Concentration in mole fraction

Figure 2. Equilibrium concentrations in mole fractions of selected compounds at 500°K. and 1 atm. with composition of 40% oxygen, the indicated percentage of carbon, and the rest hydrogen. To this basic composition is added an amount of nitrogen equal to the amount of carbon. The nitrogen remains primarily as N2 but produces significant quantities of some interesting compounds. The free energy of carbon in the system equals that of graphite at the composition indicated by the arrow. At this point solid carbon would be precipitated if it could be formed there is no inflection of the curves at this point. The asphalt threshold is shown as a sharp inflection, sharpest of all for the aromatic and related heterocyclic compounds. If an atmosphere such as this were to condense, there would be about 1 molecule of glycine per droplet of condensate (6).

HCOOH (g), (HCOOH)2 (g). Ramsperger and Porter2 and Coo-lidge1 studied the equilibrium, (HCOOH) 2 (g) =2HCOOH (g), and their data yield —14.13 for the heat of this reaction. The equilibrium concentrations in mole fraction are, for (HCOOH) 2 (g) and HCOOH (g), respectively, about 0.80 and 0.20 at 18°, and about 0.52 and 0.48 at the boiling point, 100.8°. Data on the heat of vaporization of liquid formic acid to form the equilibrium mixture of (HCOOH) 2 (g) and HCOOH (g)... 

The dynamic model of the column consists of two ordinary differential equations per tray if equimolal overflow, constant tray holdup, and instantaneous liquid hydraulics are assumed. Molar flowrates and concentrations in mole fractions are used. The liquid holdup on each tray is 0.4 kmol ... 

If one lets af = Xjy then it follows that a[ = y[- Thus, in this treatment the residual activity and residual activity coefficient are the same whether or not one expresses concentration in mole fractions or weight fractions. 

A simplified process for the production of SO3 to be used in the manufacture of sulfuric acid is illustrated in the figure. Sulfur is burned with 100% excess air in the burner, but for the reaction S + O2 —> SO2, only 90% conversion of the S to SO2 is achieved. In the converter, the conversion of SO2 to SO3 is 95% complete. Calculate the lb of air required per 100 lb of sulfur burned, and the concentration in mole fraction or percent of the exit gas from the burner and from the converter. 

The relationship between Henryan coefficients measured on the two concentration scales can be derived as follows. Consider an aqueous solute having a mole fraction X and a molality m. Because the chemical potential of this solute is the same whether we measure concentrations in mole fractions or molalities, we write... 

Concentrations in mole fractions are used in the kinetics of the TAME reactions. Aspen accepts other concentrations units such as molarity, partial pressure and activity (called... 

FIGURE 9.1 The chemical potential of paracetamol in CCl at varying concentrations (in mole fractions x) at 298 K. The intersection with the solid-state chanical potential defines the solid-liquid equilibrium (SLE) and corresponds to the solnbiUty of the dmg in this particnlar solvent. The difference between the pure liquid and the solid-state chemical potential is the free energy of fusion Also shown is the liquid-liquid equilibrium (LLE) where the virtually supercooled liquid is at equilibrium with the dissolved drug. 

We have now developed the relationship between the Gibbs energy of a component of a solution and the concentration of that component (Equations 7.26, 7.27, 7.34). However, it only applies to ideal solutions, and only for concentrations in mole fractions. Obviously we need to expand the range of applicability... 

Figure 3.63. Dependence of Y on Uie polymer critical concentration (in mole fractions 2 = 1/(1 + luoA/m/iap), where luo and lUp are the masses of the solvent and polymer, respectively, Mm is the moleculeir weight of styrene) (a). Temperature dependence of % (b). Polystyrene+cyclohexane system (Koningsveld, 1970b Koningsveld et al., 1970b) [Reprinted with permission from K.Koningsvcld. Oise. Faraday Soc. 49 (1970) 144-161. Copyrighted 1970 by the Royal Society of Chemistry]...

Mixed surfactants are often employed in commercial formulations both for cleaning and stabilization. Simple additive mixing rules can be used to estimate the CMC of the mixed surfactant system from knowledge of the CMC s of the individual surfactants and the concentration (in mole fraction) of the surfactant in the system. 

The net reaction rate on a reactive tray depends on the liquid concentrations in mole fractions and liquid holdup in kilomoles on that tray. 

The overall reaction rate is based on the concentrations in mole fractions and liquid holdups in moles. To avoid confusion, the specific reaction rates used in this control section (with the reactor half full of catalyst) are twice those used in the earlier design section in which catalyst was not considered. Thus, the total reactor volumes are the same as those used in the steady-state design. 

However, in some other cases, alternative forms of the mass transfer coefficients lead to simpler final equations. This is especially true for gas adsorption, distillation, and extraction described in Chapters 10-14. There, we will frequently use kx, the third form in Table 8.2-2, which expresses concentrations in mole fractions. In some cases of gas absorption, we will find it convenient to respect seventy years of tradition and use kp, with concentrations expressed as partial pressures. In the membrane separations in Chapter 18, we will mention forms like kx but will carry out our discussion in terms of forms equivalent to k. 

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