Volume, excess mean molar

This excess volume vE is the difference between the mean molar volume of the non-ideal binary solution, v"° dcal = V+ n2), and the mean molar volume of the perfect binary solution vper/ = XjV + x2v2 (the sum of the volume of the two pure substances before mixing... 

The subsequent step is the calculation of the quantities that appear in the matrix elements A-. By means of Equation 4.15 through Equation 4.18, all chemical potential derivatives are calculated. The partial molar volumes are obtained by adding to the molar volume of the pure components the excess partial molar volumes, obtained through Equation 4.21 with = V, by applying the same procedure used to calculate In y. The mixture molar volume is then obtained as = x V + X2V2 + 3 3 and Kj. from Equation 4.5. The values of are finally obtained from Equation 4.12, for which the calculations of the concentrations, the determinant, and the cofactors are all straightforward. 

Fig. 3.5. Volume% S02 and 02 in gas produced by burning S with excess dry air (calculated by means of S, 0 and N molar balances). N2 concentration is 79 volume% at all ratios, not shown. This is because consumption of one kg-mole of 02 produces one kg-mole of S02. ( For example, 7 kg of input air for every 1 kg of input sulfur.)...

Here Vm> Hm, and Sm denote the molar volume, enthalpy, and entropy of the binary mixture, and the molar excess volume and enthalpy of the binary mixture, and r the critical solution temperature the index c means at the critical solution point . 

This means that the excess coordination number can directly be obtained from the partial molar volume measurements. 

The various types of chloromethylation were described to illustrate that for transformations on insoluble but swelling polymers the crucial factor generally does not mean the concentration of reactants in the free liquid phase, but the concentration of reactive components at the points of reaction in the matrix. This is explained in the following example. Let us assume a reaction vessel of any type is charged with 1 g of polymer which has a capacity of reactive functions of 0.5 mmole. A soluble compound, dissolved in 20 ml of dichloromethane is added in threefold molar excess to transform the functional sites on the polymer as completely as possible. The swelling of the low cross-linked support in dichloromethane, however, has the factor of 10, which means that the inner volume of 1 g of the polymer, solvated by the dichloromethane solution, is 10 ml. Therefore the effective concentration of the dissolved excess component at the reactive sites has only half of the desired strength. 

Since Eq. (10) takes the difference between the two molar volumes into account, it is evident that means the excess amount in the adsorbed phase, which is the only directly measurable parameter. It is also evident that A means the excess surface concentration in relation to the gas (bulk) phase. The situation is quite analogous to adsorption from a two-component liquid mixture. To demonstrate the inconsistencies of limiting values [Eqs (17) and (18)] let us investigate the changes in n , n and (p - p") in the range of very high pressures (densities), that is, when p CO. After Menon [3,4] the excess character of n can also be defined by the densities of the gas phase (p, mol m ) and by that of the adsorbed phase (p ). The total amount of the adsorptive (n ) present in the sorbed phase is... 

This model overestimates the reflectivity from the solution of PiPPAD in toluene-hg, but not by more than can be accounted for by the uncertainties of making an accurate background subtraction. The values of x and X2 can be used to calculate the surface excess of polymer and the area occupied per molecule. The molar volume of a 2000 MW polyacetylene unit is 2700 A and, for ti = 8 A and x = 0.06, the area per molecule in layer 1 is 5600 A, giving a mean lateral distance between molecules of about 85 A. The area per molecule is doubled in the second bilayer. 

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