10 K
3.49
3.48
3.47
3.46
3.45
3.44 0
100
200
300
400
500 p / bar
600
700
800
900
1000
Fig. 4. Values of the best-fitting dissociation constants shown in Table I as a function of pressure, as well as polynomial fits of second (dashed line) and third (full line) order.
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the second- and the third-order polynomials provides us with an estimate of the molar volume change for the dissociation reaction: ∂G ◦ ∂RT ln K =− = V ◦ (8) ∂p ∂ p T T As shown in Table I, both functions provide reasonably consistent estimates of V◦ in the 200–800 bar range, whereas discrepancies as large as −1.0 cm3 ·mol−1 are found in the lower and upper pressure range. We propose that the third-order polynomial provides better estimates of V◦ given the better fit with the pressureexpansion constants. The small values of V◦ in this pressure range are indicative of only minor changes in the hydration of the methyl orange species for the dissociation process. An estimate of the isothermal compressibility is obtained from the second derivative of Eq. (6): ∂V ◦ = κ ◦ (9) − ∂p T but the choice of the polynomial order has a major impact on the resulting values. The second-order polynomial gives a constant value of κ ◦ =−48.4 × 10−4 cm3 ·mol−1 ·bar−1 whereas the third-order polynomial yields a linear dependence of κ ◦ ranging from −107 × 10−4 cm3 ·mol−1 ·bar−1 at 1 bar to 3.43 × 10−4 cm3 · mol−1 ·bar−1 at 1000 bars. These values are in the same order of magnitude of those proposed for other indicators including cresol red,(12) imidazole,(8) p-nitrophenol(8) and thymol blue.(13)
ACKNOWLEDGEMENTS This work was supported by the Swiss Federal Institute of Technology (ETH) Zurich and by Pacific Northwest National Laboratory.
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6. K. M. Tawarah and H. M. Abu-Shamleh, A Spectrophotometric Study of the Tautometric and Acid–Base Equilibra of Methyl-Orange and Methyl Yellow in Aqueous Acidic Solutions, Dyes Pigments 16, 241–251 (1991). 7. E. Sawicki, Physical Properties of the Aminoazobenzene Dyes. IV. The Position of Proton Addition, J. Org. Chem. 22, 365–367 (1957). 8. M. T. Rogers, T. W. Campbell, and R. W., Maatman, The Ionization Constants of some p-Substituted and p -Dimethylaminoazobenzenes, J. Am. Chem. Soc. 73, 5122–5124 (1951). 9. W. L. Marshall and E. U. Franck, Ion Product of Water Substance, 0–1000◦ C, 1–10,000 Bars—New International Formulation and its Background, J. Phys. Chem. Ref. Data 10, 295–304 (1981). 10. H. C. Helgeson, D. H. Kirkham, and G. C. Flowers, Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolyte at High-Pressures and Temperatures. 4. Calculation of Activity Coefficients, Osmotic Coefficients, and Apparent Molal and Standard and Relative Partial Molal Properties to 600 ◦ C and 5 kb, J. Am. Sci. 281, 1249–1516 (1981). 11. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd edn. (McGraw-Hill , Boston, 1990), 328 pp. 12. M. Tsuda, I. Shirotani, S. Minomura, and Y. Terayama, Effect of Pressure on Dissociation of Weak Acids in Aqueous Buffers, Bull. Chem. Soc. J. 49, 2952–2955 (1976). 13. A. Hopkins, K. S. Sell, A. L. Soli, and R. H. Byrne, In situ Spectrophotometric pH Measurements: The Effect of Pressure on Thymol Blue Protonation and Absorbance Characteristics. Mar. Chem. 71, 103–109 (2000).
