Mole fraction, definition

With proper design and implementation, however, it is possible to construct a self-sorting system whose behavior is different from its components [33c]. For example, consider the simple system comprising two hosts (A and B) and two guests (M and N) that can form four possible host-guest complexes (AM, AN, BM, and BN). We fix the total concentrations of hosts A and B ([A J and [B J) at 1 mM and choose the four equilibrium constants such that host A (KT-fold) and host B (10-fold) both prefer guest M (Scheme 4.7). The various mole fraction definitions (Scheme 4.7c) are used to construct a plot (Scheme 4.7d) of the composition of the mixture as a function of total guest concentration ([M J = [Nj J). When [AjJ = [Bj J > = [Nj j], complexes AM and BN dominate because... 

Scheme 4.7 Stoichiometry-induced partner displacement in a four-component mixture (a) equilibria considered, (b) constraints imposed, (c) mole fraction definitions, and (d) a plot of mole fraction versus guest concentration ([M ] = [N ]).

The previous discussion stated that the average molecular weight of a mixture W g may be expressed in terms of both component mole fractions x, and component mass fractions z,. Since mass fractions are used extensively in this chapter, it is useful to understand how Wjjyg may be expressed in terms of z,. Hence from the mole fraction definition of W g, show that Wavg(z) = (ziAVi -E Z2AV2 -E -E z /W )-i... 

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

Equation (4-49) is merely a special case of Eq. (4-48) however, Eq. (4-50) is a vital new relation. Known as the summahility equation, it provides for the calculation of solution properties from partial properties. Thus, a solution property apportioned according to the recipe of Eq. (4-47) may be recovered simply by adding the properties attributed to the individual species, each weighted oy its mole fraction in solution. The equations for partial molar properties are also valid for partial specific properties, in which case m replaces n and the x, are mass fractions. Equation (4-47) applied to the definitions of Eqs. (4-11) through (4-13) yields the partial-property relations ... 

Definitions Following the practice presented under Gas-Separation Membranes, distillation notation is used. Literature articles often use mass fraction instead of mole fraction, but the substitution of one to the other is easily made. 

To extract a desired component A from a homogeneous liquid solution, one can introduce another liquid phase which is insoluble with the one containing A. In theory, component A is present in low concentrations, and hence, we have a system consisting of two mutually insoluble carrier solutions between which the solute A is distributed. The solution rich in A is referred to as the extract phase, E (usually the solvent layer) the treated solution, lean in A, is called the raffinate, R. In practice, there will be some mutual solubility between the two solvents. Following the definitions provided by Henley and Staffin (1963) (see reference Section C), designating two solvents as B and S, the thermodynamic variables for the system are T, P, x g, x r, Xrr (where P is system pressure, T is temperature, and the a s denote mole fractions).. The concentration of solvent S is not considered to be a variable at any given temperature, T, and pressure, P. As such, we note the following ... 

Like mole fraction but unlike molarity, the molality is independent of temperature. The units of molality are moles of solute per kilogram of solvent (mol-kg 1) these units are often denoted m (for example, a 1 m NiS04(aq) solution) and read molal. Note the emphasis on solvent in the definition. To prepare a l m NiS04(aq) solution, we dissolve 1 mol NiS04 in 1 kg of water (Fig. 8.26). 

We connected our earlier definition of activity to a standard state of 1.0 bar or 1.0 M or a mole fraction of unity. None of these make much sense for electrons, but we may define electron... 

The activities of the various components 1,2,3. .. of an ideal solution are, according to the definition of an ideal solution, equal to their mole fractions Ni, N2,. . . . The activity, for present purposes, may be taken as the ratio of the partial pressure Pi of the constituent in the solution to the vapor pressure P of the pure constituent i in the liquid state at the same temperature. Although few solutions conform even approximately to ideal behavior at all concentrations, it may be shown that the activity of the solvent must converge to its mole fraction Ni as the concentration of the solute(s) is made sufficiently small. According to the most elementary considerations, at sufficiently high dilutions the activity 2 of the solute must become proportional to its mole fraction, provided merely that it does not dissociate in solution. In other words, the escaping tendency of the solute must be proportional to the number of solute particles present in the solution, if the solution is sufficiently dilute. This assertion is equally plausible for monomeric and polymeric solutes, although the... 

I would use the moles and or the mole fraction to determine the identity of the solvent, since it is the value that is a direct measurement of the actual number of molecules present. In this case, water is definitely the solvent. 

From the definition of mole fraction x in Equation (5.11) above, we say... 

By definition, the mole fraction of NaCl in this solution is = 0 2 35 2 = 0.0036. (Note the number of significant figures [see Section 13.4] reported here taking the density of the solution as 1, and calculating the weight of water therefore as 1000 g would not have affected this calculation. The density correction could, therefore, have been omitted. Also, as a rule of thumb, 1 liter of water can be approximated as 55 mol F O.)... 

Of these different definitions, the most important usually are g dm 3, molarity, mole fraction, and percentage (or ppm, for dilute solutions). It is often... 

As we pointed out above, there are two main reasons for the differences in the correlations in these molecules. To analyze the stmctural changes induced in the molecule, we define the cis mole fraction as the mole fraction of molecules in the range -Till < ( ) < Ji/2 and the trans isomer in the range nl2< < 3/2n. With these definitions we find for the model the following mole fractions of the different stages of occupation of the molecule. 

The definition of product oxygen recovery defines the minimum required feed rate for a specified product purity and recovery. That relationship is that the feed flow must be the product oxygen purity (%) divided by the recovery (% of feed O2) and divide also by the mole fraction of O2 in feed air. For 20.9 mol% O2 in air this is ... 

If we assume above / = 1 excess fluorine atoms over those required to fill the available surface are in a bulk solid phase of definite composition, then the second moment of the line is the weighted sum of the second moments of fluorine in the bulk phase ((AH ))b and fluorine on the filled surface That is, if n, is the mole fraction on the filled surface and... 

Note 2 Any molar-mass average can be defined in terms of mass fractions or mole fractions. In this document only a few of the important molar-mass averages are given in terms of the mass fractions, Wi, of the species with molar mass M. These definitions are most closely related to the experimental determination of molar-mass averages. 

OH. That is, it is the mass fraction of the species of two OH groups minus one oxygen. This is because in Reaction 2-79 two OH groups minus one oxygen would form one molecular H2O. This definition of OH would lead to (H20t) = (H20m) + (OH) in terms of mass fraction or wt%. The definition of mole fraction of OH is, however, the mole fraction of OH per se, not the mole fraction of 20H - O. In terms of mole fraction, [H20(] = [H20m] + [OH]/2. 

Three definitions of H2O mole fractions are encountered in the literature. They are summarized below (Zhang, 1999b) ... 

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