A new tool for an old job: Using fixed cell scanning calorimetry to investigate dilute aqueous solutions

A new tool for an old job: Using fixed cell scanning calorimetry to investigate dilute aqueous solutions

J. Chem. Thermodynamics 39 (2007) 1300–1317 www.elsevier.com/locate/jct A new tool for an old job: Using fixed cell scanning calorimetry to investigat...

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J. Chem. Thermodynamics 39 (2007) 1300–1317 www.elsevier.com/locate/jct

A new tool for an old job: Using fixed cell scanning calorimetry to investigate dilute aqueous solutions q E.M. Woolley

*

Department of Chemistry and Biochemistry, Brigham Young University, Provo, UT 84602-5700, USA Received 16 January 2007; accepted 16 January 2007 Available online 30 January 2007

Abstract The development of fixed twin cell temperature scanning calorimeters has enabled the more efficient determination of heat capacities of dilute aqueous solutions with a precision comparable to that of the Picker flow heat capacity calorimeters developed nearly 40 years ago. Experiments require less than 0.5 cm3 of solution, and results can be obtained routinely over the temperature range (278 to 395) K at pressures up to a few bars. Multiple scanning of samples by both increasing and decreasing temperature allows assessment of instrument drift, solute stability, and reproducibility of results. Chemical calibration is essential to take full advantage of the precision and sensitivity of the calorimeters. The calorimetric output is a direct measure of the difference in heat capacity per unit volume of a solution and of a reference liquid, usually water. Thus, densities of the solution and reference liquid are needed to transform the results into heat capacities per unit mass of solution. Examples of solutes that have been investigated include a variety of inorganic and organic compounds that dissolve to give simple ionic or neutral species, or that produce complexes or species that exist in equilibrium distributions that can change as the temperature is scanned. Appropriate selection of the results from experiments on combinations of solutes allows calculation of standard state (zero concentration) thermodynamic quantities for chemical processes and reactions over the ranges of temperature scanned at the solution compositions investigated. Results for a few specific systems are presented and discussed for some representative classes of solutes that have been investigated in our laboratory since 1998. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Scanning calorimetry; d.s.c.; Solution heat capacity; Apparent molar heat capacity; Fixed cell calorimetry; Temperature scanning calorimetry

1. Introduction Reliable thermodynamic information on dilute aqueous solutions continues to be of interest and relevance in such diverse areas as biochemistry, environmental chemistry, corrosion, and synthesis. Both the fundamental understanding and application of important reactions and processes in aqueous systems require access to reliable thermodynamic data, predictive correlations, or models. Data, parameters, correlations, and the principles that q

Being the 54th Huffman Memorial Award Lecture of the Calorimetry Conference delivered on 1 August 2006 at its 61st annual conference held at Boulder, CO, USA. * Tel.: +1 801 422 3669; fax: +1 801 422 0550. E-mail address: [email protected] 0021-9614/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2007.01.011

describe chemical equilibria, species concentrations, and non-ideal interactions in simple binary or more complex multi-component aqueous solutions are needed as functions of composition, temperature, and pressure. Of course, these parameters, correlations, and models themselves can be no more reliable than the available data upon which they are formulated. Thus, it is likely that there will continue to be the need for improved experimentation on at least selected aqueous systems as new materials are developed, as increased efficiency in their production is pursued, as advances continue in molecular-based medicine, and as our relationships with the environment become increasingly apparent. Reliable results from experiments on aqueous systems at temperatures and pressures far removed from ambient have always been of significance and interest, but the exper-

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2. Historical context If an aqueous solution is made by dissolving n2 mole of solute in nw mole of water, it is convenient to define the apparent molar heat capacity of the solute in the solution Cp,/ in terms of the total heat capacity of the solution Cp,s and the molar heat capacity of the pure water used to prepare the solution C p;w by the following equation: C p;/ ¼ ðC p;s  nw  C p;w Þ=n2 :

ð1Þ

For a solution that contains 1 kg of water, the molal (mol Æ kg1) concentration of solute m = n2 mole of solute of molar mass M2. Thus, if the massic heat capacity of this solution and of the solvent are cp,s and cp;w , respectively, equation (1) takes the form of the following equation: C p;/ ¼ M 2  cp;s þ fðcp;s  cp;w Þ=mg:

ð2Þ

It is seen from the second term in equation (2) that the precision and accuracy of Cp,/ is particularly sensitive to the difference ðcp;s  cp;w Þ, and that this difference is amplified increasingly as m decreases because of the factor (1/m). A simple calculation illustrates this problem in figure 1, where the uncertainties in Cp,/ for NaCl(aq) at T = 298.15 K and at p = 0.35 MPa that result from specified uncertainties in ðcp;s  cp;w Þ are shown as functions of m. This observation, coupled with the fact that experiments leading to relative uncertainties dc ¼ fðcp;s  cp;w Þ=cp;w g < 0:001 were very difficult and tedious to achieve before about 1970, illustrates a major problem faced by both theoretical and practical thermodynamicists. Even very good calorimetric measurements with dc  ±0.001 lead to calorimetric uncertainties in Cp,/ for NaCl(aq) of dC  ±4 J Æ K1 Æ mol at m  1.0 mol Æ kg1, dC  ±42 J Æ K1 Æ mol at m  0.1 mol Æ kg1, and dC  ±417 J Æ K1 Æ mol for NaCl(aq) at m  0.01 mol Æ kg1.

50

600

δ Cp,φ / (J.K-1 .mol-1 )

imental challenges have made the collection of data both difficult and tedious. It would be a daunting task to consider, for example, performing measurements of solute activities, enthalpies of dilution, partial molar volumes, and partial molar heat capacities for all species independently at {273 < (T/K) < 600}, {0.1 < (p/MPa) < 40}, and {0.01 < m/(mol Æ kg1) < 5} for an aqueous system containing even three solutes. Fortunately, thermodynamic relationships do not require that, as the properties for a given solute are interrelated. For example, the enthalpic and heat capacity properties of a solute are related directly to the first and second temperature derivatives of the free energy (activity) of that solute, and a solute’s volumetric properties are related directly to the pressure derivative of its activity. Thus, a measurement of a solute’s activity at a specified concentration and at a single (reference) temperature and pressure allows calculation of that solute’s activity at that composition at other temperatures by using enthalpic data for the solute. Furthermore, if enthalpic data are available at the single reference temperature and pressure and if heat capacity data are available over a range of temperatures for that solute, the solute’s enthalpy and activity can be calculated accurately over the range of temperatures of the heat capacity data by successive integration of that data. Analogous integration of volumetric data over pressure allows calculation of the solute activity as a function of pressure. Thus, the experimental problems for a given solute at a specified concentration can be simplified to: (1) determination of solute activity at a single reference temperature and pressure; (2) measurement of solute volumes (or, more correctly, solute apparent or partial molar volumes, perhaps through measurement of solution densities); (3) measurement of solute enthalpy at the reference temperature and pressure (or, more correctly, solute apparent or partial molar enthalpy, perhaps through measurement of dilution enthalpies of the solution); and (4) measurement of solute heat capacity as functions of temperature and pressure (or, more correctly, solute apparent or partial molar heat capacity, perhaps through measurement of solution heat capacity). Fortunately, experimental techniques to measure solution density and heat capacity have improved significantly during the past 40 years, so that it is possible to determine these derivative properties at elevated temperatures and pressures with precision sufficient to lead to uncertainties in calculated activity as small as those of the direct measurement of activity at ambient temperature and pressure, and often with much greater efficiency. The main focus of this paper is to describe recent advances in the efficient measurement of heat capacities of aqueous solutions containing relatively small amounts of dissolved solutes, {0.001 < m/(mol Æ kg1) < 5}. Although work from our lab since 1997 has focused on experiments using commercially available fixed cell temperature scanning calorimeters, a brief review of the historical development of calorimetric heat capacity instrumentation provides an important context that merits consideration.

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0 0.0

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100 0 0.0

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m / (mol.kg-1) FIGURE 1. Plot of uncertainties in apparent molar heat capacities Cp,/ of NaCl(aq) at T = 298.15 K and at p = 0.35 MPa against molality m calculated from massic heat capacity cp,s uncertainties dc = 0.00001 (d), dc = 0.00003 (s), dc = 0.0001 (.), dc = 0.0003 (n), dc = 0.001 (j), dc = 0.003 (h).

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An excellent summary of results of heat capacity experiments for aqueous 1:1 electrolytes was given in the compilation and critical review by Parker in 1965 [1]. Her summary illustrates the difficulty of measuring solution heat capacities at low solute molality m with sufficient precision and accuracy to obtain the standard state solute heat capacity values (m = 0 mol Æ kg1). This problem presents special additional difficulties when there are large solute– solute interactions and/or when other solution non-idealities occur at low m. An example of these difficulties is given for any system where a chemical reaction such as dissociation or ion pairing occurs when there is a change in temperature, pressure, or composition. A major advancement in aqueous solution heat capacity calorimetry occurred in 1971 with the innovative development of the ‘‘Picker’’ flow calorimeter in the laboratory of Jacques Desnoyers [2]. The novel flow design of the Picker calorimeter allowed the measurement of the differences in volumetric heat capacities of two solutions to be made at {275 < (T/K) < 340} with dc as low as ±0.00002, thus extending the productive composition range for the model system NaCl(aq) down to m  0.02 mol Æ kg1 while maintaining a calorimetric uncertainty dC  ± 4 J Æ K1 Æ mol. Furthermore, the efficiency of performing experiments improved significantly with the Picker calorimeter, and the amount of material needed for an experiment was also reduced to about 30 cm3 for multiple measurements at a single temperature and solution composition. The advent of the Picker calorimeter sparked renewed interest in adaptations and design developments that allowed more precise measurements to be made at much higher temperatures and pressures. These developments included the flow calorimeter of SmithMagowan and Wood [3] in their report in 1981 of Cp,/ for NaCl(aq) at {320 < (T/K) < 600}, {1 < (p/MPa) < 18}, and {0.1 < m/(mol Æ kg1) < 3}. Reviews of other calorimeter developments and applications to various systems are given in the 1994 volume edited by Marsh and O’Hare [4]. In 1995, Peter Privalov’s group reported the design and development of a twin fixed cell temperature scanning calorimeter that offered another advance to obtaining directly the differences in heat capacities of two aqueous solutions [5]. Shortly thereafter our laboratory reported the calibra-

tion and use of a Calorimetry Sciences Corporation (CSC) Nano DSC model 5100 (Lindon, UT, USA) twin fixed cell temperature scanning calorimeter based on the Privalov design to determine NaCl(aq) heat capacities [6]. We demonstrated that it was possible to use the CSC model 5100 calorimeter to obtain aqueous solution heat capacities with a precision comparable to, or even slightly better than, those obtained with the Picker calorimeter, but over the expanded temperature range {278 < (T/K) < 395}, with greatly increased sample through-put, and with a substantially reduced volume of 1 cm3 solution of a given composition. Table 1 provides a brief summary of the expected precision of classes of calorimeters that have been used to determine aqueous solution heat capacities. Solution calorimetrists and thermodynamicists should offer tribute to those many experimentalists who worked tirelessly to extract precise and useful results from instruments that they painfully designed, built, calibrated, and used. Furthermore, future calorimetric instrumentation developments will surely extend the ranges of temperature, pressure, concentration, and sample size of solutions that can be investigated. This continuing development is illustrated by the recent preliminary report by Yao et al. [7] where they have designed, built, and tested an AC calorimeter capable of measuring aqueous solution heat capacities with a precision of dc  ±0.0001 on nL-sized samples at {298 < (T/K) < 343}. 3. Experimental Each of the twin 0.9 cm3 capillary cells of the initial CSC model 5100 calorimeter that we used were made of gold and had two platinum filler tubes. A reference solution (water) was placed in one cell and a second solution {1 M NaCl(aq) to calibrate, water to determine baseline, or a solution of interest} in the other cell. The pressure was increased to above the vapor pressure of the solvent and solution (usually to p = 0.35 MPa in our experiments), and temperature scans were performed at the rate r = ±16.66667 mK Æ s1 at {273.15 < (T/K) < 403.15}. These scan rates were found to be sufficiently slow for the cells and their contents to reach thermal equilibrium, as indicated by the derived values of cp,s and Cp,/ being

TABLE 1 General historical summary of calorimetric designs and specifications as used to determine aqueous solution heat capacities Type

Volume of sample/cm3

Possible T, p ranges/K, MPa

Efficiency in time/(min-hour-day)

Relative precision dc

Adiabatic Solution Picker flow Conventional DSC Fixed cell DSC AC nanocalorimetryb

1 to 200 2 to 2000 30a 0.001 0.3 to 1.0 0.003

270 270 275 270 273 270

h-d h-d m-h m-h h m-h

>±0.0005 >±0.0005 >±0.00002 >±0.01 >±0.000005 >±0.0001

to to to to to to

600, 360, 350, 800, 420, 400,

0.1 0.1 0.1 0.1 0.1 0.1

to to to to to to

20 2 1 2 0.6 10

These qualitative specifications are approximate. a At a flow rate of 0.02 cm3 Æ s1. b See reference [7]. The ranges in T and p and the relative precision have not been fully explored and verified.

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

the same for multiple scans for a given set of solutions in the cells from scans at both increasing and decreasing temperature. Solution stability and instrument drift with time were assessed by comparison of the results of consecutive and successive scans with the same samples in the cells. The difference in electrical power DP required to keep the two cells at the same temperature, the temperature T, and the time were recorded in a computer file at 6-s intervals for later analysis. A series of at least 10 scans – five at r = +16.66667 mK Æ s1 and five at r = 16.66667 mK Æ s1 – were collected for each pair of solutions in the two cells. The sensitivity of the original CSC model 5100 calorimeter was about 50 nW, with a response half-time of about 5 s. Further details of the original experiments are given elsewhere [6]. The procedure we used initially is consistent with the slightly modified procedures we have followed for subsequent cell configurations, including for experiments with our current CSC model 6100 Nano DSC that has cell volumes 0.3 cm3. However, the current calorimeters in use in our lab have cell chambers with only one capillary filling tube per cell. See the block diagram in figure 2. Values of DP from experiments using these fixed cell calorimeters are a measure of the difference in heat capacities of the two cells and their contents. By subtracting DP for

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an experiment where water is in both cells (DPw) from DP for an experiment where water is in the ‘‘reference’’ cell but where another solution is in the ‘‘working’’ cell (DPs), we obtain a direct measure of the difference in volumetric heat capacities rp of the solutions in the working cell for the two experiments ðrp;s  rp;w Þ ¼ fðcp;s  d s Þ  ðcp;w  d w Þg as in equation (3): ðDP s  DP w Þ ¼ ðrp;s  rp;w Þ  fr=k c ðr; T ; pÞg;

ð3aÞ

ðDP s  DP w Þ ¼ fðcp;s  d s Þ  ðcp;w  d w Þg  fr=k c ðr; T ; pÞg; ð3bÞ where ds and dw are the densities of the solution and of water, respectively, and where kc(r, T, p) is the calibration constant of the calorimetric cells at a specified r, T, and p. We determined values of kc(r, T, p) by experiments with water in one cell and with a carefully prepared NaCl(aq) solution of precisely known m  1 mol Æ kg1 in the other cell. The well known values of cp,w and dw for water [8] and of cp,s and ds for NaCl(aq) [9] facilitate the calculation of r/kc(r, T, p) using equation (3b). Rearrangement of equation (3b) gives the operational equation for determination of cp,s for solutions: cp;s ¼ fk c ðr; T ; pÞ  ðDP s  DP w Þ=ðr  d s Þg þ ðcp;w  qw =qs Þ: ð4Þ

Capillary Access Tubes Pressure Port Manostat Heating and Cooling Peltier Element

Temperature Control Block

Platinum Thermometer

Temperature Control Circuit

Power Compensation Heaters Thermosensor

Components Implemented in Software

Calorimetric Cells (volume ~ 0.3 mL) Power Compensation Bridge

Signal Amplifier

Temperature Control Algorithm

Feedback Control Algorithm

FIGURE 2. Block diagram of Calorimetry Sciences Corporation model 6100 Nano DSC.

Pressure Transducer

Data File

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

The precision and reproducibility of the water baseline scans for the CSC models 5100 and 6100 Nano DSC calorimeters used in our laboratory are illustrated in figures 3 and 4. The improved baseline sensitivity and stability of the model 6100 DSC shown in figure 4 more than compensates for the decreased absolute calorimetric sensitivity related to its smaller cell volume. The calibration constants kc are a direct measure of calorimetric sensitivity, and we show in figure 5 the values of kc(T) for one of our model 6100 DSCs over a 6-week period. A comparison of figure 5 here with figure 2 in reference [6] shows that the smaller cell volumes lead to the expected proportionately larger calibration constants. For the examples shown in figure 5, relative uncertainties in values of kc(T) for our model 6100 DSC range from dk(T) = (0.0007 to 0.004) for r = +16.66667 mK Æ s1 and from dk(T) = (0.0004 to 0.002) for r = 16.66667 mK Æ s1, with the smaller dk(T) values at lower T. We also demonstrated in 1997 [6] that the relative precision in values of rp,s and cp,s for NaCl(aq) obtained with the model 5100 DSC at p = 0.35 MPa and at {283.15 < (T/K) < 398.15} ranged from dc = 5 Æ 106 at m = 0.001 mol Æ kg1 to dc = 5 Æ 105 at m = 1.0 mol Æ kg1. This precision is comparable to the relative precision of results that can be obtained for these same NaCl(aq) solutions with the model 6100 DSC, even though the twin cells for the latter instrument have volumes of 0.3 cm3, about one-third the volumes of the cells in the model 5100 DSC. As is the case for the Picker flow calorimeters, we note the importance of thoroughly degassing all water used directly in the CSC DSCs or used to prepare solutions to be used in

them in order to avoid the formation of bubbles during the temperature scans. Further details of the calibration procedure have been described [10]. As is clearly seen from equation (4), use of the fixed cell scanning calorimeter to determine cs(T, p, m) requires values of ds(T, p, m) for each solute of interest. Because values of ds(T, p, m) are not generally available in the literature with a precision dd  105 at p = 0.35 MPa, at {283.15 < (T/K) < 398.15}, and at {0.001 < (m/mol Æ kg1) < 5}, we developed an efficient method to obtain ds at these conditions using the Anton Paar (Austria) model DMA 512

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T/K FIGURE 4. Plot of differences in calorimetric power output dDPw between successive scans against temperature at p = 0.35 MPa for scan rates r = +16.66667 mK Æ s1 (solid lines) and r = 16.66667 mK Æ s1 (dotted lines) for a ‘‘baseline’’ experiment using a Calorimetry Sciences Corporation Nano DSC model 6100 when both cells contain water.

2

1

kc(up), -kc(down) / cm-3

δΔPw / οW

3.3

0

-1

3.2 3.1 3.0 2.9

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-2

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T/K 280

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T/K FIGURE 3. Plot of differences in calorimetric power output dDPw between successive scans against temperature at p = 0.35 MPa for scan rates r = +16.66667 mK Æ s1 (solid lines) and r = 16.66667 mK Æ s1 (dotted lines) for a ‘‘baseline’’ experiment using a Calorimetry Sciences Corporation Nano DSC model 5100 when both cells contain water.

FIGURE 5. Plot of calibration constant kc(r, T, p) for scans for a Calorimetry Sciences Corporation Nano DSC model 6100 calorimeter against temperature T obtained from experiments at p = 0.35 MPa and at the scan rate r = +16.66667 mK Æ s1 for scans up and r = 16.66667 mK Æ s1 for scans down. s, kc(up), 5-25-2006; h, kc(up), 6-15-2006; n, kc(up), 7-3-2006; ,, kc(down), 5-25-2006; }, kc(down), 6-152006; q, kc(down), 7-3-2006.

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and model 512P vibrating tube densimeters [11,12]. Our method is summarized below. We interfaced each Anton PAAR vibrating tube densimeter to a pressure transducer, a stepper motor driven syringe, a programmable temperature controller-circulator, a calibrated platinum RTD, and a computer as illustrated in figure 6. We used a PolyScience (Niles, IL) model 9510 temperature controller-circulator to control T of the gas in the chamber surrounding the vibrating tube of the densimeter within maximum variation of dT  ±0.008 K at {278.15 < (T/K) < 368.15}. Values of T of the gas in the chamber were monitored by a platinum RTD which was calibrated against a Hart Scientific (American Fork, UT, USA) MicroTherm model 1006 standardized reference platinum resistance thermometer. We programmed the controller-circulator to be isothermal for sufficient time (typically 1 h) such that T of the gas in the chamber surrounding the vibrating tube was stable to a root-meansquare deviation dT  ±(0.002 to 0.008) K while the recorded vibration period s  4 ms had a root-meansquare deviation ds  (3 to 15) ns, depending on T and other experimental conditions, for at least 1000 s. When these stabilities were reached, the set T of the controller-circulator was changed by 5.00 K or 10.00 K and the cycle was repeated at the new T. The pressure of the sample inside the vibrating tube was monitored at the densimeter outlet and controlled to dp  ±0.001 MPa with an Omega Engineering (Stamford, CT) model PX120-100GV pressure transducer. Changes in pressure were monitored and then compensated for via a disposable 10-cm3 syringe that contained the solution being investigated and that was connected to the densimeter inlet and driven by a stepper motor. Thus, we were able to complete in 15 h a series

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of s(T) measurements at a given p for any given solution at 11 selected temperatures {278.15 < (T/K) < 368.15}. This efficiency was necessary to take advantage of the rate at which rp,s(T, p, m) values could be obtained with the fixed cell calorimeters: five cycles in temperature between T = 273.15 K and T = 398.15 K for a given solution in 24 h. We determined solution densities from the results of our vibrating tube densimeters using Hooke’s law according to the following equation: n o 2 2 d s ðT ; p; mÞ ¼ d w ðT ; pÞ þ k d ðT ; pÞ  ss ðT ; p; mÞ  sw ðT ; pÞ ; ð5Þ where sw(T, p) and ss(T, p, m) are the vibration periods of the vibrating tube when it contains water and solution, respectively, and where kd(T, p) is the T- and p-dependent calibration constant of the vibrating tube. We determined values of kd(T, p) from measurements of sw(T, p) for water and ss(T, p, m) for m = 1.0 mol Æ kg1 NaCl(aq), whose values of dw(T, p) and ds(T, p, m) are known precisely [8,9]. Measurements of ss(T, p, m) and sw(T, p) were made periodically to verify the reproducibility of independent experiments and to account for (small) drift in the response of the instrumentation. Because we observed small differences in T (DT 6 0.1 K) for successive experiments with the same solution, we determined s at rounded T for all experiments by cubic spline interpolation of the (s versus T) curves. Interpolated values of s at these rounded T from replicate experiments with the same solution were typically consistent to within ds  ±(7 to 24) ns at all {278.15 < (T/K) < 368.15}. This procedure resulted in dd  ±(5 to 50) lg Æ cm3. As with our fixed cell calorimetric experi-

Computer

Voltmeter

Frequency Meter/ Signal Generator

Thermostat/ Circulator

Pressure Transducer

Stepper Motor

Exitation Coil

Pickup Sensor

Platinum RTD

Solution Disposable Syringe

Thermostatted Gas Chamber

FIGURE 6. Block diagram of our experimental apparatus for determination of solution densities with an Anton PAAR model 512 vibrating tube densimeter.

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ments, we again note the importance of thoroughly degassing all water used directly in the densimeters or used to prepare solutions to be used in the densimeters in order to avoid the formation of bubbles during the experiments. In all our experiments, we used samples of the same solutions in both the calorimeter and densimeter. We observed a small long term drift in our observed values of sw(T, p). Thus we interpolated (in real time) the values of sw(T, p) to the time of our experiments where we determined ss(T, p, m). We estimated overall uncertainties in ds from our estimates of the uncertainties in kd, ss, and sw through the statistics of error propagation on equation (5). These uncertainties are, in order of decreasing importance, d(ss) > d(sw) > d(kd) [12]. To further refine our ds(T, p, m) results in order to minimize the effects of their uncertainties on the values of cp,s(T, p, m) obtained by equation (4), we first calculated apparent molar volumes V/(T, p, m) of the solute by the following equation: V / ðT ; p; mÞ ¼ fM 2 =d s ðT ; p; mÞg  ½fd s ðT ; p; mÞ  d w ðT ; pÞg= fd s ðT ; p; mÞ  d w ðT ; pÞ  mg; ð6Þ and then we used weighted regression to fit a semi-empirical function to these V/(T, p, m) results as functions of T, p, and m. The regression weighting factors were taken as the square of the reciprocals of the uncertainties dV in values of V/(T, m), calculated by propagation of dd through equation (6) using the uncertainties in M2, ds, dw, and m: d(M2), d(ds), d(dw), and d(m), respectively. Not surprisingly, these uncertainties dv also scale approximately as (1/m). At constant p, the regression function might take the general form given in the following equation: XX V / ðT ; mÞ ¼ AV ðT ; zÞ  m1=2 þ mij  ðT   T ij Þi  i  j

jP0



ðm Þ þ mT  lnðT Þ; where m* = (m/ms) and ms = 1 mol Æ kg1; where T* = (T/Ts) and Ts = 1 K; where mij and Tij are the regression coefficients; and where AV(T, z) is a theoretical limiting law term for ionic interactions for an electrolyte with ionic charge z. The functional form used should be well behaved at the extremes of m and T, but the critical factor is that the function selected should represent the experimental results over the ranges of T and m of the actual experiments. Values of V/(T, m) obtained from equation (7) using the regression coefficients are then used in equation (6) to determine the smoothed values of ds(T, m) to use in equation (4) to obtain cp,s(T, m), and these are used in turn to determine Cp,/(T, m) by equation (2). 4. Results A summary of aqueous solvent systems investigated in our lab since 1998 using the CSC models 5100 and 6100 fixed cell DSC calorimeters and where manuscripts are either published or are in press as of the end of 2006 is

given in table 2 [11–55]. By classes of solutes, the table includes the protonated, zwitterionic, and deprotonated forms of 12 amino acids; protonated and deprotonated forms of 12 other monoprotic, diprotic, and triprotic acids and of two strong bases; 8 metal halides; 11 metal nitrates; a crown ether and five of its metal ion complexes; one cationic surfactant; 7 aliphatic mono-alcohols; 18 polyols including several common carbohydrates and two cyclodextrins; and 8 other nonelectrolytes of varying structures. Examples are illustrated below. As noted earlier, values of ds(T, p, m) obtained by smoothed regressions of V/(T, p, m) are needed to obtain values of cp,s(T, p, m) and thence Cp,/(T, p, m) using fixed cell DSC. Figure 7 illustrates the V/(T, p = 0.35 MPa, m) results we obtained using vibrating tube densimetry for the aqueous citric acid system [24], and figure 8 illustrates our V/(T, p = 0.35 MPa, m) results for aqueous sodium acetate [11], sodium 1-propionate [30], sodium 1-butanoate [30], and 1-butanoic acid [30]. Careful inspection of the results presented in these two representative figures also illustrates the increasing uncertainties in V/ at low m inherent in the definition of V/ given in equation (6). Figure 9 shows our experimental apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) for LiCl(aq) and CsCl(aq), along with the weighted regression surfaces using a function of T and m similar to that given in equation (7) [38]. Figure 10 shows Cp,/{M+(aq), T, p = 0.35 MPa, m} = [Cp,/{MCl(aq)}  Cp,/{HCl(aq)}] for Li+ [38], Na+ [9], K+ [20], Rb+ [38], and Cs+ [38] with Cp,/{HCl(aq)} from [20]. These values show the approximate differences in the specific contributions of the alkali metal ions to Cp,/(T, p = 0.35 MPa, m) in an aqueous matrix of chloride ions. Figure 11 shows Cp,/(T, p = 0.35 MPa, m) our results and regression surfaces for NaF(aq) [36], NaCl(aq) [9], and NaBr(aq) [36]. These results illustrate the differences in the specific contributions of the aqueous halide ions to Cp,/(T, p = 0.35 MPa, m) in an aqueous matrix of sodium ions. Inspection of the results in figures 9 and 11 also illustrate the increasing uncertainties Cp,/ at low m, as noted in the earlier discussion of equation (2) and figure 1. Figure 12 shows the differences in aqueous apparent molar heat capacities DCp,/ between a series of seven divalent metal ion nitrates and magnesium nitrate [12,35,39,55]. These results illustrate the approximate differences in the specific contributions of the divalent metal ions to Cp,/(T, p = 0.35 MPa, m) in an aqueous matrix of nitrate ions. It is interesting to note that the profiles for the Cu2+(aq), Ni2+(aq), Zn2+(aq), and Mn2+(aq) surfaces are nearly co-planar at all T and m, while those for Sr2+(aq) and Ba2+(aq) show somewhat different behavior at low T, and the surface for Pb2+(aq) is somewhat different at all T and m, perhaps reflecting differences in hydration and ion interactions. Figures 13 and 14 show our experimental apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) for three aqueous 1-alkanols [18,33] and five polyols [25,40,42,54], respectively. Each figure also shows the weighted regres-

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

1307

TABLE 2 Summary of systems and conditions for published investigations of aqueous solutions with fixed cell temperature scanning calorimetry at p = 0.35 MPa at Brigham Young University Solute compounds (listed alphabetically within each solute type)

Solute typea

Tb/K

m/(mol Æ kg1)

Reference

Alanine, alanine hydrochloride, sodium alaninate Aspartic acid, (aspartic acid + HCl), sodium aspartate, Glutamic acid, (glutamic acid + HCl), monosodium sodium glutamate Glycine, glycine hydrochloride, sodium glycinate L-Histidine, L-histidine hydrochloride, sodium L-histidinate L-Proline, L-proline hydrochloride, sodium L-prolinate L-Valine, L-valine hydrochloride, sodium L-valinate, L-2-amino-n-butanoic acid, L-2-amino-n-butanoic acid hydrochloride, sodium L-2-amino-n-butanoate Methionine, methionine hydrochloride, sodium methioninate, isoleucine, isoleucine hydrochloride, sodium isoleucinate Serine, serine hydrochloride, sodium serinate Threonine, threonine hydrochloride, sodiun threoninate, K2CO3, KHCO3 Potassium hydrogen phthalate, potassium sodium phthalate HCl, KCl, KOH, NaOH KNO3, NaNO3, HNO3 1-Propanoic acid, 1-butanoic acid 2-Amino-2-hydroxymethyl-propan-1,3-diol and its hydrochloride saltc Acetic acid, sodium acetate Citric acid, sodium dihydrogen citrate, disodium hydrogen citrate, trisodium citrate Imidazole, imidazole hydrochloride L-Tartaric acid, sodium hydrogen L-tartrate, disodium L-tartrate Phenol, sodium phenolate 1-Butanol, 2-butanol, 2-methyl-1-propanol, 2-methyl-2-propanol Ethanol, 1-propanol, 2-propanol (18-crown-6 + NaCl) (18-crown-6 + RbCl), (18-crown-6 + CsCl) {18-crown-6 + Ba(NO3)2} 18-Crown-6, (18-crown-6 + KCl) LiCl, RbCl, CsCl MgCl2, CdCl2 NaBr, NaF AgNO3 Ba(NO3)2 Mg(NO3)2, Sr(NO3)2, Mn(NO3)2 Ni(NO3)2, Cu(NO3)2, Zn(NO3)2 Pb(NO3)2 Caffeine N,N-Dimethylformamide, N,N-dimethylacetamide Urea, 1,1-dimethylurea, and N,N 0 -dimethylurea N-Acetyl-D-glucoseamine, N-methylacetamide D(+)-Cellobiose, D(+)-maltose, sucrose a-Cyclodextrin, b-cyclodextrin Adonitol, dulcitol, glycerol, meso-erythritol, myo-inositol, D-sorbitol, xylitol D-Glucose, D-galactose D-Lactose Æ H2O Ethane-1,2-diol, propane-1,2-diol, propane-1,3-diol n-Dodecanepyridinium chloride

AA, AB, NE AA, AB, NE

278.15 to 393.15 278.15 to 393.15

0.0075 to 1.0 0.002 to 1.0

[49] [53]

AA, AA, AA, AA,

278.15 278.15 278.15 278.15

393.15 393.15 393.15 393.15

0.01 to 1.0 0.015 to 0.66 0.007 to 1.0 0.015 to 0.67

[47] [21] [32] [34]

AA, AB, NE

278.15 to 393.15

0.0125 to 1.0

[52]

AA, AB, NE AA, AB, NE AB AB AB, MH AB, MN AB, NE AB, NE AB, NE AB, NE AB, NE AB, NE AB, NE AL, NE AL, NE CE CE CE CE, NE MH MH MH MN MN MN MN MN NE NE NE NE, PA PA, NE PA, NE PA, NE PA, NE PA, NE PA, NE SU

278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 278.15 283.15

0.01 to 1.0 0.01 to 1.0 0.014 to 0.51 0.006 to 0.66 0.015 to 0.5 0.015 to 0.5 0.01 to 1.0 0.005 to 0.5 0.005 to 0.5 0.01 to 1.0 0.015 to 0.5 0.006 to 1.0 0.025 to 0.50 0.025 to 0.5 0.05 to 1.0 0.02 to 0.3 0.02 to 0.33 0.02 to 0.33 0.02 to 0.3 0.02 to 1.0 0.01 to 1.0 0.01 to 1.0 0.015 to 0.5 0.0025 to 0.2 0.01 to 3.0 0.01 to 0.5 0.02 to 0.5 0.01 to 0.10 0.015 to 1.0 0.01 to 8.0 0.01 to 1.0 0.01 to 4.0 0.004 to 0.012 0.01 to 5.0 0.05 to 0.5 0.01 to 0.34 0.02 to 1.0 0.003 to 0.15

[48] [51] [37] [17] [20] [26] [30] [14] [11] [24] [27] [22] [31] [18] [33] [45] [46] [43] [41] [38] [16] [36] [28] [12] [55] [39] [35] [29] [19] [44] [50] [42] [23] [54] [15] [40] [25] [13]

AB, AB, AB, AB,

NE NE NE NE

to to to to

to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to to

393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 393.15 348.15 363.15d 393.15 393.15 363.15 393.15 393.15 393.15 393.15

a AA, amino acids; AB, acids-bases; CE, crown ethers and their metal ion complexes; AL, alcohols, mono-hydroxy; MH, metal halides; MN, metal nitrates; NE, other nonelectrolytes; PA, polyols, including carbohydrates; SU, surfactants. b Solution densities measured to T = 368.15 K. c Also called Tris or THAM. d Calorimetric measurements made to T = 393.15 K for N-methylacetamide.

sion surfaces for each solute obtained using fitting functions of T and m similar to that given in equation (7) [18,25,33,40,42,54]. The results in these two figures illustrate the effects that simple differences in the structures of similar solutes can have on the Cp,/(T, m) of their aqueous solutions. From figure 13 one can readily observe the effects that an increase in the hydrophobicity of the 1-alk-

anols has on the dependence of Cp,/ on both T and m and on the magnitude of Cp,/ at any given T and m. From figure 14, one can readily observe the effects that an increase in the number of hydroxyl groups in the solute can have on the dependence of Cp,/ on both T and m and on the magnitude of Cp,/ at any given T and m. It is also readily apparent that the general profiles of Cp,/(T, m) of the 1-alk-

1308

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

120

-1 -1 Cp,φ / (J·K ·mol )

-50 -1 3 Vφ / ( cm . mol )

110 100 90 80

-100

-150

-200

70

1.0

60 380 360

0.4

340

T / K 320

0.2

300 280

0.0

m

/ (m

0.8 0.6 1 - )

ol

. kg

FIGURE 7. Apparent molar volumes of aqueous citric acid (}), monosodium citrate (n), disodium citrate (h), and trisodium citrate (s) [24] plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by using regression functions similar to equation (7) [24].

92

0.8

/ ( 0.6 mo l·k 0.4 g -1 0.2 )

320 0.0

300 280

360

340

380

T/K

FIGURE 9. Experimental apparent molar heat capacities Cp,/ of aqueous lithium chloride (n) and cesium chloride (,) plotted against temperature T and molality m at p = 0.35 MPa [38]. The surfaces were calculated by using weighted regression to functions of T and m similar to those given in equation (7) [38].

-1 -1 Cp,φ {M+(aq)}/ (J.K .mol )

75

82 -1 3 Vφ / (cm ·mol )

m

1.0

72 62 52

50 25 0 -25 -50

395 375 355 335

42 1.0

0.8

m/

0.6

315

0.4

(mo l·kg -1 0.2 )

295 0.0

T

/K

275

1.0 0.8 380

0.6 360

340

T/K

0.4 320

0.2 300 280

0.0

m

ol· / (m

-1 )

kg

FIGURE 8. Apparent molar volumes of aqueous sodium acetate (s) [11], sodium 1-propionate (h) [30], sodium 1-butanoate (n) [30], and 1-butanoic acid (,) [30] plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by using regression functions similar to equation (7) [11,30].

FIGURE 10. Apparent molar heat capacities Cp,/{M+(aq)} = [Cp,/{MCl+(aq)}  Cp,/{HCl+(aq)}] for M+ = Li+ (n) [38], Na+ (s) [9,32], K+ (h) [20], Rb+ (,) [38], and Cs+ (}) [38], using Cp,/{HCl+(aq)} from [20], plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by using regression functions similar to equation (7) [20,32,38].

anols in figure 13 are concave, while those of the polyols in figure 14 are convex. Figure 15 shows apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of aqueous urea [44], 1,1-dimethylurea [44], N,N-dimethylformamide [19], and N,N-dimethylacetamide [19]. The slightly convex surfaces, generated by regression using functions similar to equation

(7) [19,44], are strikingly similar in functional form to those of the polyols in figure 14, as contrasted with the forms for the 1-alkanols in figure 13. Figure 16 shows apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of HCl(aq), KCl(aq), KOH(aq), and NaOH(aq) [20]. Differences between these Cp,/(T, p = 0.35 MPa, m) lead directly to values for the

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

1309

0

450

-40

-1 -1. (Cp,φ ) / (J.K mol )

-1 -1 (Cp,φ + δ) / (J·K ·mol )

40

-80 -120 -160 -200

400

350

300

1.0

1.0 0.8 0.6

0.8 340

T/K

320

0.2 300

280

0.0

m

kg

FIGURE 11. Apparent molar heat capacities (Cp,/ + d) of aqueous sodium fluoride (h), d = 60 J Æ K1 Æmol1 [36]; sodium chloride (s), d = 0 J Æ K1 Æ mol1 [9,32]; and sodium bromide (n), d = 60 J Æ K1 Æ mol1 [36] plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by regression using functions similar to equation (7) [9,32,36].

380

360

0.4 340

320

T/K

0.2 300

0.0

280

FIGURE 13. Apparent molar heat capacities Cp,/ of aqueous ethanol (s) [33], 1-propanol (h) [33], and 1-butanol (n) [18] plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by regression functions similar to equation (7) [18,33].

240

800

-1 -1 (Cp, + δ ) / (J.K .mol )

160

80

0

600

400

φ

[Cp,φ {M(NO3 )2 } - Cp, Mg(NO3)2} +δ ] / (J·K-1.mol-1) φ

250

-1 )

o l· / (m

1 )

0.4

/ (m ol . kg -

360

m

380

0.6

-80

200

-160

360

0.4

340 320

0.20 0.15

0.10

0.05 m / (m 0.00 ol·kg -1 )

280

300

320

340

T / K 300

360 380

T/K

FIGURE 12. Differences in apparent molar heat capacities (DCp,/ + d) = [Cp,/{M(NO3)2(aq)}–Cp,/{Mg(NO3)2(aq)} + d]  [Cp, /{M2+ (aq)}  Cp,/{Mg2+(aq)} + d] for several aqueous divalent metal nitrates M(NO3)2(aq) compared to Mg(NO3)2(aq) [55] plotted against temperature T and molality m at p = 0.35 MPa. s, Sr2+(aq), d = 80 J Æ K1 Æ mol1 [55]; h, Mn2+(aq), d = 0 J Æ K1 Æ mol1 [55]; d, Cu2+(aq), d = 100 J Æ K1 Æ mol1 [39]; j, Ni2+(aq), d = 130 J Æ K1 Æ mol1 [39]; m, Zn2+(aq), d = 50 J Æ K1 Æ mol1 [39]; n, Ba2+(aq), d = 200 J Æ K1 Æ mol1 [12]; ,, Pb2+(aq), d = 120 J Æ K1 Æ mol1 [35].

change in heat capacity for the ionization of water DrCp,m according to equations (8) to (10), where M is either Na or K and C p;w is the molar heat capacity of water [8]:

0.2 280

0.0

m

/

1.0 0.8 0.6 -1 )

. kg ol m (

FIGURE 14. Apparent molar heat capacities (Cp,/ + d) of aqueous glycerol (s), d = 100 J Æ K1 Æ mol1 [54]; adonitol (h), 1 1 d = 0 J Æ K Æ mol [54]; 1,2-propandiol (n), d = 0 J Æ K1 Æ mol1 [25]; maltose (,), d = 0 J Æ K1 Æ mol1 [42]; and (lactose Æ 0.94H2O) (}), d = 0 J Æ K1 Æ mol1 [40] plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by regression using functions similar to equation (7) [25,40,42,54].

MCl(aq) + H2 O = HCl(aq) + MOH(aq)

ð8aÞ

Mþ Cl(aq) + H2 O = Hþ + OH + Mþ Cl(aq)

ð8bÞ

H2 O = Hþ + OH

ð8cÞ

1310

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

600 -150

. -1.mol-1 ) r Cp, φ / ( J K

-1 -1 (Cp,φ + δ ) / (J·K .mol )

500 400 300 200

-180

-210

-240



100 -270

1.0 380

360

0.6 340

0.4 320

T/K

300

0.2 280

m

0.0

380

-1 )

kg o l· m ( /

-1 -1 (Cp, φ + δ ) / (J.K .mol )

200

100

0

-100

0.5 0.4 380

0.3 360

340

T/K

0.2 0.1

320 300 280

0.0

m

/

-1 )

. kg ol (m

FIGURE 16. Apparent molar heat capacities (Cp,/ + d) of HCl(aq) (s), d = 300 J Æ K1 Æ mol1; KCl(aq) (n), d = 200 J Æ K1 Æ mol1; KOH(aq) (h), d = 100 J Æ K1 Æ mol1; and NaOH(aq) (,), d = 200 J Æ K1 Æ mol1 plotted against temperature T and molality m at p = 0.35 MPa [20]. The surfaces were generated by regression using functions similar to equation (7) [20].

X

C p;/ ðproductsÞ 

X

C p;/ ðreactantsÞ;

Dr C p;m  C p;/ fHClðaqÞg þ C p;/ fMOHðaqÞg C p;/ fMClðaqÞg  C p;w ;

340

ð9aÞ ð9bÞ

. kg ol m (

0.2 320

0.1 300

280

0.0

m

/

0.4 0.3 1 - )

FIGURE 17. Change in apparent molar heat capacities DrCp,m for reaction (8) calculated using equation (9) with results for aqueous HCl, NaCl, and NaOH (upper surface at low m and T) and for aqueous HCl, KCl, and KOH plotted against temperature T and molality m at p = 0.35 MPa [20].

Dr C p;m ¼ Dr C p;m

-200

360

T/K

FIGURE 15. Apparent molar heat capacities (Cp,/ + d) of aqueous urea (s), d = 0 J Æ K1 Æ mol1 [44]; 1,1-dimethylurea (n), d = 150 J Æ K1 Æmol1 [44]; N,N-dimethylformamide (h), d = 0 J Æ K1 Æ mol1 [19]; and N,N-dimethylacetamide (,), d = 200 J Æ K1 Æ mol1 [19] plotted against temperature T and molality m at p = 0.35 MPa. The surfaces were generated by regression using functions similar to equation (7) [25,40,42,54].

Dr C p;m 

0.5

0.8

0

X

C p ðproductsÞ 

X

C p ðreactantsÞ;

¼ C p;2 fHClðaqÞg þ C p;2 fMOHðaqÞg C p;2 fMClðaqÞg  C p;w :

ð10aÞ ð10bÞ

Figure 17 shows values of DCp,/ for reaction (8) calculated using equation (9) for aqueous M = Na (HCl, NaCl, NaOH) and M = K (HCl, KCl, KOH) [20].The difference between these two surfaces is almost indistinguishable, with maximum differences dmaxDrCp,/ = 3.8 J Æ K1 Æ mol1 and dmax Dr C p;m ¼ 3:5 J  K1  mol1 , mean differences dmean DrCp,/ = 0.29 J Æ K1 Æ mol1 and dmean Dr C p;m ¼ 0:1 J 1 1 K  mol , median differences dmedDrCp,/ = 0.05 J Æ K1 Æ mol1 and dmed Dr C p;m ¼ 0:3 J  K1  mol1 , and standard deviations dSDDrCp,/ = 1.0 J Æ K1 Æ mol1 anddSD Dr C p;m ¼ 1:0 J  K1  mol1 . The analogous analysis of results for aqueous (HNO3, NaNO3, NaOH) and (HNO3, KNO3, KOH) [26] shows values of DCp,/ for the ionization reaction (8c) in the presence of Kþ NO 3 ðaqÞ and Naþ NO with maximum differences 3 ðaqÞ dmaxDrCp,/ = 13 J Æ K1 Æ mol1 and dmax Dr C p;m ¼ 6:4 J K1  mol1 , mean differences dmeanDrCp,/ = 1.3 J Æ K1 Æ mol1 and dmean Dr C p;m ¼ 3:4 J  K1  mol1 , median differences dmedDrCp,/ = 2.7 J Æ K1 Æ mol1 and  dmed Dr C p;m ¼ 3:3 J  K1  mol1 , and standard deviations dSDDrCp,/ = 3.1 J Æ K1 Æ mol1 and dSD Dr C p;m ¼ 0:8 J K1  mol1 . These measures of the differences between values of DrCp,/ and Dr C p;m for the four different combinations of the ions Na+, K+, Cl, and NO 3 give an indication of the overall uncertainties to be expected for determination of values of Cp,/ for simple aqueous electrolytes and the subsequent regression and extrapolation to standard state (m = 0 mol Æ kg1) at (275 < T/K < 395) using the CSC models 5100 and 6100 NanoDSCs.

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

1311

14.5 14.0

55

13.5

pQw

-1 ) . r Hm / ( kJ mol

60

50



12.5

45

12.0

40 0.0

13.0

280 300 320 0.1

m /(

380

340

0.2

360

0.3

mol . kg 1 )

380

0.4

T/

360

K

340

T/

K

320 300

0.5

280

FIGURE 18. Change in enthalpy DrHm calculated for reaction (8) using equation (11) with results for aqueous HCl, NaCl, and NaOH (lowest surface at high m and T) [20], HCl, KCl, and KOH (second lowest surface at high m and T) [20], HNO3, NaNO3, and NaOH (second highest surface at high m and T) [26], and HNO3, KNO3, and KOH (highest surface at high m and T) [26] plotted against temperature T and molality m at p = 0.35 MPa [20,26]. s, literature values for the chlorides from reference [20].

Figure 18 shows the change in enthalpy DrHm for reaction (8) calculated using equation (11) with results for aqueous (HCl, NaCl, NaOH) [20], (HCl, KCl, KOH) [20], (HNO3, NaNO3, NaOH) [26], and (HNO3, KNO3, KOH) [26]: Z Z Dr H m ðT ; mÞ ¼ Dr C p;m  dT  dm þ Dr H m ðT ref ; mÞ:

0.1 0.0

0.5

0.4

0.3

-1 . kg ) mol ( / m 0.2

FIGURE 19. Ionization constant pQw calculated for reaction (8) using equation (12) with results for aqueous HCl, NaCl, and NaOH (lowest surface at high m) [20], HCl, KCl, and KOH (second lowest surface at high m) [20], HNO3, NaNO3, and NaOH (second highest surface at high m) [26], and HNO3, KNO3, and KOH (highest surface at high m) [26] plotted against temperature T and molality m at p = 0.35 MPa [20,26]. s, literature values for the chlorides from reference [20].

HCl, KCl, and KOH [20], HNO3, NaNO3, and NaOH [26], and HNO3, KNO3, and KOH [26] plotted against temperature T and molality m at p = 0.35 MPa: fðcHþ  cOH Þ=aw g ¼ Qw =K w :

ð13Þ

ð11Þ

}

1.0

{( γ + . γ OH- ) / a w H

Values of the integration constant DrHm(Tref, m) in equation (11) were obtained by evaluation of results from the literature as described in reference [20] for the chloride systems and in reference [26] for the nitrate systems. Figure 19 shows the water ionization constant Qw for reaction (8) calculated using equation (12) with results for aqueous (HCl, NaCl, NaOH) [20], (HCl, KCl, KOH) [20], (HNO3, NaNO3, NaOH) [26], and (HNO3, KNO3, KOH) [26]: Z Z ½lnfQðT ; mÞg ¼ ðDr H m =R  T 2 Þ  dT  dmþ

0.9 0.8 0.7 0.6 0.5

0.4 0.3

½ln fQðT ref ; mref Þg:

ð12Þ

Values of the integration constant [ln {Qw(Tref, mref)}] in equation (12) were obtained by evaluation of water ionization constants from the literature as described in reference [20] for the chloride systems and in reference [26] for the nitrate systems. Figure 20 shows the activity coefficient product fðcHþ  cOH Þ=aw g for reaction (8) calculated using equation (13) with results for aqueous HCl, NaCl, and NaOH [20],

380

360

0.2 340

T/K

0.1

320 300 280

0.0

m

-1

)

. kg ol m /(

FIGURE 20. Activity coefficient product fðcHþ  cOH Þ=aw g for reaction (8) using equation (13) with results for aqueous HCl, NaCl, and NaOH (lowest surface) [20], HCl, KCl, and KOH (second lowest surface) [20], HNO3, NaNO3, and NaOH (second highest surface) [26], and HNO3, KNO3, and KOH (highest surface) [26] plotted against temperature T and molality m at p = 0.35 MPa.

1312

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

500

-1 -1 Cp,φ / (J·K mol )

400 300

200

φ

-1 -1 Cp, / (J·K ·mol )

400

100

300 200 100 0

0

-100

0.4 0.3

m/

360 0.2

(m o l·

380

m/

340 320

0.1

kg -1 )

0.0

300

T/

K

280

FIGURE 21. Apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of the aqueous zwitterionic amino acids glycine [47], alanine [49], L-2aminobutanoic acid [34], valine [52], and isoleucine [34], in order lowest to highest, plotted against temperature T and molality m.

Figures 21 to 23 show the apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of the aqueous zwitterionic, protonated cationic, and deprotonated anionic forms, respectively, of the amino acids glycine [47], alanine [49], L-2-aminobutanoic acid [34], isoleucine [52], and valine [34]. The effects of enlarging the hydrocarbon backbone are evident in each figure for this solute sequence. Figure 24 shows the apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of the aqueous zwitterionic amino acids glycine [47], serine [48], threonine [51], methionine [52], and histidine [21] to illustrate the effects of different moieties on the hydrocarbon backbone. Even the

400

380

0.3

(m 0.2 o l· kg -1 0.1 )

360 340 320 0.0

300

T/

K

280

FIGURE 23. Apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of the aqueous deprotonated anionic amino acids sodium glycinate [47], sodium alaninate [49], sodium L-2-aminobutanoate [34], sodium isoleucinate [52], and sodium valinate [34], in order lowest to highest, plotted against temperature T and molality m.

large imidazole group on histidine does not change the fundamental profile of (Cp,/–m–T). Figure 25 shows apparent molar heat capacities Cp,/(i) of the equilibrium species H2Ser+Cl(aq) and Na+Ser(aq) in solutions containing equimolal amounts of the two-solute mixtures {zwitterionic serine (HSer±) + HCl} and (HSer± + NaOH) calculated by (a) equation (14) assuming that there is no reaction between the components, and (b) taking into account the known reactions using equations (14) to (20) [48]: .X o Xn C p;/ ðobsÞ  mðiÞ mðiÞ  C p;/ ðiÞ: ð14Þ

500

-1 -1 Cp, / (J·K ·mol )

-1 -1 Cp,φ / (J·K ·mol )

0.4

300

300 200

φ

200

400

100

100 0

0 0.4

m/

380

0.3

(m ol·

360

0.2

kg -1 0.1 )

340 320 0.0

300

T/

K

280

FIGURE 22. Apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of the aqueous protonated amino acid hydrochlorides of glycine [47], serine [48], threonine [51], methionine [52], and histidine [21], in order lowest to highest, plotted against temperature T and molality m.

0.4 0.3

m/

360

0.2

(m o l·

380

340 320

0.1

kg -1 )

0.0

300 280

T/

K

FIGURE 24. Apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of the aqueous zwitterionic amino acids glycine [47], serine [48], threonine [51], methionine [52], and histidine [21], in order lowest to highest, plotted against temperature T and molality m.

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

1313

C p;/ ðrelaxÞ ¼ Dr H m  ðoa=oT ÞP :

Equations (16) and (18) also apply to reaction (19a) for aqueous (HSer± + NaOH), where equation (14) now becomes equation (20), where DrHm is for reaction (19a), and where Cp,/(Na+OH) is from [32]:

600

400

H2 O(l) + Naþ Ser (aq) = HSer (aq) + Naþ OH (aq) ð19aÞ

200

HSer (aq) = Hþ (aq) + Ser (aq) þ

0 0.6 380

0.4 360

340

T/K

0.2 320

300 280

0.0

m

o / (m

-1 )

g l·k

FIGURE 25. Apparent molar heat capacities (Cp,/ + d) of the equilibrium species H2Ser+Cl(aq) and Na+Ser(aq) in solutions containing equimolal amounts of the components (serine + HCl) and (serine + NaOH) plotted against temperature T and molality m at p = 0.35 MPa [48]. s and upper solid surface calculated using equations (14) to (18), H2Ser+Cl(aq), d = 500 J Æ K1 Æ mol1; upper mesh surface, [Cp,/{HSer±(aq)} + Cp,/{H+Cl(aq)}], d = 500 J Æ K1 Æ mol1; h and lower solid surface calculated using equations (14), (16), and (18) to (20), Na+Ser(aq), d = 0 J Æ K1 Æ mol1; lower mesh surface, [Cp,/{HSer±(aq)} + Cp,/{Na+OH(aq)}], d = 0 J Æ K1 Æ mol1.

Equation (14) is Young’s Rule, which states that the total or observed apparent molar heat capacity of a solution Cp,/(obs) is approximately equal to the molality-weighted sum of the apparent molar heat capacities Cp,/(i) of all species i in the solution at molal concentrations m(i). This relationship becomes exact at {m(i) = 0 and m = 0}. For the solution (HSer± + HCl), the protonation reaction (15) occurs, but not to completion because pKa  2 for the following reaction: H2 Serþ Cl (aq) = Hþ Cl (aq) + HSer (aq)

ð15Þ

The proton dissociation equilibrium quotient for reaction (15) thus takes the form of the following equation: Qa ¼ a2  m=ð1  aÞ:

ð16Þ

Thus equation (14) becomes equation (17) for aqueous (HSer± + HCl), where a is the fraction of total serine in solution present as HSer±(aq), and it is also the extent of reaction (15): C p;/ ðobsÞ  ð1  aÞ  C p;/ ðH2 Serþ Cl Þ þ a  C p;/ ðHSer Þþ þ



a  C p;/ ðH Cl Þ þ Cp;/ ðrelaxÞ:

ð17Þ

The last term in equation (17) is a ‘‘relaxation’’ term that arises from the shift in equilibrium that occurs in reaction (15) when the temperature is changed if the molar enthalpy change for the reaction DrHm 6¼ 0. The value of DrHm can be calculated using the van’t Hoff equation, which takes the form of equation (18) for the current system. Values of Cp,/(H+Cl) used in equation (17) are from [32]:

ð19bÞ 



C p;/ ðobsÞ  ð1  aÞ  C p;/ ðNa Ser Þ þ a  C p;/ ðHSer Þþ a  C p;/ ðNaþ OH Þ þ C p;/ ðrelaxÞ: ð20Þ Figure 26 shows the fractional contributions for apparent molar heat capacities {Cp,/(i)/Cp,/(obs)} of the various terms in equation (17) for aqueous solutions of equimolal (serine + HCl) calculated using equations (14) to (18) and figure 27 shows the fractional contributions of the various terms in equation (20) for aqueous solutions of equimolal (serine + NaOH) calculated using equations (14), (16), and (18) to (20). These two figures illustrate the importance of accounting for changes in the equilibrium distribution of species as the there are changes in T and stoichiometric molality m. This is particularly important at low m, especially as one extrapolates to m = 0 mol Æ kg1 to determine standard state values. Figure 28 shows the values of the changes in heat capacities DrCp,m,j(k) defined by equation (21) for reaction (15) (j = 1) and for reaction (19b) (j = 2) for aqueous solutions of k = glycine, alanine, and L-2-aminobutanoic acid, calculated using equations (14) to (21):

4

{Cp,φ (i) / Cp,φ (obs)}

-1 -1 ( Cp,φ + δ ) / (J·K ·mol )

ð18Þ

2 0 -2 -4

380

360

340

T/K

. kg ol m ( /

0.2 320

300

0.1 280

0.0

m

0.5 0.4 0.3 -1 )

FIGURE 26. Fractional contributions for apparent molar heat capacities {Cp,/(i)/Cp,/(obs)} of the various terms in equation (17) for aqueous solutions of equimolal (serine + HCl) calculated using equations (14) to (18), plotted against temperature T and molality m [32]. At the highest T and lowest m these surfaces are in the order [Cp,/{Ser±(aq)}/ Cp,/(obs)] > [Cp,/{H2Ser+Cl(aq)}/Cp,/(obs)] > {Cp,/(relax)/Cp,/(obs)} > [Cp,/{HCl(aq)}/Cp,/(obs)].

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

Cp,φ (i) / Cp,φ (obs)}

1314

0.8 0.6 0.4 0.2 0.0 -0.2

0.6 380

0.4 360

340

T/K

320

0.2 300

0.0

280

m

-1 )

g l. k o / (m

FIGURE 27. Fractional contributions for apparent molar heat capacities {Cp,/(i)/Cp,/(obs)} of the various terms in equation (20) for aqueous solutions of equimolal (serine + NaOH) calculated using equations (14), (16), and (18) to (20), plotted against temperature T and molality m [32]. At the lowest m and highest T these surfaces are in the order [Cp,/{Na+Ser(aq)}/Cp,/(obs)] > [Cp,/{HSer±(aq)}/Cp,/(obs)] > {Cp,/(relax)/Cp,/(obs)} > [Cp,/{NaOH(aq)}/Cp,/(obs)].

Dr Y m;j ðkÞ 

X

Y /;j ðproducts kÞ 

X

Y /;j ðreactants kÞ: ð21Þ

It is seen from figure 28 that the surfaces DrCp,m,j(k) for these three amino acids are nearly co-planar for each proton dissociation reactions (15) and (19b), with mean values

of dDrCp,m,1(dk) = (6 ± 8) J Æ K1 Æ mol1 and dDrCp,m,2 (dk) = (11 ± 15) J Æ K1 Æ mol1 over all T and m. Figure 29 shows the values of the changes in molar reaction enthalpies DrHm,j(k) for reaction (15) (j = 1) and for reaction (19b) (j = 2) for aqueous solutions of k = glycine [47], alanine [49], and L-2-aminobutanoic acid [34], calculated using equations (11) and (14) to (21), with values of the integration constant DrHm(Tref, m) in equation (11) obtained by evaluation of results from the literature. As was seen in figure 28, the surfaces DrHm,j(k) for these three amino acids are nearly co-planar for each proton dissociation reactions (15) and (19b), with mean values of dDrHm,1(dk) = (1.7 ± 0.9) kJ Æ mol1 and dDrHm,2(dk) = (1.0 ± 0.6) kJ Æ mol1 over all T and m. It is also seen that the surfaces in figure 29 all decrease with increasing T, and that the surfaces are slightly convex with increasing T at any given m, in consequence of the negative values of DrCp,m,j at all T and m in figure 28. Figure 30 shows the first and second proton dissociation equilibrium constants pQaj(k) for reaction (15) and (19b) defined by equation (16) for aqueous solutions of k = glycine [47], alanine [49], and L-2-aminobutanoic acid [34], calculated using equations (14) to (21), plotted against temperature T and molality m. There are slight minima in pQa1(k) with T as a consequence of the values of DrHm,1(k) being positive at low T and decreasing below zero at intermediate T as seen in figure 29. This is contrasted with the large changes in pQa2(k) with T that are a consequence of the large values of DrHm,2(k) seen in figure 29. The slight convex contours of all of these pQaj(k) surfaces with T at constant m are the consequence of all

-20 40

-60

-1 ΔrHm,i / (kJ.mol )

-1 -1 ΔrCm,p,i / (J.K .mol )

-40

-80 -100 -120 -140

30 20 10 0

-160

0.5 0.4 380

0.3 360

340

T/K

0.2 320

0.1 300 280

0.0

m

-1

. kg ol / (m

0.5

-10

)

FIGURE 28. Changes in heat capacities DrCp,m,j(k) defined by equation (21) for reaction (15) (j = 1) and for reaction (19b) (j = 2) for aqueous solutions of k = glycine [47], alanine [49], and L-2-aminobutanoic acid [34], calculated using equations (14) to (21), plotted against temperature T and molality m. At the lowest T and highest m these surfaces are in the order DrCp,m,1(glycine) < DrCp,m,1(L-2-aminobutanoic acid) < DrCp,m,1(alanine) < DrCp,m,2(alanine) < DrCp,m,2(L-2-aminobutanoic acid) < DrCp,m,2 (glycine).

380

0.4 360

0.3 340

0.2

T / K 320 300

0.1 280

0.0

m

-1 )

. g ol k / (m

FIGURE 29. Changes in enthalpies DrHm,j(k) defined by equation (21) for reaction (15) (j = 1) and for reaction (19b) (j = 2) for aqueous solutions of k = glycine [47], alanine [49], and L-2-aminobutanoic acid [34], calculated using equations (14) to (21), plotted against temperature T and molality m. At the lowest T and highest m these surfaces are in the order DrHm,1(L-2-aminobutanoic acid) < DrHm,1(alanine) < DrHm,1(glycine) DrHm,2(glycine) < DrHm,2(alanine) < DrHm,2(L-2-aminobutanoic acid).

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

1315

8

1100

-1 . K-1 . mol ) C p,φ / (J

1000

0.5 0.4

4

340 700

/( m ol . kg 1 )

320

T/K

0.1 300

280

0.0

FIGURE 30. First and second proton dissociation equilibrium constants pQaj(k) for reaction (15) (j = 1) and for reaction (19b) (j = 2) defined by equation (16) for aqueous solutions of k = glycine [47], alanine [49], and L2-aminobutanoic acid [34], calculated using equations (14) to (21), plotted against temperature T and molality m. The lower three nearly coincident surfaces are pQa1(k) for reaction (19b) and the upper three nearly coincident surfaces are pQa2(k) for reaction (15). See text for discussion.

values DrCp,m,j(k) being negative as seen in figure 29. As was seen in figure 30, the surfaces pQaj(k) for these three amino acids are nearly co-planar for each proton dissociation reaction (15) and (19b), with mean values of dpQa1 (dk) = (0.026 ± 0.018) and dpQa2(dk) = (0.047 ± 0.012) over all T and m.

300

0.12 0.08

m / (mo . -1 l kg )

m

340

320

0.16

0.2 360

360

800

0.3

380

380

900

K

6

T/

pQa1, pQa2

10

280

0.04 0.00

FIGURE 32. Apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of aqueous n-dodecanepyridinium chloride [13], s and surface, plotted against temperature T and molality m.

Figure 31 gives an expanded view of figure 30 to show pQa1(k) for reaction (19b) for aqueous solutions of k = glycine [47], alanine [49], and L-2-aminobutanoic acid [34]. The minima at (300 < T/K < 330) are readily apparent in this figure. They arise naturally through the thermodynamic relationships of equations (11) and (12) and the values of DrHm,1(k) and DrCp,m,1(k) in figures 29 and 28, respectively. The minima coincide with the T and m where DrHm,1(k) = 0. Figure 32 shows our experimental Cp,/(T, p = 0.35 MPa, m) for the aqueous ionic surfactant n-dodecanepyridinium chloride [13], and figure 33 gives an expanded view of

2.45

pQa1

2.40

2.35

340

T/K

320

0.1 300

280

0.0

1000 380 360

900

340 800

FIGURE 31. First proton dissociation equilibrium constant pQa1(k) for reaction (15) (j = 1) defined by equation (16) for aqueous solutions of k = glycine [47], alanine [49], and L-2-aminobutanoic acid [34], calculated using equations (14) to (18), plotted against temperature T and molality m. At high T these surfaces are in the order pQa1(glycine) < pQa1(alanine) < pQa1(L-2-aminobutanoic acid), and at low T they are in the order pQa1(L-2-aminobutanoic acid) < pQa1(alanine) < pQa1(glycine). This is an expanded view of figure 30 to show the minima in the surfaces. The minima coincide with the T and m where DrHm,1(k) = 0.

320 0.04

300 0.03

0.02

m / (mo . -1 l kg )

0.01

K

360

m

0.2

T/

/( m ol . kg 1 )

0.3

380

1100

-1 . K-1 . mol ) C p,φ / (J

0.5 0.4

2.30

280 0.00

FIGURE 33. Apparent molar heat capacities Cp,/(T, p = 0.35 MPa, m) of aqueous n-dodecanepyridinium chloride [13], s and surface, plotted against temperature T and molality m. This is an expanded view of figure 32 to show the details of the surface at low m.

1316

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317

figure 32. The Cp,/(T, m) profile of this surfactant shows the complicated thermodynamic behavior of aqueous surfactant solutions. At low m, this ionic surfactant behaves as a strong hydrophobic electrolyte, with simple Debye–Hu¨ckel-like dependence on m. At (288 < T/K < 320) and near m > 0.02 mol Æ kg1, Cp,/(m) decreases markedly as the surfactant aggregates into micelles that behave as if they are composed of 52 n-dodecanepyridinium cations and 40 chloride ions. The value of DrHm  0 and DrCp,m  26 kJ Æ K1 Æ mol1 for this micellization reaction to form 1 mol of micelles from the component ions at T = 305 K. Equation (18) shows that the value of Cp,/(relax)  0 when DrHm  0. However, by equation (11) we also see that DrHm can become increasingly quite large and either negative or positive as T becomes far removed from T  305 K because DrCp,m  26 kJ Æ K1 Æ mol1. Therefore, Cp,/(relax) also becomes large and positive at T far removed from T  305 K, because (oa/oT)P is also proportional to DrHm [13]. One can readily see in figures 32 and 33 the effect on the observed Cp,/ that

TABLE 3 Summary of names co-authors and others who have contributed directly or indirectly to the calorimetric work summarized here and elsewhere Undergraduates students

Tim Ford

Todd Call

Ben Patterson

Marissa Stark

Kyle Sullivan

Joshua Price

Eric Sorenson

Eric Merkley

Bryan McRae

Jason Jardine

Brent Clayton

John Sargent

Steven Ziemer

Blair Brown

Megan Gould

Dave Swenson

Matt Blodgett

Jaylan Jones Post-doctoctorals and technicians

Steven Ziemer

Travis Niederhauser

Luisa Origlia-Luster

Karine Ballerat-Busserolles

Claudio Bizzo

Luca Pezzini Mentors and collaborators

Andy Hakin

Mike Simonson

Bob Mesmer

Loren Hepler

Tom Burchfield

Bevan Ott

Rex Goates

Reed Izatt

Rusty Russell

Ed Lewis

is caused by this increase in Cp,/(relax). One can also see clearly in figure 33 the effect of DrHm on the equilibrium constant for formation of micelles by noting that the cmc is at a minimum near T  305 K, but that it increases as T either increases or decreases, as required by equation (12). 5. Conclusions The use of fixed cell temperature scanning calorimetry to efficiently obtain precise heat capacities of small volumes of aqueous solutions at (278.15 < T/K < 393.15) and at p = 0.35 MPa has been described. The importance of using chemical calibration and of determining densities of the solutions investigated for determination of Cp,/ of solutes has been shown. Results from selected experiments have been given to illustrate the heat capacity behavior of a variety of solutes that dissolve to give simple ionic or neutral species, or that produce species that exist in T- and m-dependent equilibrium distributions. Examples have been given to illustrate how combinations of results of experiments on related solutes allows calculation of thermodynamic quantities for chemical processes and reactions over the ranges of T and solution compositions. Table 3 lists those who have contributed as co-authors of work in our laboratory with fixed cell temperature scanning calorimetry. The table also lists those who have had a significant impact on my sometimes slow and meager efforts to contribute something in solution calorimetry and thermodynamics over the past nearly four decades. I also acknowledge family members whose encouragement and sacrifice has enabled me to spend intense time doing the work summarized in this paper and elsewhere. References [1] V.B. Parker, Thermal Properties of Aqueous Uni-univalent Electrolytes, National Standard Reference Data Series, National Bureau of Standards 2, US Government Printing Office, Washington, DC, USA, 1965. [2] P. Picker, P.A. Leduc, P.R. Philip, J.E. Desnoyers, J. Chem. Thermodyn. 3 (1971) 631–642. [3] D. Smith-Magowan, R.H. Wood, J. Chem. Thermodyn. 13 (1981) 1047–1073. [4] K.N. Marsh, P.A.G. O’Hare (Eds.), Solution Calorimetry. Experimental Thermodynamics, IUPAC Chemical Data Series No. 39, vol. IV, Blackwell, Oxford, 1994. [5] G. Privalov, V. Kavina, E. Freire, P.L. Privalov, Anal. Biochem. 232 (1995) 79–85. [6] E.M. Woolley, J. Chem. Thermodyn. 29 (1997) 1377–1385. [7] H. Yao, K. Ima, I. Hatta, Jpn. J. Appl. Phys. 38 (1999) 945–950. [8] P.G. Hill, J. Phys. Chem. Ref. Data 19 (1990) 1233–1274. [9] D.G. Archer, J. Phys. Chem. Ref. Data 21 (1992) 793–829. [10] K. Ballerat-Busserolles, M.L. Origlia, E.M. Woolley, Thermochim. Acta 347 (2000) 3–7. [11] K. Ballerat-Busserolles, T.D. Ford, T.G. Call, E.M. Woolley, J. Chem. Thermodyn. 31 (1999) 741–762. [12] T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 325–330. [13] K. Ballerat-Busserolles, C. Bizzo, L. Pezzini, K. Sullivan, E.M. Woolley, J. Chem. Thermodyn. 30 (1998) 971–983.

E.M. Woolley / J. Chem. Thermodynamics 39 (2007) 1300–1317 [14] T.D. Ford, T.G. Call, M.L. Origlia, M.A. Stark, E.M. Woolley, J. Chem. Thermodyn. 32 (2000) 499–516. [15] M.L. Origlia, T.G. Call, E.M. Woolley, J. Chem. Thermodyn. 32 (2000) 847–856. [16] T.G. Call, K. Ballerat-Busserolles, M.L. Origlia, T.D. Ford, E.M. Woolley, J. Chem. Thermodyn. 32 (2000) 1525–1538. [17] T.D. Ford, T.G. Call, M.L. Origlia, M.A. Stark, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 287–304. [18] M.L. Origlia, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 451– 469. [19] M.L. Origlia, B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 917–927. [20] B.A. Patterson, T.G. Call, J.J. Jardine, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1237–1262. [21] J.J. Jardine, T.G. Call, B.A. Patterson, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1419–1440 [Corrigendum: J.L. Price, J.J. Jardine, T.G. Call, B.A. Patterson, M.L. OrigliaLuster, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 195–198]. [22] B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1567– 1585. [23] M.L. Origlia, T.G. Call, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1587–1596. [24] B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 33 (2001) 1735– 1764. [25] M.L. Origlia-Luster, B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 34 (2002) 511–526. [26] B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 34 (2002) 535–556. [27] J.J. Jardine, B.A. Patterson, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 34 (2002) 895–913. [28] W.B. Clayton, B.A. Patterson, J.J. Jardine, E.M. Woolley, J. Chem. Thermodyn. 34 (2002) 1531–1543. [29] M.L. Origlia-Luster, B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 34 (2002) 1905–1917. [30] B.R. McRae, B.A. Patterson, L.M. Origlia-Luster, E.C. Sorenson, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 301–329. [31] M.L. Origlia-Luster, K. Ballerat-Busserolles, E.D. Merkley, J.L. Price, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 331–347. [32] E. Sorenson, J.L. Price, B.R. McRae, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 529–553. [33] M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 1101–1118. [34] J.L. Price, E.C. Sorenson, E.D. Merkley, B.R. McRae, E.M. Woolley, J. Chem. Thermodyn. 35 (2003) 1425–1467. [35] B.R. Brown, T.L. Niederhauser, E.D. Merkley, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 71–77.

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[36] S.P. Ziemer, T. L Niederhauser, J.D. Sargent, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 147–154. [37] E.C. Sorenson, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 289– 298. [38] B.R. Brown, M.L. Origlia-Luster, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 331–339 [Corrigendum: B.R. Brown, M.L. Origlia-Luster, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 1025]. [39] B.R. Brown, E.D. Merkley, B.R. McRae, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 437–446. [40] J.D. Sargent, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 603–608. [41] T.L. Niederhauser, B.R. Brown, S.P. Ziemer, J.D. Sargent, E.M. Woolley, J. Chem. Thermodyn. 36 (2004) 1067–1077. [42] B.R. Brown, S.P. Ziemer, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 37 (2005) 843–853. [43] S.P. Ziemer, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 37 (2005) 984–995. [44] B.R. Brown, M.E. Gould, S.P. Ziemer, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 38 (2006) 1025–1035. [45] S.P. Ziemer, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 37 (2005) 1071–1084. [46] S.P. Ziemer, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 38 (2006) 323–336. [47] S.P. Ziemer, T.L. Niederhauser, E.D. Merkley, J.L. Price, E.C. Sorenson, B.R. McRae, M.L. Origlia-Luster, E.M. Woolley, J. Chem. Thermodyn. 38 (2006) 467–483. [48] S.P. Ziemer, T.L. Niederhauser, E.D. Merkley, J.L. Price, E.C. Sorenson, B.R. McRae, B.A. Patterson, E.M. Woolley, J. Chem. Thermodyn. 38 (2006) 634–648. [49] S.P. Ziemer, S.P. Ziemer, T.L. Niederhauser, J.L. Price, E.M. Woolley, J. Chem. Thermodyn. 38 (2006) 939–951. [50] D.M. Swenson, S.P. Ziemer, M.B. Blodgett, J.S. Jones, E.M. Woolley, J. Chem. Thermodyn. 38 (2006) 1523–1531. [51] S.P. Ziemer, E.M. Woolley, J. Chem. Thermodyn. 39 (2007) 67–87. [52] S.P. Ziemer, E.M. Woolley, J. Chem. Thermodyn. 39 (2007) 493–506. [53] S.P. Ziemer, E.M. Woolley, J. Chem. Thermodyn. 39 (2007) 645–666. [54] M.B. Blodgett, S.P. Ziemer, B.R. Brown, T.L. Niederhauser, E.M. Woolley, J. Chem. Thermodyn. 39 (2007) 627–644. [55] J.S. Jones, S.P. Ziemer, B.R. Brown, E.M. Woolley, J. Chem. Thermodyn. 39 (2007) 550–560.

JCT 07-14