Mole Fraction and Concentration

The mole fraction of a component in a mixture is defined as the ratio of number of moles of the component to the total number of moles in the mixture as 

Number of moles of component i Total number of moles in the mixture 

The relation between mass fraction and mole fraction is given as 

Application of the ideal gas law model leads to the following two important relations for ideal gas mixtures  

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This provides the connection between partial pressure (that is, pressure times mole fraction) and concentration. Therefore, the following substitution can be made for the molar flux ... 

From the real gas law, the relationship between mole fraction and concentration can be inserted in (19) and the mass balance equation can then be written for a component with stoichiometric coefficient + 1 appearing in reaction j only ... 

For an ideal gas, an exactly equivalent procedure can be used to relate the mass-transfer coefficient based on partial pressure to those based on mole fraction and concentration. If P is the total pressure... 

Surface tensions for aqueous solutions are more difficult to predict than those for nonaqueous mixtures because of the nonlinear dependence on mole fraction. Small concentrations of the organic material may significantly affect the mixture surface tension value. For many binary organic-water mixtures, the method of Tamura, Kurata, and Odanfi maybe used ... 

Feed analyses in terms of component concentrations are usually not available for complex hydrocarbon mixtures with a final normal boihng point above about 38°C (100°F) (/i-pentane). One method of haudhug such a feed is to break it down into pseudo components (narrow-boihng fractions) and then estimate the mole fraction and value for each such component. Edmister [2nd. Eng. Chem., 47,1685 (1955)] and Maxwell (Data Book on Hydrocarbons, Van Nostrand, Princeton, N.J., 1958) give charts that are useful for this estimation. Once values are available, the calculation proceeds as described above for multicomponent mixtures. Another approach to complex mixtures is to obtain an American Society for Testing and Materials (ASTM) or true-boihng point (TBP) cui ve for the mixture and then use empirical correlations to con-strucl the atmospheric-pressure eqiiihbrium-flash cui ve (EF 0, which can then be corrected to the desired operating pressure. A discussion of this method and the necessary charts are presented in a later subsection entitled Tetroleum and Complex-Mixture Distillation. ... 

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 ... 

Two measures of concentration that are useful for the study of colligative properties, because they indicate the relative numbers of solute and solvent molecules, are mole fraction and molality. We first met the mole fraction, x, in Section 4.8, where we saw that it is the ratio of the number of moles of a species to the total number of moles of all the species present in a mixture. The molality of a solute is the amount of solute species (in moles) in a solution divided by the mass of the solvent (in kilograms) ... 

Here Xgq may be a mixed expression involving pressures, mole fractions, and molar concentrations. 

If the same criteria are applied to the analysis of the H2-air results in Figs. 4.1H12, some initially surprising conclusions are reached. At best, it can be concluded that the flame thickness is approximately 0.5 mm. At most, if any preheat zone exists, it is only 0.1 mm. In essence, then, because of the formation of large H atom concentrations, there is extensive upstream H atom diffusion that causes the sharp rise in H02. This H02 reacts with the H2 fuel to form H atoms and H202, which immediately dissociates into OH radicals. Furthermore, even at these low temperatures, the OH reacts with the H2 to form water and an abundance of H atoms. This reaction is about 50kJ exothermic. What appears as a rise in the 02 is indeed only a rise in mole fraction and not in mass. 

In the molality concentration scale, the molality m. of solute i is the amount of solnte i per kg of solvent. If the solvent is water (subscript w), the following relation between mole fraction and molahty of solute i can be derived ... 

Using nitrogen as the adsorbate at a concentration of 0.3 mole fraction and assuming Pq is 15 torrs above ambient pressure, equation (15.14) can be expressed as... 

Triethanolamine was also used as a complexant to deposit these films from thiourea baths [18]. As with the previous study, there was a maximum Hg content in the bath (0.05 mole fraction—absolute concentrations were not given), which led to a 0.18 Hg mole fraction in the films, above which, although films were formed, the Hg content decreased, also explained by rapid precipitation of HgS in the solution. X-ray diffraction showed the formation of a single phase, up to a Hg content (in the bath) of 0.15, and two-phase formation at higher concentrations. The optical bandgap dropped from 2.4 eV (pure CdS) to 1.76 eV (0.05 Hg in bath. 

This definition of x and y is more realistic at low and moderate salt concentrations and is in agreement with that of Sada and Morisue (17). Broul and Hala also assumed complete salt dissociation. The assumption of full dissociation of the salt may not be entirely valid at high salt concentrations, especially where the concentration of the nonaqueous solvent is also high. However, even in those instances where the assumption of full dissociation of the salt may be invalid, it appears to describe the system better than ignoring salt ionization completely. The terms x/ and y/ are referred to hereafter as ionic mole fraction and ionic activity coefficient, respectively. These should not be confused with the mean ionic terms used by Hala which are also based on complete salt dissociation, but are defined differently. No convergence problems were encountered when the ionic quantities were employed. 

Assume that we wish to design a high-pressure combustion chamber where complete oxidation of CO to C02 is an important design consideration. For this purpose we extrapolate our global rate expression for CO oxidation to higher pressure. The right-hand side of Eq. 13.6 can be rewritten in terms of mole fractions and the total molar concentration [M],... 

We really should use mole fraction, and not concentration, in our description of y and x, but for our work, we will just say that the term concentration refers to the percent of a component that the operator would see in the gas-chromatographic (GC) results, as reported by the lab. The equilibrium constant, assuming the ideal-gas law applies, is defined as... 

See also Molal Concentration Molar Concentration Mole (Stoichiometry) Mole Fraction and Mole Volume,... 

What are the mole fractions and molal concentrations in a 10% by weight solution of CH3OH in water ... 

Molar concentrations are converted into mole fractions, and volumetric flowrates are converted to molar flowrates for the tray-to-tray calculations in the column. The fresh feedstream F0 is 0.03506 kmol/s with a composition zo = 1 mole fraction A. Since the reaction is equimolar (one mole of A produces one mole of B), the molar flowrate of the bottoms from the column P is equal to the fresh feed flowrate F(). The overall conversion is set at 98%, so the concentration of reactant in the column bottoms (the product stream P) is xP = 0.02 mole fraction A. 

Ionic strength ranges are applicable for the equations Yi yL where and y, are the activity coefficients on the mole fraction and molarity concentration/activity scales, respectively. The parameter A depends on T(K) according to the equation A = 1.92 x 106 (sT) 3/2 where e is the temperature-dependent dielectric constant of water B = 50.3 (eT) 1,2. For water at 298 K (25°C), A = 0.51 and B = 0.33. Applicable ionic strength range obtained from Stumm and Morgan (1981). 

Figure A.l. displays the various forms of writing equilibrium constants involving pressure, concentration, molality, mole fractions and fugacity etc - for a general reaction of the form ...

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