Mole fraction The number

Mole fraction The number of moles of a component of a mixture divided by the total number of moles in the mixture. 

For a system consisting of C components, the phase rule indicates that, in the two-phase region, there are F=C-2 + 2 = C degrees of freedom. That is, it takes C independent variables to define the thermodynamic state of the system. The independent variables may be selected from a total of 2C intensive variables (i.e., variables that do not relate to the size of the system) that characterize the system the temperature, pressure, C - 1 vapor-component mole fractions, and C - 1 liquid-component mole fractions. The number of degrees of freedom is the number of intensive variables minus the number of equations that relate them to each other. These are the C vapor-liquid equilibrium relations, Yj = K,X, i=l,. .., C. The equilibrium distribution coefficients, AT, are themselves functions of the temperature, pressure, and vapor and liquid compositions. The number of degrees of freedom is, thus, 2C - C = C, which is the same as that determined by the phase rule. 

We present here some experimental data on gas solubilities in liquids obtained in our laboratory. The liquid previously degassed is saturated by the unreacted gas, in a thermostated autoclave, provided with a mechanically bladed stirrer under a solute partial pressure p. After saturation attainment, a sample of the saturated liquid is taken via a syringe of high precision and injected into a gas-chromatograph in order to extract the solute dissolved in a known volume of the liquid sample V. By the way of calibration gas of known solute mole fraction, the number of... 

If the total pressure of a mixture is known, the partial pressure of each component can be calculated from the mole fraction. The total number ol moles in the mixture is the sum of the individual component moles. 

Mole fraction. The ratio of the number of moles of one constituent of a mixture or solution to the number of moles of all the constituents. 

Mole fraction, often symbolized by x or X followed by a subscript denoting the entity, represents the amount of a component divided by the total amount of all components. Thus, the mole fraction of component B of a solution, xb, is equal to hb/Xhi where Hb is the amount of substance B and Sni is the total amount of all substances in solution. In biochemical systems, usually the solvent is disregarded in determining mole fractions. The mole fraction, a dimensionless number expressed in decimal fractions or percentages, is temperature-independent and is a useful description for solutions in theoretical studies and in physical biochemistry. 

When the concentration of a multicomponent system is expressed in terms of the molalities of the solutes, the expression for the chemical potential of the individual solutes and for the solvent are somewhat different. For dilute solutions the molality of a solute is approximately proportional to its mole fraction. (The molality, m, is the number of moles of solute per kilogram of solvent. When two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be clearly stated.) In conformity with Equation (8.68), we then express the chemical potential of a solute in a solution at a given temperature and pressure as... 

The effect of methanol on micellar solutions is slight at the low concentration used (5% v/v = 1.3 mol/L = 0.022 mole fraction). The effect of NaCl however, is more significant the CMC is greatly decreased, the degree of counterion binding and the aggregation number are increased. 

The other temperature-independent concentration unit introduced in this chapter is the mole fraction. 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... 

Mole Fraction = the fraction of the total number of moles present represented by the compound in question... 

Mole fraction If you know the number of moles of solute and solvent, you can also express the concentration of a solution in what is known as a mole fraction—the ratio of the number of moles of solute in solution to the total number of moles of solute and solvent. 

Also for calculation purposes, in every theoretical plate the ascending vapour is in thermodynamic equilibrium with the refluxing liquid. Therefore, together with the mass flow and the mole fractions, the calculations in the rectification unit are performed from plate to plate. The minimal theoretical plate number can be graphically and analytically solved by the method of Fenske, using the following assumptions ... 

It is frequently more convenient to determine the partial specific properties, defined in terms of grams instead of moles, of the constituents of a solution, and then to multiply the results by the respective molecular weights to yield the partial molar properties. Any of the methods described above may be adapted for this purpose. The value of the property G or of AG per mole is replaced by the value per gram, and n or n, the mole fraction or number of moles, is replaced by the corresponding gram fraction or number of grams, respectively. 

The program VDWMIX is used to calculate multicomponent VLE using the PRSV EOS and the van der Waals one-fluid mixing rules (either IPVDW or 2PVDW see Sections 3.3 to 3.5 and Appendix D.3). The program can be used to create a new input file for a multicomponent liquid mixture and then to calculate the isothermal bubble point pressure and the composition of the coexisting vapor phase for this mixture. In this mode the information needed is the number of components (up to a maximum of ten), the liquid mole fractions, the temperatures at which the calculations are to be done (for as many sets of calculations as the user wishes, up to a maximum of fifty), critical temperatures, pressures (bar), acentric factors, the /f constants of the PRSV equation for each compound in the mixture, and, if available, the experimental bubble point pressure and the vapor phase compositions (these last entries are optional and are used for a comparison between the experimental and calculated results). In addition, the user is requested to supply binary interaction parameteifs) for each pair of components in the multicomponent mixture. These interaction parameters can be... 

If the overall composition variables in a two-phase mixture are included, the number of variables will increase by C - 1 overall component mole fractions. This requires C - 1 additional equations to relate the overall component mole fractions to the liquid and vapor component mole fractions (Section 2.3). These equations include one additional variable, the vapor mole fraction (the ratio of vapor moles to total moles). Thus, the total number of variables becomes 2C+C-1 + 1 = 3C, and the total number of equations becomes C+C-1 = 2C-1, bringing the number of degrees of freedom to C -i-1. If the overall composition of a mixture is set, C - 1... 

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