Fraction molar

Figure Bl.22.8. Sum-frequency generation (SFG) spectra in the C N stretching region from the air/aqueous acetonitrile interfaces of two solutions with different concentrations. The solid curve is the IR transmission spectrum of neat bulk CH CN, provided here for reference. The polar acetonitrile molecules adopt a specific orientation in the air/water interface with a tilt angle that changes with changing concentration, from 40° from the surface nonnal in dilute solutions (molar fractions less than 0.07) to 70° at higher concentrations. This change is manifested here by the shift in the C N stretching frequency seen by SFG [ ]. SFG is one of the very few teclnhques capable of probing liquid/gas, liquid/liquid, and even liquid/solid interfaces.

Catalyst Selectivity. Selectivity is the property of a catalyst that determines what fraction of a reactant will be converted to a particular product under specified conditions. A catalyst designer must find ways to obtain optimum selectivity from any particular catalyst. For example, in the oxidation of ethylene to ethylene oxide over metallic silver supported on alumina, ethylene is converted both to ethylene oxide and to carbon dioxide and water. In addition, some of the ethylene oxide formed is lost to complete oxidation to carbon dioxide and water. The selectivity to ethylene oxide in this example is defined as the molar fraction of the ethylene converted to ethylene oxide as opposed to carbon dioxide. 

Taking the molar fractions of water, methanol and water/methanol associate to be (Xm),(X v) and (Xmw)> respectively. 

Instead of the mean velocity weighted with the molar fractions, a velocity weiglited with the mass fractions—the mass center velocity —can be... 

EM1M]CI/A1C13 (Al molar fraction= 0.53) 25°C, 1 bar ethene pressure... 

In order to draw the property - composition diagram, coordinates are usually chosen so that the ideal system values correspond with the additive law regarding concentration [313]. It is known, for instance, that in an ideal system, molar volume changes additively with the concentration, and is expressed in molar fractions or molar percentages, whereas specific volume changes linearly with the concentration, and is expressed in mass fractions or mass percentages. 

Where [KF], [KTaF6] and [K2TaF7] are molar concentrations of KF, KTaF6 and K2TaF7 respectively Nt = variable molar fraction of TaF5 = variable degree of dissociation of K2TaF7. 

Based on the assumption that the total specific volume can be calculated as the sum of the partial specific volumes of the initial and forming components, and expressed pj by TaF5 molar fraction - N,- using equation (64), an equation representing the total variable density of the melt (p ) can be written as follows ... 

Fig. 76. IR spectra of the systems Na2TaF7 - NaF (a), K2TaF7 - KF (b), Rb2TaF7 - RbF (c). Curves 1, 2, 3 etc. correspond to 0, 0.1, 0.3 etc. molar fraction of alkali fluoride. The CsTaFf, - CsF system (d) is represented by spectra of CsTaF6 (curve 1), Cs2TaF7 (curve 2) and Cs2TaF8 (curve 3). Reproduced from [358], A. I. Agulyansky, Zh. Neorg. Khim. 25 (1980) 2998, Copyright 1980, with permission of Nauka (Russian Academy of Sciences) publishing.

Selective solvation of the cations and anions takes place if the molar fraction xs of the solvent S differs from that in the vicinity of the ions ... 

In accordance with Eq. (3.4) or Eq. (3.6), the concentration selectivity of ion exchange is variable depending on the degree of ideality of the solution and CP phase. For dilute solutions at a constant ionic strength, it is possible to take into account as a variable only the degree of non-ideality of the CP phase. For the systems considered here, it is convenient to study the effect of the molar fraction of organic counterions (NJ on the concentration selectivity constant. Fig. 14 shows the dependences of Ks on the molar fraction of oxytetracycline in CP. For CP... 

Fig. 14. Selective bonding of oxytetracycline vs its molar fraction (Nj) in Dowex 50 x 1 sulfonated cation exchangers with different exchange capacity 1) 5.0 mg-equiv/g 2) 2.3 mg-equiv/g...

The transition obtained under stress can be in some cases reversible, as found, for instance, for PBT. In that case, careful studies of the stress and strain dependence of the molar fractions of the two forms have been reported [83]. The observed stress-strain curves (Fig. 16) have been interpreted as due to the elastic deformation of the a form, followed by a plateau region corresponding to the a toward [t transition and then followed by the elastic deformation of the P form. On the basis of the changes with the temperature of the critical stresses (associated to the plateau region) also the enthalpy and the entropy of the transition have been evaluated [83]. 

Fig. 16 a. Stress dependence of the molar fraction of the P form (x ) and b) bulk stress-strain curve measured for uniaxially oriented polybutyleneterephtalate [83]... 

Based on results of NMR and of gel permeation chromatography studies, a simplified composition for the PGCBA that yielded the epoxide equivalent of 0.137 kg/mol was assumed. The molar fraction of tetra functional molecules was taken as v4 = 0.45 and of trifunctional molecules was taken as v3 = 0.55. 

In these equations A and np are the molar fractions of A and P (8 v) = v - vp is the difference between the resonance frequencies of the nuclei in positions A and P, usually determined from the low-temperature limit A is the full-width at half height in the absence of exchange (r - °°) and v is the variable radio frequency of the NMR experiment. 

The plot of the optical yield, Gcmax, of the eso] when plotted vs. the DMSO molar fraction has a broad minimum between 0.43 and 0.93 mole fraction DMSO. It is unlikely that the minimum in G ma). arises from a minimum in smal alone (especially as AIT was found to be nearly constant over the full range) and it seems more reasonable that the main reason is a minimum in the radiation yield, G. Cooper and coworkers30 suggested that the minimum in G(esol ) is the result of a decreased fraction of the free electron which become solvated. 

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