Na mole fraction

FIGURE 5.7 Homovalent K+-Na+ exchange on a Brucedale subsoil (Bond 1995) at I = 0.05 M. (a) Measured exchange isotherms open symbols—K+ mole fraction, closed symbols—Na+ mole fraction. Dashed line nonpreference isotherm, (b) In Ky plot to determine the equilibrium constant The dotted lines are extrapolations and the stars represent extrapolated points. 

AP Differential pressure between solution and pure solvent tti Solvent activity Oi Solute activity Na Mole fraction of alcohol N Mole fraction of water a Alcohol activity Ou, Water activity... 

In an ideal solution the components A, B, and C. . . are on an equal footing, and there is no distinction between solvent and solute. In this book we are mainly interested in very dilute ionic solutions, where the mole fraction of one component, known as the solvent, is very near unity, and where (at least) two solute species are present, the positive and the negative ions we shall use nA and xA to refer to the solvent particles and shall denote the solute species by B and C. Let us write... 

Mole fraction of methanol Fiu 64. AF, —T AS, and AH for the transfer of the ion pair (Na+ + CS-) from water to methanol-water mixtures. 

By substituting from equations 10.7a and 10.76 into equation 10.4, the mass transfer rates NA and NB can be expressed in terms of partial pressure gradients rather than concentration gradients. Furthermore, NA and Ns can be expressed in terms of gradients of mole fraction. 

The easiest way to express the relation between the total pressure of a mixture and the partial pressures of its components is to introduce the mole fraction, x, of each component A, B,. . ., the number of moles of molecules of the gas expressed as a fraction of the total number of moles of molecules in the sample. If the amounts of gas molecules present are nA, B, and so forth, the mole fraction of A is... 

For a polymer possessing the most probable distribution, the mole fraction Na is given by Eq. (1) hence... 

The ratio NjJ (NA + NB) represents the mole fraction of the solvent in the solution, where Nb and Na are the numbers of moles of the solute B and the solvent A respectively present in the solution, and K is a constant. In the case of the pure solvent NB = 0 and the fraction Na/(Nb + Na) is equal to 1. This leads to the equality K - PA (where PA is the vapor pressure of the pure solvent A). The expression for the vapor pressure of the solvent now takes the following form... 

The mole fraction of a substance in a solution is the ratio of the number of moles of that substance to the total number of moles in the solution. The symbol for mole fraction of A is usually XA, although some texts use the symbol NA. Thus, for a solution containing x mol of A, y mol of B, and z mol of C, the mole fraction of A is... 

The chemical shift and line width observed for each water content were taken as weighted averages of the values in the free and bound states, and from two equations expressing these averages, Fb and Ff, the mole fractions of bound and free Na+ ions, respectively. were extracted. Fb significantly increases as the approximate hydration number that might be expected for a SOs Na pair is approached from the direction of considerable hydration. 

Figure 2-3 A Mossbauer spectrum for an orthopyroxene sample with ferrosilite mole fraction of 1.1% equilibrated at 900°C. The solid curve is the fit to the spectrum, and the dashed curves are individual fit lines. The residual is also shown (shifted upward by 0.989 units so that it can be shown clearly). The area ratio of two Ml peaks to two M2 peaks is 0.2367 0.0055. Fe " is negligible. The cation distribution (or formula) of this orthopyroxene (4 cation and 6 oxygen basis) is as follows tetrahedral site, Alo.oi8Si1.982 Ml Fe0.0041Mg0.9776Ti0.0007Al0.0176 M2, Cao.ooi6Feo.oi72Mgo.9803-There is also minor amount of Na (0.0004) and Mn (0.0005) in M2 site. From Wang et al. (2005).

Here is Boltzmann s constant, or the gas constant per molecule, R/Nq, where No is Avogadro s number (or Na + Nb for one mole of solution) and va and are the volume fractions of solvent and polymer. Comparison of Eq. (2.76) with the entropy of mixing presented earlier in the chapter by Eq. (2.30) shows that they are similar in form, except that now the volume fractions of the components, va and vg, are found to be the most convenient way of expressing the entropy change for polymers, rather than the mole fraction used for most small molecules. This change arises from the differences in size between the large polymer molecules and the small solvent molecules which would normally mean mole fractions close to unity for the solvent, especially when dilute solutions are being studied. 

The (able below contains solubility and density data lor the salts Na SQ4 and MgS()4. Express their solubilities in terms of molar concentrations, molalities and mole fractions. Calculate the contractions in volume that occur when the solutions are made from the solid salts and the solvent. Comment on the results in terms of the ell ect of ionic charges. The concentrations have been cho-.cn to be comparable. 

The ratios NfNA and N2/NA are mole fractions of the two components since NA is the total number of molecules in a mole of solution. On the other hand, TV is the total number of lattice sites and TV, and nN2 are the numbers of sites occupied by solvent and solute, respectively. Since all of the lattice sites have equal volumes, the ratios in the logarithms are the volume... 

The compositions of mixed solvents are expressed by mole fraction (x), mass fraction (w) or volume fraction (0). If a mixed solvent consists of nA moles of solvent A and nB moles of solvent B, xA, wA and 0A for component A can be expressed by xA=nA/ nA+nB), wA=nA/(nA+nBMB/MA) and 0A = nA/(nA+ BVB/VA). Here, M is the molecular weight of component i and V the molar volume of i before mixing. It is assumed that the volume of the mixed solvent is equal to the sum of the volumes of the two constituent solvents, although some volume contraction may occur by mixing. 

Dioxane and Water. Grunwald and co-workers (GBK) (7) used a vapor pressure method to obtain the differential of the free energy of transfer of a solute with respect to solvent mole fraction at 50 wt% dioxane. On the basis of what has now become known as the large-ion assumption (8), they separated cation and anion effects by equating the free energies of transfer for tetraphenylborate and tetraphenylphosphonium ions. They concluded that Na+ was preferentially solvated by dioxane, a surprising result then, but less unexpected now that complexes of the alkali metals with polyethers have been discovered (dioxane... 

It is convenient to express this on a per-mole basis, dividing through by the total number of moles (nA + nB) to obtain the equivalent equation in terms of mole fraction xB... 

It has been mentioned that mole fractions are not always the most convenient composition variables since they often do not take into account particular features and conditions of the crystal structure. Normally, statistical considerations require composition variables which refer to the number of sites in a sublattice rather than to the number of component atoms. Let us discuss a simple example. Component B is dissolved in the interstitial lattice of crystal A. NH = nB/(nA + nB) does not have an immediate statistical meaning. However, if we know from the crystal structure condition that the number of interstitial sites per A-lattice site is miy then the fraction... 

The basic parameters which determine the kinetics of internal oxidation processes are 1) alloy composition (in terms of the mole fraction = (1 NA)), 2) the number and type of compounds or solid solutions (structure, phase field width) which exist in the ternary A-B-0 system, 3) the Gibbs energies of formation and the component chemical potentials of the phases involved, and last but not least, 4) the individual mobilities of the components in both the metal alloy and the product determine the (quasi-steady state) reaction path and thus the kinetics. A complete set of the parameters necessary for the quantitative treatment of internal oxidation kinetics is normally not at hand. Nevertheless, a predictive phenomenological theory will be outlined. 

In the binary copolymer the two molecular weights of the monomeric units are MoA and MoB, the corresponding refractive index increments vA and vB, and the overall composition (mole fractions) nA and nB. This overall composition will in general differ from the composition of individual molecules. Thus, the molecular weight MXI of the i-th isomer with polymerization degree x is given by... 

The free-energy difference for the conformational interconversion, which can be calculated directly if the mole fractions of the two forms are determined from a spectrum recorded at low temperature, can also be obtained by the method of averaging of coupling constants, by relating the observed coupling in the time-averaged spectrum with the couplings observed at low temperature for the isolated conformers. The values for Na and Ne thereby determined allow the calculation of the... 

Bismuth-Sodium Solutions. G.P.Smith et al (Ref 4) detd the compn limits of reactions of air with solns of Na and Bi or Hg in the temp range 600-800°. For Na-Bi, the reaction was accompanied by flame or a weak expln at high temp and high Na concn. No reaction occurred at mole fraction of Na<0.45 Refs l)Kirk Othmer 2(1948),p 531 2)Partington(1950),p 873 3)Anon, Common Defense Bulletin No l43(Sept 1952),Washington,DC 4)G.P.Smith et al.JACS 77,4533 (1955 CA 49,15393(1955) 5)Cond Chem-Dict( 1961), 152-3... 

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