Relative partial molar enthalpy defined

The heat absorbed or evolved when liquids or solutions are mixed or diluted is obtained from the calculation of AH for the solution process.kk The calculation of AH is usually obtained from the relative partial molar enthalpy defined as... 

In equation (7.70), we defined the relative partial molar enthalpy L, as... 

Besides the partial molar and the relative partial molar free energies of the components, some other important thermodynamic properties are the partial molar and the relative partial molar enthalpies and entropies. The partial molar enthalpy and entropy of the component A are defined by... 

The relative partial molar enthalpy, AHa, and the relative partial molar entropy, A,S a, are defined as... 

The relative values of partial molar enthalpies are used so frequently that it has become customary to use the special symbol to represent them. Thus, L i, which is the relative partial molar enthalpy, is defined by the equation... 

The relative partial molar enthalpies of the species are defined as the partial derivatives, in the last term,... 

But by Eq. (27) the chemical potential difference in parentheses is zero when the solution is in internal equilibrium. Therefore using Eq. (41), defining the relative partial molar enthalpies of the species, Eq. (40) reduces to... 

The relative partial molar enthalpies of the species are obtained by using Eqs. (70) and (75) in Eq. (41). When the interaction coefficients linear functions of T as assumed here, these enthalpies can be written down directly from Eq. (70) since the partial derivatives defining them in Eq. (41) are all taken at constant values for the species mole fractions. Since the concept of excess quantities measures a quantity for a solution relative to its value in an ideal solution, all nonzero enthalpy quantities are excess. The total enthalpy of mixing is then the same as the excess enthalpy of mixing and a relative partial molar enthalpy is the same as the excess relative partial molar enthalpy. Therefore for brevity the adjective excess is not used here in connection with enthalpy quantities. By definition the relation between the relative partial molar entropy of species j, Sj, and the excess relative partial molar entropy sj is... 

The relative partial molar enthalpy of the solvent is defined by... 

The quantity often reported is the relative partial molar enthalpy Z, of component / defined by the equation ... 

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