Calculating Partial Molal Quantities

Herasymenko (6) has observed sharply varying partial molal heats and entropies of solution of cadmium in gold or in silver. Although he calculated continuous partial molal quantities, he noted that his changes appeared almost discontinuous. ... 

In thermodynamics of solutions, the partial molal quantity and the apparent molal quantity for a component are usually defined [66]. In the properties of enthalpy, one deals with quantities which cannot be measured in an absolute sense. It is thus necessary to use a reference state from which to make the evaluations. Since the state of infinite dilution of the solute in the solvent is taken as reference, the specification of the composition of the solution by means of the molality m2 of the solute is consequently most convenient for the calculation of enthalpy. 

In order to obtain thermodynamic properties of hydride compositions other than the hydrogen-deficient dihydride phase (which is normally in equilibrium with the metal phase), it is necessary to use partial molal quantities of hydrogen in the hydride, as illustrated for the calculation of enthalpy (n the following expression ... 

The enthalpies of formation of the stoichiometric trihydrides of the first group of rare earths (La through Nd) also may be calculated from eq. (26.5) by integrating the last term up to H/M = 3. Using fig. 26.7 for cerium hydride, the partial molal quantity data of Hardcastle and Warf (1966) and Messer and Hung (1968) for lanthanum hydride, and Messer and Park (1972) for praseodymium and neodymium hydrides along with the data in table 26.3, the values for AHi shown in table 26.5 were calculated. Within the uncertainty of the data and the calculations therefrom, the value for AHi is approximately the same, -58 kcal/mole, for all four trihydrides. 

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. 

CALCULATION OF PARTIAL MOLAR QUANTITIES AND EXCESS MOLAR OUANTITIES If we assume that L ,2/ 2 can be expressed as a polynomial in the molality m,... 

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 ... 

A change in partial molal free energy of the adsorbent calculated from adsorption isotherms is an average for the exterior and interior adsorbent because we have taken the total number of moles of adsorbent as rq. This average, multiplied by the total number of moles of adsorbent, is an extensive free energy function. Its temperature variation yields a heat of adsorption which is also extensive. This heat divided by the number of moles of adsorbent is the average heat of adsorption per mole. Fortunately, it is this quantity which is most directly determined in a calorimeter. 

There have been numerous attempts to determine HLB numbers from other fundamental properties of surfactants, e.g., from cloud points of nonionics (Schott, 1969), from CMCs (Lin, 1973), from gas chromatography retention times (Becher, 1964 Petrowski, 1973), from NMR spectra of nonionics (Ben-et, 1972), from partial molal volumes (Marszall, 1973), and from solubility parameters (Hayashi, 1967 McDonald, 1970 Beerbower, 1971). Although relations have been developed between many of these quantities and HLB values calculated from structural groups in the molecule, particularly in the case of nonionic surfactants, there are few or no data showing that the HLB values calculated in these fashions are indicative of actual emulsion behavior. 

T is temperature, Ak is the change in compressibility caused by the reaction, V indicates partial molal volume, and sub- scripts refer to pressure in atmospheres. Determination of AV would allow calculation of stCOYOACaa) quantity necessary for predicting the direction of tne pressure effect for several geochemical reactions which are difficult to investigate experimentally, for exaniple, mineral formation at sea floor conditions. However, this calculation demands accuracy in knowledge of the atmospheric pressure solubility, and confidence in the reproducibility of the pressure versus solubility plots. 

It should be added that the is-log mMe0 dependence can be used for subsequent calculations, since the values of the e.m.f. in the saturated solution section permit the determination of the total concentration of the oxide dissolved in the melt and, consequently, the quantity of the precipitated oxide. The first point, which falls off the linear dependence (it is located above the approximating line), is the point of the partial oxide powder dissolution. The formed solution is saturated with respect to the oxide powder, which possesses a higher molar surface area as compared with the initial commercial powder. In this case, the quantity of oxide dissolved in the melt is calculated using the dependence E-log mMe0. The difference between the initial molality of the oxide and its equilibrium one yields the quantity of the precipitated oxide powder. 

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