Concentration mole fraction

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

A plug-flow, liquid-liquid, extraction column is represented in Fig. 4.19. For convenience, it is assumed that the column operates under low concentration conditions, such that the aqueous and organic flow rates, L and G, respectively are constant. At low concentration, mole fraction x and y are identical to mole ratios X and Y, which are retained here in the notation for convenience. This however leads to a more complex formulation than when concentration quantities are used, as in the example AXDISP. 

Consider now two practically immiscible solvents that form two phases, designated by and ". Let the solute B form a dilute ideal solution in each, so that Eq. (2.19) applies in each phase. When these two hquid phases are brought into contact, the concentrations (mole fractions) of the solute adjust by mass transfer between the phases until equilibrium is established and the chemical potential of the solute is the same in the two phases ... 

K = vapor-liquid equilibrium ratio, y lx, y = gas-phase concentration at equilibrium (mole fraction), x = liquid-phase concentration (mole fraction),... 

See also Denial Solution Gram-Equivalent Gram-Molecular Weight Molal Concentration Molar Concentration Mole Fraction Mole (Stoichiometry) Mnle Volume and Normal Concentration. 

Here, is a constant, which defines the activity scale, and yA is the activity coefficient. For the moment we will disregard the units of concentration (mole fraction, moles per kg. solution, moles per kg. water). Changing to a new activity scale means that /xA is shifted by a constant and that all activities are multiplied by the same factor. 

Henry s law states that the vapor pressure of a solute in solution is proportional to the concentration (mole fraction xi, molality m, or molarity c). That is,... 

In a solution, the equilibrium concentration (mole fraction 2) of solute is affected by the gravitational field and varies with height h. To find this effect we write... 

Calculation of the oxygen vacancy concentration at the interconnector surface On the basis of the point defect theory, the oxygen vacancy concentration (mole fraction) 8 on the fuel and air side surfaces of the interconnector are calculated [34], In an equilibrium state, the formation of the oxygen vacancy can be described as follows using Kroger-Vink notation [35] ... 

Outlet solvent pollutant concentration, mole fraction 0.0964... 

Since the reduced and relative surface excess isotherms convey composite information on the adsorption of the two components, there is a strong incentive to determine the individual (or separate ) isotherms, i.e. the adsorbed amount n (or ) versus concentration, mole fraction or mass fraction. It will be recalled that this implies some assumptions about the thickness, composition and structure of the adsorbed layer, and therefore is not to be recommended for reporting adsorption from solution data in a standard form. Indeed, this second step is already part of the theoretical interpretation of the adsorption mechanisms. 

D. Water Vapor Concentrations, Mole Fractions and Partial Pressures for Leaves... 

Equations (13-88) for ideal gas mixtures may be derived by using nothing more complicated than Newton s second law The sum of the forces acting on the molecules of a particular species is directly proportional to the rate of change of momentum. The rate of change of momentum between different species is proportional to the concentrations (mole fractions) of the different species and to their relative velocity [see also Taylor and Krishna (op. cit.) for a more complete derivation]. Equation (13-88) is more familiar in the form... 

Stream Number Tenqjerature F Pressure psia Flow Rate lbmoWi Concentration, Mole Fraction ... 

What would your concentration (mole fraction) profile look like Using the same values for Dab. and so on, in Example I 1-1, what is the fluxdfA ... 

State is the ionic medium (i.e., infinitely diluted with respect to HCl only). In such a medium /hci (solid line, right ordinate) is very nearly constant, that is,/Hci = 1- Both activity coefficients are thermodynamically equally meaningful. (Adapted from P. Schindler.) (b) A comparison of activity coefficients (infinite dilution scale) of electrolytes and nonelectrolytes as a function of concentration (mole fraction of solute) m = moles of solute per kg of solvent (molality) = number of moles of ions formed from 1 mol of electrolyte 1 kg solvent contains 55.5 mol of water. (From Robinson and Stokes, 1959. Reproduced with permission from Butterworths, Inc., London.)... 

Use the Clapeyron equation to estimate the vapor pressure of acetone at 0°C. (2) Use the Antoine equation to estimate the vapor pressure of acetone at 0°C. (3) If the vapor pressure of acetone is 71 mm Hg, calculate the maximum concentration (mole fraction) of acetone at 1 atm total pressure. 

Classically, the plot of the surface excess of one component of a binary mixture versus its concentration (mole fraction) in the mixture can belong to one of five different types, as illustrated in Figure 3.3. In type I, the plot has a maximum arormd X = 0.5. In type II, there is still a maximum, but it takes place at a lower mole fraction. In type III, the curve has an inflection point but does not intersect the concentration axis, and the maximxmi occurs at a low value of the mole fraction. 

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