Average mole fraction

Equations (13-111) to (13-114), (13-118) and (13-119), contain terms, Njj, for rates of mass transfer of components from the vapor phase to the liquid phase (rates are negative if transfer is from the liquid phase to the vapor phase). These rates are estimated from diffusive and bulk-flow contributions, where the former are based on interfacial area, average mole-fraction driving forces, and mass-... 

Xa average mole fraction of a-type units in a copolymer hap element of covariance matrix of SCD... 

There is a growing interest in the use of 15N NMR spectroscopy for elucidation of various structural problems of azole chemistry, especially tautomerism. For example, the mole fractions of the prototropic tautomers were obtained from the 15N chemical shifts of the NH tautomers and the corresponding N-methyl derivatives. By this method, the average mole fraction for the 2-NH tautomer of benzotriazole is 0.02 in both CDC13 and DMSO, and that of 1,2,3-triazole is 0.34 in CDC13 and 0.55 in DMSO (82JOC5132). 

Figure 1.2 Representation of all possible values of system molar free energy in Fig. 1.1. X) is the average mole fraction of component B.

It should be mentioned that the viscometric technique yields a weight-average degree of association159), Nw, while a number-average (mole fraction) degree of association is actually required for the calculation of equilibrium constants associated with processes such as shown in Eq. (11). However, as is shown in the Appendix the near-monodisperse nature of these polymer systems permits the use of Nw in the calculation of these equilibrium constants. 

The concentrated solution viscosity measurement yields the weight-average degree of association of active chain ends rather than the more conventional number-average (mole fraction) value. However, the calculation of the equilibrium constant for association, K, can be accomplished if Mw and the heterogeneity index of the polymer sample are known. The latter parameter can be determined via postpolymerization characterization. 

Liquid-vapour equilibrium data for the binary mixture w-hexane-ethyl acetate have been scarcely reported in the scientific literature [8], Those authors reported a minimum boiling temperature azeotrope with an average mole fraction of w-hexane equal to 0.6565 and a temperature of 65.15°C at 101.3kPa. A more detailed experimental study, at atmospheric pressure, of liquid-vapour equilibrium was performed by Acosta et al. [9], Their estimation of the azeotropic mixture corresponds to a temperature of 64.85 °C with a molar fraction of w-hexane of 0.657 with an average experimental error for the temperature and composition measurements of 0.02 °C and 0.003 mole fraction, respectively. 

For the species profiles obtained by laser Raman spectroscopy several profiles were measured in a specific flame and the average mole fraction is reported at a given flame position. 

Use this equation and the ideal gas equation of state to derive the following expression for the average mole fraction of A in the room air ... 

In this connection it is of some interest to establish how much of each phase must be present to form a heterogeneous mixture of average mole fraction x. The reader may consult Table 3.16.1, in deriving Eqs. (3.15.2). 

The average mole fraction is the logarithmic mean of the two values xB1 and xB2 It is therefore possible to write (1.172) as... 

We emphasize the difference between the Toor, Stewart, and Prober approach and the exact method considered above by using the subscript av thus, [Pavl- For practical purposes, this means that [Pavl has to be evaluated by employing suitable average mole fractions, av iri the definition of the (Eqs. 2.1.21 and 2.1.22). The arithmetic average mole fraction av = + F/sX normally is recommended for calculation of (Stewart... 

The use of average mole fractions rather than the boundary conditions in the calculation of [/ ]. 

The first step is to determine the matrix of Fick diffusion coefficients [ >]. The arithmetic average mole fractions will be needed in the evaluation of the [D] these average mole fractions are... 

Arithmetic average mole fractions were used in the computation of... 

The subscripts 0 and 5 serve as reminders that the appropriate compositions, x q and respectively, have to be used in the defining equations for (Eqs. 2.1.20 and 2.1.21). The subscript av on [F] emphasizes the assumption that the matrix of thermodynamic factors evaluated at the average mole fraction and is assumed constant along the diffusion path. 

The same approach may be used in conjunction with the linearized equations and explicit methods of Section 8.5. Basically, [A ] is calculated from Eq. 8.3.25 using the average mole fractions and the binary i — j pair mass transfer coefficients in the evaluation of [7 ]. 

SOLUTION With the Maxwell-Stefan diffusion coefficients and thermodynamic factors as given in Example 8.7.1, the matrix of Fick diffusivities [D] can be evaluated from Eqs. 4.2.12 using the average mole fractions with the following results ... 

The average mole fractions were obtained by converting the average mass fractions and not by averaging the mole fractions at the interface and in the bulk fluid. 

The arithmetic average mole fractions will be needed in the calculation of the matrix of Fick diffusivities [D]. 

Converting the average mole fractions to mass fractions yields... 

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