Enthalpies, partial molal

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

Robinson and Baker,18 and Wai and Yates 19 below 71 wt% they can be converted to other temperatures using partial molal enthalpies calculated from the relative enthalpies given by Bidinosti and Biermann.47 Similar values for HC1 in Tables 7 and 8 are obtained from Randall and Young48 and Akerlof and Teare,49 quoted by Bunnett,50 and can be converted to other temperatures using coefficients supplied by Liu and Gren.51 The author uses computer programs, written in Microsoft Basic for the Macintosh, that compute these quantities and others. 

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 standard partial molal volumes (V ), heat capacities (C >), and entropies (S ) of aqueous /i-polymers, together with their standard partial molal enthalpies AHj) and Gibbs free energies of formation from the elements AGf), are linear functions of the number of moles of carbon atoms in the alkyl chains (figure 8.28). 

In Figure 6 we show that good theoretical representations are obtained for different temperatures with a small change in the parameter a. On such evidence we might expect to obtain a consistent description of partial molal enthalpies and entropies. However, discussion of these quantities, along with a fuller consideration of solvation aspects, the a parameters, and the dielectric decrements (27, 28), is deferred until a later stage. 

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 ... 

Table XIV. Relative Partial Molal Enthalpy (//2 — H°) and Relative Partial Molal Heat Capacity (Cp — Cp°) of HBr in 50 Mass Percent Aqueous Monoglyme and in Water at 298.15°K (cal = 4.184/)...

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 ... 

The physical state of each substance is indicated in the column headed State as crystalline solid (c), liquid (liq), gaseous (g), or amorphous (amorp). Solutions in water are listed as aqueous (aq). Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std state, m = 1). In this state the partial molal enthalpy and the heat capacity of the solute are the same as in the infinitely dilute real solution (aq. m). 

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... 

Probably the most significant comparisons which can be made are of values of properties determined from calorimetric measurements with values calculated from adsorption isotherms. Two general methods are available for the comparison of values of enthalpies determined from experiments of the two types. One involves two differentiations The change in the partial molal enthalpy, AH2, of X2, for Process 4, is determined from the differentiation with respect to n2/n1 of the integral heat of adsorption measured in a series of calorimetric experiments of the type represented by Equation 1. The values of the differential heats of adsorption (heats corresponding to the differential Process 4) are compared with values determined from the temperature variation of AG2/T for a series of values of n2/n in Process 4. This type of comparison has been made successfully by several groups of authors (3, 5, 10). 

The differential enthalpies can be deduced either by differentiation of the integral enthalpy with respect to the amount of each component or from the expressions for the corresponding differential free energies. The partial molal enthalpy of the adsorbent is... 

This equation is similar to Equation 7, except that nl9 n2, and T are the independent variables rather than nl9 G2, and T. Similarly, the partial molal enthalpy of the adsorbate is... 

The maximum magnitude of the change in partial molal enthalpy of the... 

Values of the partial molal enthalpies (H) and entropies (S) were calculated from the temperature coefficient of G(()z). The values of (— S) consistently increased with x in UC +a, and tended to 0 as x - 0 much higher values of (—S) were obtained for the U4Os 2/ phase, increasing as y increased. Values obtained for the entropy change, AS, for the reaction... 

Figure 5. Partial molal enthalpy change for solution of 02 in UxTh1 3.02+y...

Here we first utilized Eq. (2.5.3) and then introduced the second criterion for ideal gaseous and liquid solutions, whereby the molar enthalpies for the pure components, H and H°, are equal, respectively, to the partial molal enthalpies of the same constituent in solution (Hi) and in the vapor phase (H ). ... 

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-... 

Here also, Hi, being derived from p., (T, F,, ), is the partial molal enthalpy of i in solution at pressure P, while H, being derived from p, (F, 1, xf), is the enthalpy of pure i at unit pressure. 

Conceptually, the solid salt (sodium chloride, for instance) is converted to the gaseous (g) state, Na+(g) -n Cl (g), and each unit is then hydrated to form the species Na (aq) and Cl (aq). If the heat of hydration is sufficient to provide the energy needed to overcome the lattice forces, the salt will be freely soluble at a given temperature and the ions will readily dislodge from the crystal lattice. If the partial molal enthalpy of solution of the substance is positive, the solubility will increase with increasing temperature if it is negative the solubility will decrease, in agreement with Le Chatelier s principle. 

Here we have assumed ideal behavior so that the partial molal enthalpies h) are only functions of temperature and we are thinking in terms of cooling the reactor by making 0 positive when heat is removed. Thus... 

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