Solute moles

Fig. Ill-13. (a) Plots of molecular density versus distance normal to the interface a is molecular diameter. Upper plot a dielectric liquid. Lower plot as calculated for liquid mercury. (From Ref. 122.) (b) Equilibrium density profiles for atoms A and B in a rare-gas-like mixmre for which o,bb/ o,aa = 0.4 and q,ab is given by Eq. III-56. Atoms A and B have the same a (of Eq. m-46) and the same molecular weight of SO g/mol the solution mole fraction is jcb = 0.047. Note the strong adsorption of B at the interface. [Reprinted with permission from D. J. Lee, M. M. Telo de Gama, and K. E. Gubbins, J. Phys. Chem., 89, 1514 (1985) (Ref. 88). Copyright 1985, American Chemical Society.]...

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

FIG. 4-11 Plot of solute fiigacity i vs. solute mole fraction. 

Here Q is the solute concentration and R the gas constant. This is in fact obeyed over a rather wide range of concentrations, almost up to solute mole fractions of 0.61, with an error of only 25 percent. This is remarkable, since the van t Hoff equation is rigorous only in the infinitely dilute limit. Even in the case of highly nonideal solutions, for example a solution with a ratios of 1.5 and e ratios of 4, the van t Hoff equation is still obeyed quite well for concentrations up to about 6 mole percent. It appears from these results that the van t Hoff approximation is much more sensitive to the nonideality of the solutions, and not that sensitive... 

Vapor pressure lowenng is direcdy proportional to solute mole fraction. 

Molality Mass Percent Ppm Solvent Solute Mole Fraction Solvent... 

There is a reasonable explanation of the data in Table 17-IV. When a solute dissolves, the solute molecules must be separated from each other and then surrounded by solvent molecules. Furthermore, the solvent molecules must be pushed apart to make room for the solute mole-... 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

Point c is a critical point known as the upper critical end point (UCEP).y The temperature, Tc, where this occurs is known as the upper critical solution temperature (UCST) and the composition as the critical solution mole fraction, JC2,C- The phenomenon that occurs at the UCEP is in many ways similar to that which happens at the (liquid + vapor) critical point of a pure substance. For example, at a temperature just above Tc. critical opalescence occurs, and at point c, the coefficient of expansion, compressibility, and heat capacity become infinite. 

The first part of this problem appears in numerous problems involving solutions. Moles are critical to all stoichiometry problems, so you will see this step over and over again. This is so common, that anytime you see a volume and a concentration of a solution, you should prepare to do this step. 

Solvent Solubility (moles solute / moles solvent) Experimental [11] Predicted Error (%)... 

Calcite mole fraction X, solid state activity coefficients X, and Yp, the solute mole fractions of calcium at equilibrium in seawater. 

Moles of solute/mole of solvent (X) (liquid phase)... 

Molality a way to express concentration of a solution, moles of solute per kilogram of solvent... 

Polyfmethyl methacrylate), initiated and polymerized at 250 by t-butylmagnesium bromide in toluene-THF solution (—). Mole fraction of monomer, X.VJM = 0.1 OM. XTHF is indicated in each case. A mixture of standard polystyrene samples of indicated molar mass (------). All traces are aligned so that the elution volumes correspond. 

FIG. 7.18 Adsorption on carbon from the ethanol-benzene system. The ordinate equals the total number of moles of solution times the change in solution mole fraction per unit weight of carbon. (Data from F. E. Bartell and C. K. Sloan, J. Am. Chem. Soc., 51, 1643 (1929).)... 

Lactose in solution <%> Lactose solution mole Temp. <°C) Time (Min) after heating (pH) Lactose hydrolyzed <%) Velocity constant [Pg.324]

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. 

The concentration of a solution can be expressed in many ways, including molarity (moles of solute per liter of solution), mole fraction (moles of solute per mole of solution), mass percent (mass of solute per mass of solution times 100%), and molality (moles of solute per kilogram of solvent). When equilibrium is reached and no further solute dissolves in a given amount of solvent, a solution is said to be saturated. The concentration at this point represents the... 

This system of equations (equations 23-26) involves the three solid-phase-composition variables x, y, and xAC. The other three solid-solution mole fractions are related to x, t/, and xAC by the following relations ... 

Determination of T y. In the formulation of the phase equilibrium problem presented earlier, component chemical potentials were separated into three terms (1) 0, which expresses the primary temperature dependence, (2) solution mole fractions, which represent the primary composition dependence (ideal entropic contribution), and (3) 1, which accounts for relative mixture nonidealities. Because little data about the experimental properties of solutions exist, Tg is usually evaluated by imposing a model to describe the behavior of the liquid and solid mixtures and estimating model parameters by semiempirical methods or fitting limited segments of the phase diagram. Various solution models used to describe the liquid and solid mixtures are discussed in the following sections, and the behavior of T % is presented. 

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