Heat capacity of solution

No adequate theoretical treatment has been developed that might serve as a guide in interpreting and correlating data on the heat capacities of liquids, but a critical review and recommended values are available for several hquids [18], However, it has been observed that the molar heat capacity of a pure hquid generally is near that of the sohd, so if measurements are not available we may assume that Cvm is 25 J mol K However, the heat capacities of solutions carmot be predicted reliably from the corresponding properties of the components. Empirical methods of treating solutions will be considered in later chapters. 

Heat capacity of solutes, as partial molal volume, compressibility, and thermal expansion, is composed of the contributions of nonsolvation (AC% ) and solvation (ACp ) ... 

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. 

There are several advantages, particularly in the context of aqueous solutions, in representing water using eqn (16). Thus, to a first approximation, a solute which increases (H20)b at the expense of (H20)d is a structure former a structure breaker has the opposite effect. The large heat capacity for water can be attributed to the need to melt part of (H20)b. In these terms, the partial molar heat capacity of solutes in water often indicates their effect on water structure. 

Equations (15) and (16) suggest that for ideal solutions, i.e., for the solutions involving molecules of similar sizes and intermolecular forces, Yj = 1 and the solubility can be estimated based on enthalpy of fusion, heat capacities of solute in solid and liquid states, and triple point temperature. Moreover, Eqs. (15) and (16) imply that solubility increases with temperature. 

Vasilev and Kruchina [91VAS/KRU] determined the heat capacity of solutions of sodium selenate m< 1.50 mol-kg ) at 298.15 K ... 

The heat capacity of solutions of solids dissolved in liquids is usually not available. If the solution is dilute, the usual practice is to neglect the solute and to use the solvent heat capacity. For a concentrated solution, neglecting the solute can lead to inaccuracies so that the use of enthalpy data is suggested. 

The heat capacity of solution at finite concentrations is analogous to volume, in that they can be measured directly in calorimeters, so that (Cp — can be evaluated by knowing both quantities, not just the difference. Like volume, is evaluated by extrapolating measurements of Cp to infinite dilution, or, as above, by manipulating other infinite dilution quantities. 

FIGURE G3. Relative partial molal heat capacity of solute in KCI solutions. (Data from R. Parsons, Handbook of Electrochemical Constants, Academic Press Inc., New York (1959), p. 43.)... 

The progress in this area of research is hampered by uncertainties in the current force fields, mixing rules, and other details of simulation protocols. In addition, some thermodynamic properties of solution like, the enthalpy or heat capacity of solution, caimot be simulated with sufficient accuracies to be tested against the experimental data for polyelectrolyte solutions. Further development of the force fields and methods to calculate solution thermodynamic parameters is needed to advance this area of science. 

This calorimeter was used to measure the heat capacity of solutions with a claimed uncertainty of 2% in the temperature and pressure region of 300-600 K and 0.2-30 MPa, respectively. 

The molar differential heat capacity of solution AsoLaC = Cp,A(sln) - C, a(s) is treated as a constant that can be determined from calorimetric measurements. 

Heat capacity of uranyl sulfate solutions. Van Winkle [57] estimated the heat capacity of dehydrated uranyl sulfate by comparison with uranyl nitrate and with salts of other metals and has estimated the heat capacity of solutions of uranyl sulfate in heavy water and in light water. The effect of temperature on the heat capacity of solutions was assumed to be the same, percentagewise, as the effect on the heat capacity of the pure solvent. Table 3-10 shows the influence of uranyl sulfate concentration upon the heat capacity of solutions at 25 and 250°C. No experimental measurements have been reported for temperatures above 103°C values below this temperature differ from the estimates by as much as 10% [57],... 

Perron, G., DeLisi, R., Davidson, L, Genereux, S., Desnoyers, J.E. On the use of thermodynamic transfer functions for the study of the effect of additives on micellization volumes and heat capacities of solutions of sodium octanoate systems. J. Colloid Interface Sci. 1981, 79(2), 432-442. 

Solution calorimetry covers the measurement of the energy changes that occur when a compound or a mixture (solid, liquid or gas) is mixed, dissolved or adsorbed in a solvent or a solution. In addition it includes the measurement of the heat capacity of the resultant solution. Solution calorimeters are usually subdivided by the method in which the components are mixed, namely, batch, titration and flow. 

Grolier J-P E 1994 Heat capacity of organic liquids Solution Calorimetry, Experimental Thermodynamics vol IV, ed K N Marsh and PAG O Hare (Oxford Blackwell)... 

Fig. 12. Correlatioa of AT. The three lines represeat the best fit of a mathematical expressioa obtaiaed by multidimensional nonlinear regressioa techniques for 99, 95, and 90% recovery the poiats are for 99% recovery. = mean molar heat capacity of Hquid mixture, average over tower AY = VA2 slope of equiHbrium line for solute, to be taken at Hquid feed temperature mg = slope of equilibrium line for solvent.

Then, assuming the heat capacity of the solute is negligible,... 

The deviation of the heat capacity of a solid solution from the heat capacity calculated by the additivity hypothesis (Kopp-Neumann rule), a quantity of importance for the evaluation of the... 

Figure 5.1 Specific heat capacity of aqueous sulfuric acid solutions at 298.15 K as a function of A, the ratio of moles of H O to moles of H2SO4.

Note that the m(dstrong electrolytes in dilute solution. It results because the charged ions break up the hydrogen bonded structure of the water and decrease the heat capacity of the solution over that of pure water. Thus, the contribution of Cp. 2 to Cp m is negative. 

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