Heat capacity changes

Jorgensen, W. L. Gao, J. Ravimohan, C. J. Phys. Chem. 1985, 89, 3470 Recently a similar linear dependence of the heat capacity change upon solvation has been observed Madan, B. Sharp, K. J. Phys. Chem. B 1997, 707, 11237... 

If the heat capacities change with temperature, an empirical equation like Eq. (6.13) may be inserted in Eq. (6.23) before integration. Usually the integration is performed graphically from a plot of either... 

The standard Gibbs-energy change of reaction AG° is used in the calculation of equilibrium compositions. The standard heat of reaclion AH° is used in the calculation of the heat effects of chemical reaction, and the standard heat-capacity change of reaction is used for extrapolating AH° and AG° with T. Numerical values for AH° and AG° are computed from tabulated formation data, and AC° is determined from empirical expressions for the T dependence of the C° (see, e.g., Eq. [4-142]). 

In dre present case of dre nucleation of solid particles from a liquid, dre heat capacity change from liquid to solid may be ignored, and hence AGj can be... 

The number of terms required in equation (2.19) depends upon the substance and the temperature interval. For small temperature differences, heat capacity changes with temperature are small and Cp can be represented reasonably well by the constant term a. For larger temperature changes a and b are used in equation (2.19), and over very large temperature ranges, higher power terms are included. Tables of the coefficients for equation (2.19) for a number of substances are summarized in the literature,2 with an abbreviated list3 summarized in Table 2.1. 

The fugacity coefficient for C02(g) at this temperature and total pressure is 1.188 and the heat capacity change for the reaction is given by... 

To take into account the possibility that the heat capacity changes with temperature, we go back to the expression... 

Schematic DTA curve of a typical polymer. Note glass transitions reflect a heat capacity change and thus they are seen as steps on the baseline rather than peaks.

A tangent is a straight line that meets a curve at a point, but not does cross it. If the heat capacity changes slightly with temperature, then we obtain the value of Cv as the gradient of the tangent to a curve of AU (as y) against T (as x). 

The ideal solubility of a non-dissociating solute, assuming the effects of pressure and specific heat capacity change on melting are negligible is [7,8] ... 

H. M. Heuvel, K. C. J. B. Lind. ComputerizedAnalysis and Correction of Differential Scanning Calorimetric Data for Effects Due to Thermal Lag and Heat Capacity Changes. Anal. Chem. 1970, 42, 1044—1048. 

Matveev, Y. I., Elankin, N. Y., Kalistrova, E. N., Danilenko, A. N., Niemann, C., and Yuryev, V. P. (1998). Estimation of contributions of hydration and glass transition to heat capacity changes during melting of native starches in excess water. Starch/Starke 50, 141-147. 

Heat capacity change, 269 Height equivalent to a theoretical plate. 8 Helium sparge, 188 Hemodialysis, 283 Heptane, 72,76. 173 Heptanoic acid, 260 1-Heptanol, 182, 183 Herbicides, analysis by RPC, 292 Herbicides, chromatography on polar sorbents, 103 Hesperidin, 293... 

This approximation is good enough to allow extrapolations of equilibrium constants over modest temperature ranges for many commonly encountered reactions. The reason is that the molar heat capacities C°P of the reactants and the products tend to cancel, giving a standard heat capacity change of reaction ACp which is often negligible ... 

If the standard heat capacity change of reaction is ACp, we can write... 

Figure 17.4 Ellingham plot (free energy of formation per mole O atoms versus temperature) for the reaction (metal) + (O2 gas) —> (metal oxide) the metal is not necessarily divalent. The plot is rectilinear if the heat capacity change of the reaction is negligible.

The activity coefficients of hydrobromic acid in the mixed solvents are lower, as expected, than those in water (20). Hydrobromic acid completely dissociates in the mixed solvents (e = 49.5 at 298.15° K for the 50 mass percent monoglyme) under investigation. Figure 2 clearly indicates that at a particular molality, the stoichiometric activity coefficient of hydrochloric acid is lower than that of hydrobromic acid in the same mixed solvent, and the heat capacity changes (Cp — Cp) also suggest that there are no ion-pair formations. 

Entropy is a measure of disorder. The largest negative entropy of solution in Table 3.1 is generally considered as evidence of the creation of structure (increased order) within the body of water. More recently it has been suggested that the creation of a cavity can explain the entropy decrease. Large heat capacity changes also indicate the structuring effect of the solute on the water molecules. The size of the solute molecule has a substantial effect on solubility. 

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