Integral enthalpy of dilution

In this process, the original solution is diluted by the addition of pure solvent, and hence, the enthalpy change is called an integral enthalpy of dilution. 

The enthalpy change for this process is an integral enthalpy of dilution for which we saw earlier that... 

The enthalpies of dilution of BE were required to calculate the enthalpies of transfer (19). From these Integral enthalpies of dilution AHj.jj the relative apparent molar enthalpies were derived following the technique of Fortier et al (21). The values of AHjjj corresponding to the Initial and final molalities are given In Table 1 along with the parametric equation for. ... 

An integral enthalpy of dilution, A7/(dil), refers to the enthalpy change for transfer of a finite amount of solvent from a pure solvent phase to a solution, T and p being the same before and after the process. The molar integral enthalpy of dilution is the ratio of... 

By combining Eqs. 11.4.10 and 11.4.11, we obtain the following expression for a molar integral enthalpy of dilution in terms of molar enthalpies of formation ... 

From tabulated values of molar enthalpies of formation, we can calculate molar integral enthalpies of solution with Eq. 11.4.11 and molar integral enthalpies of dilution with Eq. 11.4.12. Conversely, calorimetric measurements of these molar integral enthalpies can be combined with the value of AfH(B ) to establish the values of molar enthalpies of solute formation in solutions of various molalities. 

Table 11.2 Data for Problem 11.6. Molar integral enthalpies of dilution of aqueous HCl...

The data required to carry out such a calculation are the enthalpies of dilution as a function of molality at each temperature of interest. The integration would have to be carried out numerically. Enthalpy data for aqueous calcium chloride have been reported by Simonson, et al. [5]. 

In the former case, the solid remains suspended in the liquid in the microcalorimeter cell. Then a mother solution is added, either in one step (to obtain an integral heat. A ffUnt)) or in several steps, leading to differential heats, A H(dlff)l). In the latter case one could also speak of titration calorimetry. some commercial microcalorimeters are especially constructed for such titrations. Since, with these techniques, part of the added adsorptive remains in solution, the enthalpy of dilution A yH must be subtracted it is dependent on composition and can be determined in a blank without adsorbent. The difference between A y H(int) and A y H(dlff) has been discussed before, see sec. 1.3c. 

Integral enthalpy of dissolution is the same as in the previous case, when one of the components is in the solid or gaseous state it depends on the composition of the solution and for dilute solutions, it approaches a certain limiting value ... 

The integral enthalpy of dissolution of H2Se04(cr) to H2Se04(aq, 1 2000) was determined as well as the enthalpies of dilution of H2Se04(aq, 1 750). The latter measurements are only presented as a small graph. As this reference may be difficult to find some enthalpies of dissolution of H2Se04(cr) estimated from the data are presented here (dilution, (H2Se04(cr), aq dilution)) kJ-mof (750, - 58.6) (1000, - 59.6) ... 

Enthalpies of mixing or intermediary enthalpies of dilution, copolymer partial enthalpies of mixing (at infinite dilution), or copolymer (first) integral enthalpies of solution... 

Note that because the values of and are independent of the solution composition, the molar differential and integral enthalpies of solution at infinite dilution are the same. 

There is a simple relation between molar integral enthalpies of solution and dilution, as the following derivation demonstrates. Consider the following two ways of preparing a solution of molality mg from pure solvent and solute phases. Both paths are at constant T and p irn, closed system. 

Equation 11.4.10 is the desired relation. It shows how a measurement of the molar integral enthalpy change for a solution process that produces solution of a certain molality can be combined with dilution measurements in order to calculate molar integral enthalpies of solution for more dilute solutions. Experimentally, it is sometimes more convenient to carry out the dilution process than the solution process, especially when the pure solute is a gas or solid. 

Molar integral enthalpies of solution and dilution are conveniently expressed in terms of molar enthalpies of formation. The molar enthalpy of formation of a solute in solution is the enthalpy change per amount of solute for a process at constant T and p in which the solute, in a solution of a given molality, is formed from its constituent elements in their reference states. The molar enthalpy of formation of solute B in solution of molality will be denoted by Afi/(B, hib). 

If the immersion experiment is repeated at different solution concentrations, the enthalpy isotherm of immersion, A Hvs. Ci, is obtained. For immersion calorimetry, the presentation of the results is often more appropriate in terms of the relative enthalpy of immersion, AnH, which, for dilute solutions, is equal to the integral enthalpy of displacement A2 Hi, more generally obtained Ifom batch or flow sorption microcalorimetric measurements. The relative enthalpy of immersion is defined as the enthalpy of immersion in the solution minus the enthalpy of immersion in pure solvent 2 ... 

Values of partial and integral enthalpies of mixing have been obtained by calorimetric methods in liquid-phase Cu-R (table 25). The variation of the partial enthalpy at infinite dilution of rare earth elements in liquid copper is displayed in fig. 75 as a function of atomic number. Even though large discrepancies exist between the reported values, one observes a slight decrease of these values from La to Lu. 

POLYMER PARTIAL ENTHALPIES OF MIXING (AT INFINITE DILUTION) OR POLYMER (FIRST) INTEGRAL ENTHALPIES OF SOLUTION... 

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