Heat capacity of association

The term hydrophobic interaction refers to the solvent-induced interaction between nonpolar solutes in water. While experimental information on hydrophobic hydration is readily available, comparable information is nearly nonexistent for hydrophobic interactions, particularly for simple systems where interpretation of data would be unambiguous. This is due to the very low solubility of nonpolar solutes in water. Computational investigations have therefore been used extensively to investigate the nature of hydrophobic interactions. Early calculations in this area dealt primarily with the free energy of association, or potential of mean force (PMF), between pairs of nonpolar solutes in water, and have been reviewed by Blokzijl and Engberts. More recent calculations have included evaluations of the entropy and heat capacity of association. 

The variation of Cp for crystalline thiazole between 145 and 175°K reveals a marked inflection that has been attributed to a gain in molecular freedom within the crystal lattice. The heat capacity of the liquid phase varies nearly linearly with temperature to 310°K, at which temperature it rises more rapidly. This thermal behavior, which is not uncommon for nitrogen compounds, has been attributed to weak intermolecular association. The remarkable agreement of the third-law ideal-gas entropy at... 

Assuming that the heat capacity of an ideal gas is independent of temperature, calculate the entropy change associated with lowering the temperature of 2.92 mol of ideal gas atoms from 107.35°C to —52.39°C at (a) constant pressure and (b) constant volume. 

As with any calorimeter, each part of the coffee-cup calori-meter has an associated heat capacity. Because these heat capacities are very small, however, and because a coffee-cup calorimeter is not as accurate as other calorimeters, the heat capacity of a coffee-cup calorimeter is usually assumed to be negligible. It is assumed to have a value of 0 J/ C. 

Dulong was also an associate of Berthollet and a member of the Societe d Arcueil. His 1819 paper on heat capacities of elements in collaboration with Alexis-Therese Petit was widely interpreted as support for the atomic hypothesis. They noted that the product of specific heat times atomic weight was very nearly the same for a large number of sohd elements. They recognized that the quantity in qnestion represents the heat capacities of the atoms—or in modem terms, molar heat capacities. And they generalized the resnlts, asserting that, atoms of all simple bodies have exactly the same capacity for heat. (7)... 

In the remainder of this section it is desired to obtain the relative, constant-pressure heat capacity of the liquid at x=j and the concentration fluctuation factor for all compositions. Since the latter equation is complicated, it is not written out in full here. This has been done in Eqs. (37)-(45) of the paper by Liao et al. (1982) for the special case that 14 = 34 = 0 and / l3 is the only nonzero cubic interaction term, i.e., the version of the model applied here to the Ga-Sb and In-Sb binaries. Bhatia and Hargrove (1974) have given equations for the composition fluctuation factor at zero wave number for the special cases of complete association or dissociation and only quadratic interaction coefficients. 

With additional information, including the heat capacity of the buffer solvent, the partial specific volumes (volume per gram of the solute), and the specific volume of the solvent, one can extract the partial specific heat capacity (J K 1g I) of the solute. Privalov has summarized these calculations.8 Because the solutions are studied at very low concentrations, it is assumed that the contribution to the total heat capacity from the solvent cancels out when one calculates the excess heat capacity. With only minor exceptions, the procedures used to calculate parameters associated with the transformations in nucleic acids and in proteins are the same and yield quantities that are interpreted in similar ways, although researchers in these two fields may use a different notation for the same quantity. 

Halogenation, nitrosation, and nitration, diffusion control and pre-association in, 16, 1 Heat capacities of activation and their uses in mechanistic studies, 5, 121 Heterolysis, gas-phase, 3, 91... 

The physical state of each substance is indicated in the column headed State as crystalline solid (c), liquid (liq), gaseous (g), or amorphous (amorp). Solutions in water are listed as aqueous (aq). Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std state, m = 1). In this state the partial molal enthalpy and the heat capacity of the solute are the same as in the infinitely dilute real solution (aq. m). 

We must also consider the conditions that are implied in the extrapolation from the lowest experimental temperature to 0 K. The Debye theory of the heat capacity of solids is concerned only with the linear vibrations of molecules about the crystal lattice sites. The integration from the lowest experimental temperature to 0 K then determines the decrease in the value of the entropy function resulting from the decrease in the distribution of the molecules among the quantum states associated solely with these vibrations. Therefore, if all of the molecules are not in the same quantum state at the lowest experimental temperature, excluding the lattice vibrations, the state of the system, figuratively obtained on extrapolating to 0 K, will not be one for which the value of the entropy function is zero. 

The measured heat capacity increment associated with the transfer of an apolar hydrogen from a crystalline amino acid solid into water is 6.7 0.3 cal K-1 mol-1 or 0.45 0.02 cal (mol A2)-1 of apolar surface (Murphy and Gill, 1990, 1991). This same value is observed for the transfer of 1-alkanols into water (Hall n et al., 1986). The same value is also observed for the transfer of liquid hydrocarbons into water (Gill and Wadso, 1976), and for the dissolution of alkane... 

Calculation of A//e -quantities from the dependence of AG on temperature is less reliable than direct calorimetric measurements (Franks and Reid, 1973 Frank, 1973 Reid et al., 1969). However, disagreement between published A//-functions for apolar solutes in aqueous solutions may also stem from practical problems associated with low solubilities (Gill et al., 1975). Calorimetric data have the advantage that, as theory shows, the standard partial molar enthalpy H3 for a solute in solution is equal to the partial molar enthalpy in the infinitely dilute solution, i.e. x3 - 0. A similar identity between X3 and X3 (x3 - 0) occurs for the volumes and heat capacities but not for the chemical potentials and entropies. The design of a flow system for the measurement of the heat capacity of solutions (Picker et al., 1971) has provided valuable information on aqueous solutions. 

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