Partial molal enthalpy of mixing

Consider the case of an ideal solution involving a solute, which is a crystalline material at the solution temperature, dissolved in a liquid solvent. Even though the partial molal enthalpy of mixing is still zero because it is an ideal solution, there is an enthalpy requirement to overcome the crystal structure interactions. The van t Hoff equation (Adamson, 1979) gives... 

The theoretical partial molal enthalpy of mixing resulting from mixing two compounds with different cohesive energy densities was estimated by ... 

Substituting Equation 2.35 for the partial molal enthalpy of mixing, along with Equation 2.2 for the partial molal entropy of mixing, which is still considered ideal, and Equation 2.10 for the free energy change in Equation 2.6, gives... 

To calculate the partial molal enthalpies of mixing J//y, the enthalpy of vaporization at each temperature should be obtained from tabulated data and then substracted from AHt- In the case of reactive gases the enthalpies of mixing are in general exothermic. 

To calculate the heats of mixing it is necessary to know the relative partial molal enthalpies of the salt and the water in the sea salt solutions. This quantity for the water, Llf is arrived at as follows ... 

There shall be no volume change in preparing the solution from its individual components. Then, for all i, Vj, the molar volume of pure i, must match V its partial molal volume in solution. (2) There shall be no enthalpy change in the mixing process. Let and //, represent the molar and partial molal enthalpies of i in the pure state and in the final solution, respectively. Then the equality Hj = Hi shall apply to every i. (3) Raoult s law shall be obeyed the partial pressure of species i in the gas phase... 

In step a) the end-member pyroxenes are dissolved separately and in step b) the solid solution is dissolved. The assumption is made that the partial molal enthalpies of the components in the Pb2B205 melt are the same in steps a) andb) that is, they are independent of the way in which the components are introduced. This will be valid to a hi degree so long as the solutions are very dilute in CaAl2Si0g and CaMgSi20g. Thus it is seen that negative departures from linearity in the heat of solution versus composition curve correspond to positive enthalpies of mixing. 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

We have been actively developing two types of calorimeters which will operate at elevated temperatures and pressures. One type is a heat of mixing calorimeter to measure enthalpies of dilution in order to obtain differences in partial molal enthalpy... 

The mean ionic activity coefficients of hydrobromic acid at round molalities (calculated by means of Equation 2) are summarized in Tables XI, XII, and XIII for x = 10, 30, and 50 mass percent monoglyme. Values of —logio 7 at round molalities from 0.005 to 0.1 mol-kg-1 were obtained by interpolating a least squares fit to a power series in m which was derived by means of a computer. These values at 298.15° K are compared in Figure 2 with those for hydrochloric acid in the same mixed solvent (I) and that for hydrobromic acid in water (21). The relative partial molal enthalpy (H2 — Hj>) can be calculated from the change in the activity coefficient with temperature, but we have used instead the following equations ... 

Substituting for the partial molal change in molar enthalpy of mixing with respect to the solute (Equation 2.5) gives... 

We are neglecting any enthalpy changes on mixing so that the partial molal enthalpies are equal to the molal enthalpies of the pure components. Tlie molal enthalpy of species i at a particular temperature and pressure, H , is usually expressed in terms of an enthalpy of formation of species i at some reference temperamre 7), plus the change in enthalpy that results when the tem-... 

Partial molal free energies, enthalpies and entropies were calculated from the activity data. The integral free energy, enthalpy and entropy of mixing were... 

If the partial molar enthalpy is the same as the pure species molar enthalpy, then (dQldn n is zero and there is zero heat of mixing. Most solutions of chemically similar materials, such as benzene and toluene, have negligible heats of mixing, so for them the partial molar enthalpy is practically the same as the pure species molar enthalpy. For a mixture with zero heat of mixing, a plot of enthalpy per 1000 g of solvent vs. molality would have to be a straight line with slope A), the same as is shown for volume in Figure 6.4. 

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