Absolute calibration of flow calorimeters used for measuring differences in heat capacities. A chemical standard for temperatures between 325 and 600K

Two methods for the absolute calibration of flow calorimeters (used for measuring the differences in heat capacities of two fluids) have been investigated. In the recommended method of calibration, a change in the flow rate of the fluids is used to minic a change in the heat capacity of the fluid. In the other method of calibration, heat loss is measured using a fluid of known heat capacity, and it is assumed this heat loss is constant. This calibration method is not recommended because the heat loss is, in general, not constant. For some calorimeters the difference between the two methods of calibration is negligible, while for others erros as high as 40% are caused by choosing the wrong method. A detailed analysis of the heat losses in this kind of calorimetry shows why the two calibration methods give different results and leads to various methods of improving calorimeter construction and operation. Because chemical standardization is far more convenient for routine use, the recommended absolute calibration method has been used to establish 3.00 mol-kg^–1 aqueous NaCl as a chemical standard for temperatures between 325 and 600K at 17.7 MPa.     

Limiting Partial Molar Excess Heat Capacities and Volumes of Selected Organic Compounds in Water at 25°C

Well-known Picker flow microcalorimeters for the differential measurements of volumetric heat capacities have been employed in conjunction with vibrating tube densimeters to determine the molar heat capacity, volume, and the apparent properties in dilute aqueous solutions for 17 organic solutes of moderate hydrophobicity. The dependence on concentration of the apparent properties allowed the limiting partial molar quantities at infinite dilution to be extrapolated and the limiting partial molar excess quantities to be evaluated. Comparison with available literature data shows good agreement. The application of group contribution rules to the limiting partial properties has been tested using the original method and parameters proposed by Cabani et al. The predicted values of the partial molar volumes are in fair agreement with the present data except for some less common solutes. With partial molar heat capacities, the agreement is less satisfactory. To improve the performance of the method, missing parameters for some types of monofunctional and bifunctional molecules have been evaluated.     

Apparent molar volumes and heat capacities of aqueous solutions of sodium benzenesulfonate at 25°C

Apparent molar volumes and heat capacities of sodium benzenesulfonate have been measured at 25°C and at molalities up to 1.1 molal using a Picker flow densimeter and a Picker flow heat capacity calorimeter. Data for both properties have been modeled with Pitzer equations for the respective functions, and the standard state values evaluated. The apparent molar volume of sodium benzenesulfonate appears to be relatively insensitive to sample preparation. Possible reasons for the difference in the apparent molar volume reported here and the literature value are discussed.     

Thermodynamic properties of DCl in D2O solution from 5 to 50°C

The themodynamic properties of solutions of deuterium chloride (DCl) in deuterium oxide (D₂O) have been determined from emf measurements of the electrochemical cell without transference from 5 to 50°C, and from 0.002 to 1.0 mol-kg^–1. The standard potential of the silver/silver chloride electrode relative to the platinum/deuterium electrode has been determined. An equation for the Gibbs energy as a function of temperature has been derived from which the enthalpy, entropy, and heat capacity have been computed. Equations for the activity coefficient and the osmotic coefficient of DCl in D₂O have been developed. The excess Gibbs energy of the solution and the excess partial molar free energy as a function of temperature have been calculated, from which the other excess thermodynamic properties have been computed. The values for the heat capacity and the apparent molar heat capacity have been compared with calorimetric data in the literature. The relative partial molar enthalpy has been calculated. The solvent isotope effect on the excess thermodynamic functions is discussed.     

Enthalpies of Dilution of Aqueous Solutions of LiCl, KCl, and CsCl at 300, 325, and 350°C

Dilution enthalpies, measured using isothermal flow calorimetry, are reported for aqueous solutions of LiCl, KCl, and CsCl at 300°C and 11.0 MPa, 325°C and 14.8 MPa, and 350°C and 17.6 MPa. The concentration range of the chloride solutions was 0.5 to 0.02m. Parameters for the Pitzer excess Gibbs ion-interaction equation were determined from the fits of the experimental heat data. Equilibrium constants, enthalpy changes, entropy changes, and heat capacity changes for ion association of the chloride salts were estimated from the heat data. For all systems, the enthalpy and entropy changes were positive and had accelerating increases with temperature. The resulting equilibrium constants show significant, but smaller, increases with temperature.     

Enthalpies of Dilution of Aqueous Solutions of NaOH, KOH, and CsOH at 300, 325, and 350°C

Dilution enthalpies, measured using isothermal flow calorimetry, are reported for aqueous solutions of KOH and CsOH at 300°C and 11.0 MPa, 325°C and 14.8 MPa, and for aqueous solutions of NaOH, KOH, and CsOH at 350°C and 17.6 MPa. Previously collected dilution enthalpies for aqueous solutions of NaOH at 300°C and 9.3 MPa and at 325°C and 12.4 MPa were included when fitting the Pitzer parameters. The concentration range of the hydroxide solutions was 0.5–0.02 molal. Parameters for the Pitzer excess Gibbs ion-interaction equation were determined from the fits of the experimental heat data. Equilibrium constants, enthalpy changes, entropy changes, and heat capacity changes for alkali metal ion association with hydroxide ion were estimated from the heat data. For all systems, the enthalpy changes and entropy changes were positive and had accelerating increases with temperature. The resulting equilibrium constants show significant, but smaller, increases with temperature.     

Model systems for hydrophobic interactions: Volumes and heat capacities ofn-alkoxyethanols in water

The densities and heat capacities of the first four members of the 2-n-alkoxyethanols were measured in water over the whole mole fraction range with a flow densimeter and a flow microcalorimeter. The methoxy and n-propoxy homologs were studied at 25°C, ethoxyethanol at 19, 25, and 40C, andn-butoxyethanol at 4, 10, 25, 40, and 55°C. While methoxyethanol behaves as a fairly typical polar nonelectrolyte in water,n-butoxyethanol shows trends in the concentration dependence which resemble micellization; some pseudo-microphase transition occurs at about 0.02 mole fraction, and this transition concentration decreases with increasing temperature. There is no simple relationship between this phenomenon and the existence of a lower critical solution temperature at 49°C since the sharpness of the thermodynamic changes is maximum at the lowest temperature and at 55°C the apparent molal quantities on both sides of the two-phase region appear to fall on the same continuous curve. In the region prior to the pseudo-microphase separation the apparent and partial molal heat capacities decrease regularly but beyond approximately 0.01 mole fraction increase sharply to a maximum, suggesting some type of pre-association. The apparent molal heat capacity of water in the binary solutions is larger than the molar heat capacity of water over the whole mole fraction range. The present data seem to be consistent with a clathrate model for hydrophobic hydration and interactions with these systems.     

Apparent molar heat capacities of aqueous solutions of acetic,propanoic and succinic acids,sodium acetate and sodium propanoate from 300 to 525 K and a pressure of 28 MPa

The apparent molar heat capacities of dilute aqueous solutions of acetic, propanoic and succinic acid and sodium salts of the two monofunctional acids were measured at 300 Kp,2 ^o . After subtracting the heat capacity of a point mass, the remaining heat capacity was successfully decomposed into functional group contributions at all temperatures. Together with the results of our previous paper on alcohols and diols the heat capacity contributions of the CH₂, CH₃, OH, COOH, (COOH)₂, and COONa groups are now available and these allow reasonably accurate predictions of the heat capacities of all compounds composed of these groups in this temperature range.     

Heat capacities of tetraphenyl phosphonium chloride in methanol; ethanol; acetonitrile and water

Measurement of heat capacities Cp at 308.65, 311.65 and 314.65 K have been made for solutions of tetraphenyl phosphonium chloride (TPPC) with methanol, ethanol, acetonitrile and water for dilute solutions (up to 0.1 M) by means of a microcalorimeter (Setaram C-80, model from France). The experimental values of heat capacity for the various solutions have been used to calculate the values of partial molar heat capacities Cp_2,m of the salt in different solutions. The results are studied in relation to the special features of solvations in solutions of the TPPC.     

Single run heat capacity measurements

An outline for the data analysis of single-run heat capacity measurments by dual sample DSC is presented with the following features: 1. Heat flow correction by subtracting the contribution due to the sample pan, including correction for mismatched pan masses. 2. Heat flow and temperature correction with a nonlinear temperature calibration, temperature lag correction, and heating rate correction. 3. Calculation of the cell constants for both cell positions and evaluation of the asymmetry factor between cell positions A and B. 4. Heat capacity calibration and calculation with slope and asymmetry correction. 5. Calculation of heat capacity for multiple runs. 6. Data curve fitting for heat capacity.This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 8818412 and the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. Thanks are given to TA Instruments, Inc. (New Castle, DE) for providing the commercial heat capacity software and helping with the acquisition of the calorimeter.     

Enthalpies of Dilution of Aqueous Solutions of HCl, MgCl2}, CaCl2, and BaCl2 at 300, 325, and 350°C

Dilution enthalpies, measured using isothermal flow calorimetry, are reported for aqueous solutions of BaCl₂ at 300°C and 11.0 MPa, MgCl₂, CaCl₂, and BaCl₂ at 325°C and 14.8 MPa, and at 350°C and 17.6 MPa. Previously collected dilution enthalpies for aqueous solutions of MgCl₂ and CaCl₂ at 300°C and 10.3 MPa and for aqueous solutions of HCl at 250, 275, and 300°C at 10.3 MPa and 320°C at 12.8 MPa were included with the new data at 300°C and 11.0 MPa and at 350°C and 17.6 MPa when fitting the Pitzer parameters. The concentration range of the chloride solutions was 0.5 to 0.02 molal. Parameters for the Pitzer excess Gibbs ion–interaction equation were determined from the fits of the experimental heat data. Equilibrium constants, enthalpy changes, entropy changes, and heat-capacity changes for the association of alkaline earth metal ions and H⁺ with chloride ion were estimated from the heat data. For all systems, the enthalpy and entropy changes are positive and show accelerating increases with temperature. The resulting equilibrium constants show significant, but smaller, increases with temperature.     

Heat capacity of alcohols in aqueous solutions in the temperature range from 5 to 125°C

Using a precise technique of scanning microcalorimetry the heat capacity differences between water and dilute aqueous solutions of ethanol, n-propanol, n-butanol and n-pentanol were measured from 5 to 125°C and the partial molar heat capacities of these substances in water were determined. It was found that the heat capacity increment for alcohol disolved in water is proportional to the number of the-CH ₂ ^– groups and decrease with a temperature increase. The heat capacity increment of hydration of non-polar groups is shown to be positive and large at room temperature and decreases in magnitude as the temperature increases. In contrast, the heat capacity increment of hydration of polar groups is negative at room tempreature and increases as the temperature increases. From the temperature dependence of the heat capacity increment one can assume that the water molecules solvated by the non-polar groups of the alcohols behave in a non-cooperative manner.     

Hydration heat capacities of hydrophobic solutes at 248–373 K

A new equation is suggested to define the temperature dependence of the Gibbs energy of hydration of hydrophobic substances: ΔG ⁰ = b ₀ + b ₁ T + b ₂lnT. According to this equation, the hydration heat capacity is in inverse proportion to temperature. Consistent values of hydration heat capacity of nonpolar solutes have been obtained for different temperatures using data on solubility and dissolution enthalpy. The contributions of the hydrocarbon radicals and OH group to the heat capacity of hydration of the compounds were found for the temperature range 248–373 K. The hydration heat capacity of the hydroxyl group has a weak dependence on temperature and increases by only 12 J/(mol·K) in the specified temperature interval. Changes in the hydration entropy of hydrophobic and OH groups are calculated for the temperature increasing from 248 K to 373 K.     

Thermodynamics of aqueous phosphate solutions: Apparent molar heat capacities and volumes of the sodium and tetramethylammonium salts at 25°C

A Picker flow microcalorimeter and a flow densimeter were used to obtain apparent molar heat capacities and apparent molar volumes of aqueous solutions of Na₃PO₄ and mixtures of Na₂HPO₄ and NaH₂PO₄. Identical measurements were also made on solutions of tetramethylammonium salts to evaluate the importance of anion-cation interaction. The experimental apparent molar properties were analyzed in terms of a simple extended Debye-Hückel model and the Pitzer ion-interaction model, both with a suitable treatment for the effect of chemical relaxation on heat capacities, to derive the partial molar properties of H₂PO ₄ ^– (aq), HPO ₄ ^2– (aq) and PO ₄ ^3– (aq) at infinite dilution. The volume and heat capacity changes for the second and third ionization of H₃PO₄(aq) have been determined from the experimental data. The importance of ionic complexation with sodium is discussed.     

Determination of unfrozen matrix concentrations at low temperatures using stepwise DSC

The aim of the current study was to determine whether stepwise DSC (SW-DSC) is a suitable method for measuring the unfrozen matrix concentration (C_g) of binary aqueous solutions at temperatures as low as −50 °C. The optimal experimental conditions were determined using water. Reliable heat capacity values were determined at nominal scanning rates between 10 and 100 K min⁻¹, sample weights between 8 and 15 mg, and with the sample completely covering the base of the DSC pan. These conditions were then applied to aqueous solutions of ethylene glycol, glycerol and sodium chloride.The apparent heat is the sum of all heat including latent heat, heat capacity and heat of dilution. The influence of each term on the apparent heat was discussed in detail. The apparent heat values of the frozen samples were then used to calculate the ice fraction in the solution and were expressed as the C_g. The calculated C_g values were similar to previously published values. This study showed that SW-DSC can be used to determine the C_g over a wide temperature range using only one single solution. This technique is advantageous for solutes that are not available in large quantities.     

Heat Capacity Measurements Using Temperature-modulated Heat Flux DSC with Close Control of the Heater Temperature

The determination of heat capacity data with sawtooth-type, temperature-modulated differential scanning calorimetry is analyzed using the Mettler-Toledo 820 ADSC™temperature-modulated differential scanning calorimeter (TMDSC). Heat capacities were calculated via the amplitudes of the first and higher harmonics of the Fourier series of the heat flow and heating rates. At modulation periods lower than about 150 s, the heat capacity deviates increasingly to smaller values and requires a calibration as function of frequency. An earlier derived correction function which was applied to the sample temperature-controlled power compensation calorimeter enables an empirical correction down to modulation periods of about 20 s. The correction function is determined by analysis of the higher harmonics of the Fourier transform from a single measurement of sufficient long modulation period. The correction function reveals that the time constant of the instrument is about 5 s rad⁻¹ when a standard aluminum pan is used. The influence of pan type and sample mass on the time constant is determined, the correction for the asymmetry of the system is described, and the effect of smoothing of the modulated heat flow rate data is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat capacity of poly(butylene terephthalate)

The low‐temperature heat capacity of poly(butylene terephthalate) (PBT) was measured from 5 to 330 K. The experimental heat capacity of solid PBT, below the glass transition, was linked to its approximate group and skeletal vibrational spectrum. The 21 skeletal vibrations were estimated with a general Tarasov equation with the parameters Θ₁ = 530 K and Θ₂ = Θ₃ = 55 K. The calculated and experimental heat capacities of solid PBT agreed within better than ±3% between 5 and 200 K. The newly calculated vibrational heat capacity of the solid from this study and the liquid heat capacity from the ATHAS Data Bank were applied as reference values for a quantitative thermal analysis of the apparent heat capacity of semicrystalline PBT between the glass and melting transitions as obtained by differential scanning calorimetry. From these results, the integral thermodynamic functions (enthalpy, entropy, and Gibbs function) of crystalline and amorphous PBT were calculated. Finally, the changes in the crystallinity with the temperature were analyzed. With the crystallinity, a baseline was constructed that separated the thermodynamic heat capacity from cold crystallization, reorganization, annealing, and melting effects contained in the apparent heat capacity. For semicrystalline PBT samples, the mobile‐amorphous and rigid‐amorphous fractions were estimated to complete the thermal analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4401–4411, 2004     

Deuterium isotope effect on molar heat capacities and apparent molar heat capacities in dilute aqueous solutions: A multi-channel heat-flow microcalorimeter study

The molar heat capacities of chloroform, dichloromethane, methanol, acetonitrile, acetone, dimethyl sulfoxide, benzene, dimethylformamide, toluene, and cyclohexane, as well as their deuterated isotopologues, were measured using a multi-channel heat conduction TAM (Thermal Activity Monitor) III microcalorimeter. In addition, the apparent molar heat capacities of some of the associated dilute aqueous solutions (0.0039 < solute mole fraction, x_i < 0.0210) were also measured. A temperature drop method from (298.15 to 297.15) K at 0.1 MPa was employed. The corresponding heat capacities were determined from the integration of the measured heat flow. The heat capacity results are shown to be in good to very good agreement with the available literature values. In addition, good correlations were obtained for the effect of isotopic substitution on both molar heat capacity and apparent molar heat capacity in aqueous solutions. These correlations should be useful in the prediction of the molar heat capacities or the apparent molar heat capacities of other deuterated compounds. Since these measurements were conducted with ampoules, the effects of heat of condensation and/or vapor space on the accuracy of the heat capacity determinations are discussed. The overall results from this study demonstrate the utility of a multi-channel heat conduction microcalorimeter in obtaining good reproducibility and good accuracy for molar heat capacities as well as apparent molar heat capacities from simultaneous samples.     

Reversible and irreversible heat capacity of poly[carbonyl(ethylene‐co‐propylene)] by temperature‐modulated calorimetry

The heat capacity of poly[carbonyl(ethylene‐co‐propylene)] with 95 mol % C₂H₄? CO? (Carilon EP®) was measured with standard differential scanning calorimetry (DSC) and temperature‐modulated DSC (TMDSC). The integral functions of enthalpy, entropy, and free enthalpy were derived. With quasi‐isothermal TMDSC, the apparent reversing heat capacity was determined from 220 to 570 K, including the glass‐ and melting‐transition regions. The vibrational heat capacity of the solid and the heat capacity of the liquid served as baselines for the quantitative analysis. A small amount of apparent reversing latent heat was found in the melting range, just as for other polymers similarly analyzed. With an analysis of the heat‐flow rates in the time domain, information was collected about latent heat contributions due to annealing, melting, and crystallization. The latent heat decreased with time to an even smaller but truly reversible latent heat contribution. The main melting was fully irreversible. All contributions are discussed in the framework of a suggested scheme of six physical contributions to the apparent heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1565–1577, 2001     

Partial molar heat capacities and volumes of transfer of nucleic acid bases,nucleosides and nucleotides from water to aqueous solutions of sodium and calcium chloride at 25°C

Partial molar heat capacities and volumes of some nucleic acid bases, nucleosides and nucleotides have been measured in 1m aqueous NaCl and CaCl₂ solutions using Picker flow microcalorimeter and a vibrating tube digital densimeter. The partial molar heat capacities of transfer and volumes of transfer from water to the electrolyte solutions were calculated using earlier data for these compounds in water. The values of these transfer parameters are positive. The higher values for transfer to aqueous CaCl₂ solutions reflect the stronger interactions of the constituents of the nucleic acids with Ca⁺² ions than with the Na⁺ ions.