Molar enthalpy partial

Charged particles such as ions and electrons play an important role in what is called electrochemical processes. We shall now discuss the energy level of ions and electrons in an electrochemical system. The partial molar free enthalpy (partial molar Gibbs energy) of a charged particle i, as described in the foregoing chapter (section 8.7), is represented by the electrochemical potential r)t shown in Eq. 9.1 ... 

Changes in Partial Molar Enthalpy, Partial Molar Entropy, and Heat Capacity for the Transfer of Hydrocarbons from Their Own Medium to Water (20°C)... 

G, G,, [G] free enthalpy, partial molar free enthalpy of /, generalized free enthalpy. 

The partial molar enthalpy for every component i is found from an appropriate form of the Gibbs-Helmholtz equation... 

PARTIAL MOLAR EXCESS ENTHALPY AT INFINITE DILUTION OF THIAZOLE IN VARIOUS SOLVENTS AT SIS.IS K... 

We may define, say, partial molar volume, enthalpy, or entropy by analogy with Eq. (8.5) ... 

The driving force for the transport of all particles is a change in the electrochemical potential /i, which is related to the partial molar free enthalpy /i, and the electric potential 0 as follows ... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

Thalium, excess entropy and partial molar enthalpy of solutions of noble metals in, 133... 

Thermodynamics gives limited information on each of the three coefficients which appear on the right-hand side of Eq. (1). The first term can be related to the partial molar enthalpy and the second to the partial molar volume the third term cannot be expressed in terms of any fundamental thermodynamic property, but it can be conveniently related to the excess Gibbs energy which, in turn, can be described by a solution model. For a complete description of phase behavior we must say something about each of these three coefficients for each component, in every phase. In high-pressure work, it is important to give particular attention to the second coefficient, which tells us how phase behavior is affected by pressure. 

In Chapter 7, we will describe relative partial molar enthalpy in more detail. 

From the Debye-Hiickel expressions for lny , one can derive equations to calculate other thermodynamic properties. For example L2, the relative partial molar enthalpy,q and V2, the partial molar volume are related to j by the equations... 

We described methods for obtaining values for V,-, Cpi, and S but did not apply the methods to //, and G, (or w), since absolute values of Gm and Hm cannot be obtained. We did describe a procedure for obtaining the volume difference V,— Vf using equations (5.40). (5.41) and (5.42),r where V is the volume of the pure substance, and indicated that equations of the same form can be used to obtain //, - Hf. We will return to this method later in this chapter as we describe ways for measuring relative partial molar enthalpies. 

The quantity //, - H° is called the relative partial molar enthalpy and given the symbol L,. It is the difference between the partial molar enthalpy in the solution and the partial molar enthalpy in the standard state. That is,... 

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°. 

Also tabulated is 4>L, the apparent partial molar enthalpy. We will define this quantity and describe its application later. 

Substitution of relative partial molar enthalpies gives... 

The last term in the calculation is L f, the relative partial molar enthalpy for pure water, which is zero. 

Figure 7.9 (a) Enthalpies of dilution starting with a solution containing 3 moles fEO per 1 mole HC1 (m = 18.50 or w1/2 = 4.30) and (b), relative apparent molar enthalpies (4>L) and relative partial molar enthalpies (L and L >) for the resulting mixtures. 

Figure 7.9(b) shows a graph of values of qL obtained from the series of dilutions of the starting solution as calculated from equation (7.81). Also shown in Figure 7.9(b) are values for L and Lj. These relative partial molar enthalpies can be obtained from 4>L. To find the relationship, we start with the equation... 

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

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