Partial molar heat of mixing

This excess enthalpy hE corresponds to the heat of mixing of the non-ideal binary solution at constant pressure. Namely, hE = xf + x2h with - ht -h - -RT2(dlny JdT), where hf is the partial molar heat of mixing of substance i, ht is the partial molar enthalpy of i in the non-ideal binary solution, and h° is the molar enthalpy of pure substance i. Remind ourselves that the reference system for the activity coefficients is symmetrical. 

DiPaola-Baranyi, G. Braun, J.-M. Guillet, J. E., "Partial Molar Heats of Mixing of Small Molecules with Polymers by Gas Chromatography," Macromolecules, 11,224 (1978). 

Differentiating the enthalpy equation with respect of N, will give the partial molar heat of mixing of component i, which in turn is related to the enthalpy interaction parameter,... 

Since the initial work of Smidsrod and Guillet numerous investigators have used I.G.C. to determine physicochemical parameters characterising the interaction of small amounts of volatile solutes with polymers Baranyi has shown that infinite dilution weight fraction activity coefficients, interaction parameters and excess partial molar heats of mixing can be readily determined with this technique. Partial molar heats and free energies of mixing, and solubility parameters of a wide variety of hydrocarbons in polystyrene and poly(methyl methacrylete) have been determined The temperature dependence of the interaction parameter between two polymers has also been studied... 

From the variation of the interaction parameter or the activity coefficient with temperature, the partial molar heat of mixing at infinite dilution of the probe, Ah, can be computed... 

It should be noted that Eq. (13) does not apply to the interaction parameter based on volume fractions (x), due to the inclusion of a temperature dependent combinatorial entropy. In computing partial molar heats of mixing at infinite dflution, it is essential that the correction for gas pha% nonideality ( n) be included, owing to the magnitude of (< 100—300 cal/mol). 

Table 6. Partial molar heats of mixing (Ah °) of some alkanes in poly(dimethyl siloxane) at 25 °C (57)...

Lucassen-Reynders and Benjamins -2) derived an equation for protein mono-layers, considered to be purely two-dimensional. The protein molecules are treated as discs of molecular area, floating in a solvent (water) of molecular area. Lateral interaction is accounted for in terms of a partial molar heat of mixing, related to w in the FFG equation 13.4.37] or x in the Flory Huggins picture. Their equation reads... 

Thus hf is equal to the heat absorbed (per mole of 1) when a small quantity 8ui of substance 1 is dissolved in the solution at constant T and p. For this reason it is often called the heat of solution of component 1, differential heat of mixing or partial molar heat of mixing." The partial molar heats may be determined readily from the heat of mixing h by the Bakhuis-Rooseboom method described in 3 of chap. I. 

The enthalpy interaction parameter xh is obtained from the partial molar heat of mixing. For component 1 this has the form... 

If the composition and activity of all components in a system are measured, then the total Gibbs energy of mixing can be determined by Equation 48.42, where X is the mole fraction. Measuring the partial pressure of all components is not common, but in this case the temperature dependence of the logarithm of activity can be used to determine the partial molar heat of mixing as shown in Equation 48.43 ... 

Here Xi is the mole fraction of a component. Equation 48.45d is equivalent to Equation 48.45c, where Ya is the activity coefficient of component A, which is given by Ua/xa. This change is made because Equation 48.45d is readily integrated graphically. Similar to Equation 48.43, the partial molar heats of mixing are obtained by the temperature dependence of activity or in terms of ion current ratios as ... 

Mass number of peak adjacent to peak with mass number M Partial molar free energy of mixing Partial molar heat of mixing... 

DIP1 DiPaola-Baranyi, G., Braun, J.-M., and Guillet, J.E., Partial molar heats of mixing of small molectrles with polymers by gas chromatography, Macromolecules, 11, 224, 1978. 

K1M Kim, N.H., Won, Y.S., and Choi, J.S., Partial molar heat of mixing at infinite dilution in solvent/polymer (PEG, PMMA, EVA) solutions. Fluid Phase Equil, 146, 223,1998. 

Calculate the partial molar heats of mixing of zinc and of cadmium in a Zn-Cd alloy,containing 0.6 atom fraction zinc, from the following data at 700°C (97Z K) ... 

Calculate the partial molar heat of mixing of zinc in a solid Cd-Zn alloy containing 20 atom % zinc at 530°C (803 k) from the following data ... 

Physical solubilities are usually low in magnitude and are accompanied by endothermic partial molar heats of mixing. However, the overall heat effect for dissolution could still be exothermic because of the predominance of the heat contribution due to condensation. 

Since the partial molar heat of mixing for AgBr in the AgBr concentrated solution should be almost zero, then from Eq. (39) it follows that... 

In these expressions Y and v refer to the solute species and X and x to the solvent Nx and Yy are the mole fractions. With ntot as the total number of moles and y the number of moles Y, b an interaction parameter of the system, y the activity coefficient, and a Henrian activity coefficent, the equation for the partial molar heat of mixing is derived as... 

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