Enthalpy from heat capacity

Figure 2J Enthalpy, entropy, heat capacity, and volume modification in a-quartz/ /3-quartz transition region. Reprinted from H. C. Helgeson, J. Delany, and D. K. Bird, American Journal of Science, 278A, 1-229, with permission.

Medium-chain alcohols such as 2-butoxyethanol (BE) exist as microaggregates in water which in many respects resemble micellar systems. Mixed micelles can be formed between such alcohols and surfactants. The thermodynamics of the system BE-sodlum decanoate (Na-Dec)-water was studied through direct measurements of volumes (flow denslmetry), enthalpies and heat capacities (flow microcalorimetry). Data are reported as transfer functions. The observed trends are analyzed with a recently published chemical equilibrium model (J. Solution Chem. 13,1,1984). By adjusting the distribution constant and the thermodynamic property of the solute In the mixed micelle. It Is possible to fit nearly quantitatively the transfer of BE from water to aqueous NaDec. The model Is not as successful for the transfert of NaDec from water to aqueous BE at low BE concentrations Indicating self-association of NaDec Induced by BE. The model can be used to evaluate the thermodynamic properties of both components of the mixed micelle. 

With most properties (enthalpies, volumes, heat capacities, etc.) the standard state is infinite dilution. It is sometimes possible to obtain directly the function near infinite dilution. For example, enthalpies of solution can be measured in solution where the final concentration is of the order of 10-3 molar. With properties such as volumes and heat capacities this is more difficult, and, to get standard values, it is usually necessary to measure apparent molal quantities 0y at various concentrations and extrapolate to infinite dilution (y° = Y°). Fortunately, it turns out that, at least with volumes and heat capacities, the transfer functions AYe (W — W + N) do not vary significantly with the electrolyte concentration as long as this concentration is relatively low (3). With most of the systems investigated, the transfer functions were calculated from apparent molal quantities at 0.1m and assumed to be equivalent to the standard values. 

On the basis of initial calorimetric measurements (Gill et al., 1976 Olofsson et al., 1984 Dec and Gill, 1984, 1985), one can represent the enthalpy of transfer of hydrocarbons from the gaseous phase to water by a linear function of temperature in the temperature range 15-35°C. Bearing in mind Kirchhoff s relation between enthalpy and heat capacity change in the reactions, one can conclude that the transfer of nonpolar molecules to water leads to an increase of heat capacity by a value that is independent of temperature in the mentioned temperature range. 

Comparison of the enthalpy of protein denaturation (Table I) with the enthalpy of solution of liquid hydrocarbons at Ts (Table II) shows also a great difference in their values the enthalpy of protein denaturation at Ts is about 6 kJ per mole of amino acid residues with an average molecular weight of 1 IS the enthalpy of solution of hydrocarbons of comparable size (ethylbenzene, Afw = 106) is almost five times larger at this temperature. For denaturation of solutions of proteins in water AnCp(25°C) is about 70 J K-1 per mole of amino acid residues, whereas A"Cp(250C) for ethylbenzene is 318 J K-1 mol-1. However, this difference in the enthalpy and heat capacity increment is quite understandable, as not all of the groups in a protein are nonpolar, not all are screened from water in the native state, and not all are in contact with water in the denatured state. 

To obtain ACp they subtracted their measured values from heat capacities of the bulk. The surface enthalpy at 298 K / 298 was taken from solubility experiments. For MgO and using /i 298 = I040 mN/m they obtained a surface tension of 957 mN/m and a surface entropy of 0.28 mNJm-lK l. 

Thermochemical data on the separate phases in equUibrium are needed to constmct accurate phase diagrams. The Gibbs energy of formation for a pure substance as a function of temperature must be calculated from experimentally determined temperature-dependent thermodynamic properties such as enthalpy, entropy, heat capacity, and equihbrium constants. By a pure substance, one generally means a stoichiometric compound in which the atomic constituents ate present in an exact, simple reproducible ratio. 

ProTherm (16) is a large collection of thermodynamic data on protein stability, which has information on 1) protein sequence and stmcture (2) mutation details (wild-type and mutant amino acid hydrophobic to polar, charged to hydrophobic, aliphatic to aromatic, etc.), 3) thermodynamic data obtained from thermal and chemical denaturation experiments (free energy change, transition temperature, enthalpy change, heat capacity change, etc.), 4) experimental methods and conditions (pH, temperature, buffer and ions, measurement and method, etc.), 5) functionality (enzyme activity, binding constants, etc.), and 6) literature. 

The low temperature heat capacity, 14.0-315 K was measured by Getting (7). Janz et al. (8) measured the heat content by drop calorimetry in the temperature range 630-1250 K, and gave enthalpy and heat capacity equations based on their measurements. The above information was used in a Shomate analysis in order to smooth the enthalpy and calculate heat capacity above 298.15 K. The values from the low and high temperature sources join smoothly at 298.15 K. The heat capacity was graphically extrapolated above the melting point. The entropy at 14.0 K was calculated from the extrapolated low temperature... 

The entropy of CuCl was obtained from the several pieces of equilibrium data reported above and the adopted A.H (298J.5 K). A -1 -1 weighted average of 20.8 1 cal K mol was adopted for S CCuCl, cr, 298.15 K). The enthalpy and heat capacity above 298.15 K have... 

Reproduced by permission from G. E Boyd, Thermal Effects In Ion-Exchange Reactions With Organic Exchangers Enthalpy and Heat Capacity Changes , in Ion Exchange In The Process Industries , Society of Chemical Industry, London, 1970, p. 261)... 

Calculate enthalpy (and internal energy) changes (excluding phase changes) from heat capacity equations, graphs and charts, tables, and computer data bases given the initial and final states of the material. 

Step 3 First we have to get some pertinent enthalpy or heat capacity data so that the energy balances can be used. If you used a computer program, the data would be retrieved from a data base. (The exit streams have the same composition as the solutions in the condenser or reboiler, respectively.) The heat capacity data for liquid benzene (Bz) and chlorobenzene (Cl) will be assumed to be as follows (no enthalpy tables are available) ... 

Simple FORTRAN programs have been prepared for the reader s use that solve linear and nonlinear equations, retrieve the properties of water and steam, and of air-water mixtures, calculate the vapor pressure of pure substances, calculate enthalpy changes from heat capacity equations, and so on. A disk containing these codes will be found in a pocket in the back of the book. (Readers are encouraged to use library codes when available, codes that may be more accurate and robust than the simple codes provided.) As a result, the portions of the book formerly treating... 

Determined experimentally from heat capacity data (C/ m), enthalpy data (A77) for phase changes, and the third law of thermodynamics... 

From COF 2 hydrolysis. From the enthalpy of combustion of CH in O j-F j mixtures. From heat capacity data. Based on the data of [1078c]. Based on the data of [17SSJ. Based on the data of 213I. ... 

ACp = —210 J K moT both enthalpy and entropy possess substantial temperature dependencies, yet, AC does not change by more than 8 kJ over the span from 10 to 40 °C rendering the estimation of binding enthalpies or heat capacity changes by noncalorimetric methods quite problematic. Reproduced with permission from A. Velasquez-Campoy et al., Biophys. Chem. 2005, 115, 115. 

The sum of the two values, the enthalpy of cooling, Acooi f, and the enthalpy of dissolution, AgoiT/, is the so-called relative enthalpy, Hrei, of the sample. From the temperature dependence of the relative enthalpy, the heat capacity as well as all the following enthalpy, changes could be calculated. 

RAS/MED2] Rasulov, S. M., Medzhidov, R. A., Enthalpy and heat capacity of lead selenide in the temperature interval 300-1480°K, High Temp., 16, (1978), 251-256. From a citation in this Bibliography... 

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