Mole fraction expression

Combining all of the normalized mole fraction expressions, to account for all reactions gives ... 

According to the first method the indicated multiplication would be performed, the mole fractions expressed in terms of the mole numbers and the differentiation carried out. According to the second method the indicated... 

The mole fraction expresses the number of moles of solvent and solute relative to the total number of moles of solution. Each mole fraction can be thought of as a percent. For example, the mole fraction of water (X q) is 0.771, which is equivalent o saying the solution contains 77.1% water (on a mole basis). 

A Mole fraction expresses the proportion of a component in a solution relative to the entire number of moles present. If you were able to pick out a molecule at random from a solution, the mole fraction of a component represents the probability that the molecule you picked would be from that particular component. Mole fractions for all components must sum to one, and mole fractions are just numbers with no units. 

Mole Fraction The mole fraction (Y) of a solute is the ratio of number of solute moles to the total number of moles (solute plus solvent), that is, parts by mole. The mole percent is the mole fraction expressed as a percentage ... 

The concentration of a component in a mixture may be expressed in different forms. For example, mass and mole fractions express the concentration of a component as a portion of the total stream. Molar concentration is another popular measure of concentration, and it will be used extensively in this book. To calculate the molar concentration of species i in solution, c, we divide the number of moles of component i in the mixture, by the total volume of solution, V ... 

A mole percent is a mole fraction expressed on a percentage basis, that is, mole fraction X 100%. 

Equation (1) is of little practical use unless the fuga-cities can be related to the experimentally accessible quantities X, y, T, and P, where x stands for the composition (expressed in mole fraction) of the liquid phase, y for the composition (also expressed in mole fraction) of the vapor phase, T for the absolute temperature, and P for the total pressure, assumed to be the same for both phases. The desired relationship between fugacities and experimentally accessible quantities is facilitated by two auxiliary functions which are given the symbols (f... 

The solubility of hydrocarbon liquids from the same chemical family diminishes as the molecular weight increases. This effect is particularly sensitive thus in the paraffin series, the solubility expressed in mole fraction is divided by a factor of about five when the number of carbon atoms is increased by one. The result is that heavy paraffin solubilities are extremely small. The polynuclear aromatics have high solubilities in water which makes it difficult to eliminate them by steam stripping. 

In the case of three-phase equilibria, it is also necessary to account for the solubility of hydrocarbon gases in water. This solubility is proportional to the partial pressure of the hydrocarbon or, more precisely, to its partial fugacity in the vapor phase. The relation which ties the solubility expressed in mole fraction to the fugacity is the following ... 

The moles of a solute species adsorbed per gram of adsorbent nl can be expressed in terms of the mole fraction of the solute on the surface N and the moles of adsorption sites per gram as... 

It is perhaps fortunate that both versions lead to the same algebraic formulations, but we will imply a preference for the two-dimensional solution picture by expressing surface concentrations in terms of mole fractions. The adsorption process can be written as... 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

It should be noted that, whatever the fonu of Henry s law (i.e. in whatever composition units), Raoult s law must necessarily be expressed in mole fraction. This says nothing about the appropriateness of mole fractions in condensed systems, e.g. in equilibrium expressions it arises simply from the fact that it is a statement about... 

There are two ways to express the fraction which one gaseous component contributes to the total mixture (1) the pressure fmction, pJP, and (2) the mole fraction, nfn. ... 

The relative amount of ligand and metal in each solution is expressed as the mole fraction of ligand, (Xy) , and the mole fraction of metal, (Xm) ,... 

This expression gives the number fraction or mole fraction of n-mers in the polymer and is thus equivalent to Eq. (5.25) for step-growth polymerization. 

There are two ways to arrive at the relationship between aj and the concentration expressed as, say, a mole fraction. One is purely thermodynamic and involves experimental observations the other involves a model and is based on a statistical approach. We shall examine both. 

Multiplying and dividing the right-hand side of this expression by N converts the Nj s to mole fractions, and, if N is taken to be N, Avogadro s number, kN becomes R. Accordingly, we write for 1 mol of mixture... 

Since Api and Ap2 are both obtained from differentiating the same expression for AGj, it makes no difference which of these we work with further. In addition, it makes no difference whether we differentiate with respect to X2 or Xi, since dxi = -dx2 and we are setting the results equal to zero. Furthermore, since higher derivatives will be set equal to zero, we can differentiate with respect to volume fraction instead of mole fraction. This is because 9/9x =... 

For linear equiHbrium and operating lines, an expHcit expression for the number of theoretical plates required for reducing the solute mole fraction... 

The stabiHty criteria for ternary and more complex systems may be obtained from a detailed analysis involving chemical potentials (23). The activity of each component is the same in the two Hquid phases at equiHbrium, but in general the equiHbrium mole fractions are greatiy different because of the different activity coefficients. The distribution coefficient m based on mole fractions, of a consolute component C between solvents B and A can thus be expressed... 

Although PVT equations of state are based on data for pure fluids, they are frequently appHed to mixtures. 7h.e virial equations are unique in that rigorous expressions are known for the composition dependence of the virial coefficients. Statistical mechanics provide exact mixing rules which show that the nxh. virial coefficient of a mixture is nxh. degree in the mole fractions ... 

The equihbrium partitioning of a chemical solute between a Hquid and vapor phase is governed by Henry s law when the Hquid mixture is very dilute in the solute. Henry s law generally is vaHd at concentrations below 0.01 mol/L of solution, although the upper limit can sometimes extend to 0.1 mol/L or higher (10). Over this concentration range, a direct proportionaHty, ie, Henry s constant, is observed between the partial pressure of the chemical in the gas phase and its mole fraction in the Hquid phase. Henry s constant, when expressed in this way, has units of pressure (3). 

The H in solubility tables (2-121 to 2-144) is the proportionahty constant for the expression of Henry s law, p = Hx, mere x = mole fraction of the solute in the liqiiid phase p = partial pressure of the solute in the gas phase, expressed in atmospheres and H = a. proportionality constant expressed in units of atmospheres of solute pressure in the gas phase per unit concentration of the solute in the hquid phase. (The unit of concentration of the solute in the liquid phase is moles solute per mole solution.)... 

Binary interaction parameters are determined for each pq pair p q) from experimental data. Note that = k and k = k = 0. Since the quantity on the left-hand side of Eq. (4-305) represents the second virial coefficient as predicted by Eq. (4-231), the basis for Eq. (4-305) lies in Eq. (4-183), which expresses the quadratic dependence of the mixture second virial coefficient on mole fraction. 

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