Volume mixture molar

Here a suitable equation of state is required to provide a mathematical expression for the mixture molar volume, V. For some equations of state, it is better to use a form of equation 28 in which the integral is volume expHcit (3). Note also that for an ideal gas — Z — 1, and 0 = 1. 

If 17,y is set equal to zero, a temperature-dependent A ,y is needed to obtain a good fit of the P-x data over the entire temperature range. Although not explicitly mentioned earlier, the Peng-Robinson equation of state does predict the mixture molar volume of the equilibrium vapor and liquid phases. Figure... 

Here n and n2 are the refractive indices of pure n-decane and chlorex. These have been determined by Chu (11) at the wavelength used (546 nm) to be 1.4100 and 1.4596, respectively. The mixture molar volume is ... 

Here V is the mixture molar volume, Vi,2 the pure component molar volume, and VE the molar excess volume. No excess volumes were available for this system (II), requiring these measurements to be made as part of this study. 

An alternative approach is to use an equation of state to describe behavior of the excess volume VE(P, T, x). Excess volume is defined in terms of the mixture molar volume (V) and the component molar volumes (Vi) at the same pressure and temperature ... 

An equation of state is used to calculate V and the V values, and the excess volume is then obtained from Equation 1. For practical applications, VE from the equation of state must be combined with known component molar volumes to obtain the mixture molar volume. The hope is that, due to a cancellation of errors, much simpler equations of state can be used to accurately describe VE(P, T, x) than would be necessary to yield directly V(P, T, x) to the required accuracy. The VE method is only of practical use when the temperature of the solution is below the critical temperatures of the major components. 

Table 1 Mole fraction solubility of COj in several ILs and the corresponding mixture molar volumes at 50 °C and ca. 9.2 MPa.

Another remarkable property of these biphasic systems is the unusual volumetric behavior illustrated for [BMIM PF ] in Figure 3 [5]. The volume expansion of the IL is comparatively small even at high mole fractions of dissolved CO2. This phenomenon is represented in Figure 3 by a dramatic drop in mixture molar volume, which simply reflects a negligible liquid volume expansion. Similarly to the gas solubility, a weak temperature dependence is observed. 

Here, as in (4.1.16), the pure ideal-gas molar volumes are related to the mixture molar volume by t , = Nv/N. Equation (4.2.13) applies to both first-law and second-law properties, and we have... 

Here v is the mixture molar volume, while p and are dimensionless groups ... 

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. 

Wu, P.C., and P. Ehrlich Volumetric Properties of Supercritical Ethane- -Heptane Mixtures Molar Volumes and Partial Molar Volumes, AlChE J. p. 553, May 1973. 

Binary systems Density and refractive index Liquid mixtures Molar volume Redlich-Kister equation Ternary mixtures... 

PC Wu, P Ehrlich. Volumetric properties of supercritical ethane-n-heptane mixtures molar volumes and partial molar volumes. AIChE J 19 533, 1973. 

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