Solutions mole fraction and

Dalton s Law of Partial Pressures for Gas Mixtures (Solutions). Mole Fractions and Partial Pressures... 

Strictly speaking, the concentration measures per volume of solvent (Bunsen), per number of moles in the solution (mole fraction), and per mass of solution (samples) are not linearly related, and hence Henry s law cannot simultaneously be valid for all forms. To illustrate the problem, consider the conversion from mole fraction concentrations Xi to per weight concentrations Ci ... 

Data from heats of dilution are also useful for obtaining parameters for solute-solute interaction theories. Kozak et al. [23] in their paper on solute-solute interactions in aqueous solution express the activity coefficient of the solvent in terms of solute mole fraction and B and C coefficients as... 

It is interesting to note that the grouping defined as the reference time, T2SM, is inversely proportional to the density of the fluid, the initial solute mole fraction, and the volume that the particles Anally attain. 

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.]...

Figure 1.4. Temperature dependence of the change in Gihhs energy, enthalpy and entropy upon transfer of ethane and butane from the gas phase to water. The data refer to transfer from the vapour phase at 0.101 MPa to a hypothetical solution of unit mole fraction and are taken from ref. 125.

For polymer solutions we seek the relationship between mole fraction and volume fraction. Since 02/0i = nNj/Ni, Nj/Ni = (1/n) (02/01). Also,... 

Osmotic pressure is one of four closely related properties of solutions that are collectively known as colligative properties. In all four, a difference in the behavior of the solution and the pure solvent is related to the thermodynamic activity of the solvent in the solution. In ideal solutions the activity equals the mole fraction, and the mole fractions of the solvent (subscript 1) and the solute (subscript 2) add up to unity in two-component systems. Therefore the colligative properties can easily be related to the mole fraction of the solute in an ideal solution. The following review of the other three colligative properties indicates the similarity which underlies the analysis of all the colligative properties ... 

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

The general XT E problem involves a multicomponent system of N constituent species for which the independent variables are T, P, N — 1 liquid-phase mole fractions, and N — 1 vapor-phase mole fractions. (Note that Xi = 1 and y = 1, where x, and y, represent liquid and vapor mole fractions respectively.) Thus there are 2N independent variables, and application of the phase rule shows that exactly N of these variables must be fixed to estabhsh the intensive state of the system. This means that once N variables have been specified, the remaining N variables can be determined by siiTUiltaneous solution of the N equihbrium relations ... 

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... 

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. 

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) ... 

C12-0035. A solution contains 1.521 g of maleic acid, HO2 CCHICHC02H, dissolved in 85.0 mL of acetone (p — 0.818 g/mL). Calculate the molality, mole fraction, and mass percent of maleic acid in the solution. 

C12-0082. A commercial solution contains 2.0 M ammonia in methanol. The density of the solution is 0.787 g/mL. Calculate the molality, the mole fraction, and the percent by mass of the ammonia solution. 

With the equations entered as listed above, press F5 or solve/sweep under the solutions menu to solve the equations. The software indicates that x = 0.333. From this, the following mole fractions and partial pressures are obtained ... 

If we furthermore assume that the solid and liquid solutions are ideal the activities can be replaced by mole fractions and eqs. (4.19) and (4.20) rearrange to... 

Of these different definitions, the most important usually are g dm 3, molarity, mole fraction, and percentage (or ppm, for dilute solutions). It is often... 

D—Cooling the solution will change the temperature and the volume of the solution. Volume is important in the calculation of molarity and density. A volume change eliminates answers A and C. The mass and the number of moles are not affected by the temperature change. Mole fraction and molality will not change. This eliminates B and E. 

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

It may be assumed that dilute solutions are used so that mole fractions and mole ratios are approximately equal. Each plate is taken as an ideal unit, so that the gas leaving of composition yn is in equilibrium with the liquid of composition xn leaving the plate. 

For solvents, 1, is equal to V because the standard state is the pure solvent, if we neglect the small effect of the difference between the vapor pressure of pure solvent and 1 bar. As the standard state for the solute is the hypothetical unit mole fraction state (Fig. 16.2) or the hypothetical 1-molal solution (Fig. 16.4), the chemical potential of the solute that follows Henry s law is given either by Equation (15.5) or Equation (15.11). In either case, because mole fraction and molality are not pressure dependent. 

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 ... 

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. 

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