Mole fractions of solvent

In this equation, Pt is the vapor pressure of solvent over the solution, P° is the vapor pressure of the pure solvent at the same temperature, and Xj is the mole fraction of solvent. Note that because Xj in a solution must be less than 1, P must be less than P°. This relationship is called Raoult s law Francois Raoult (1830-1901) carried out a large number of careful experiments on vapor pressures and freezing point lowering. 

Step 2 If there is only one solute, the mole fraction of solvent molecules is 1 — xso ute. The amount of solvent molecules in a total of 1 mol of molecules is then ,()ivent = (1 — A n utc) mol. Convert this amount into mass in grams by using the molar mass of the solvent, Mso vent ... 

Ni, N2, Ni Mole fractions of solvent, of polymer (total), or of polymer species in a solution (Chaps. VII and XII). 

TABLE 3 Interfacial Widths, Bulk Composition, and Interfacial Tension in erg cm at the Interface Between Two Dipolar Liquids [5]. x Denotes the Mole Fraction of Solvent Si in Phase i... 

It should be noted that the local composition model is not consistent with the commonly accepted solvation theory. According to the solvation theory, ionic species are completely solvated by solvent molecules. In other words, the local mole fraction of solvent molecules around a central ion is unity. This becomes unrealistic when applied to high concentration electrolyte systems since the number of solvent molecules will be insufficient to completely solvate ions. With the local composition model, all ions are, effectively, completely surrounded by solvent molecules in dilute electrolyte systems and only partially surrounded by solvent molecules in high concentration electrolyte systems. Therefore, the local composition model is believed to be closer to the physical reality than the solvation theory. 

In the preceding chapters we considered Raoult s law and Henry s law, which are laws that describe the thermodynamic behavior of dilute solutions of nonelectrolytes these laws are strictly valid only in the limit of infinite dilution. They led to a simple linear dependence of the chemical potential on the logarithm of the mole fraction of solvent and solute, as in Equations (14.6) (Raoult s law) and (15.5) (Heiuy s law) or on the logarithm of the molality of the solute, as in Equation (15.11) (Hemy s law). These equations are of the same form as the equation derived for the dependence of the chemical potential of an ideal gas on the pressure [Equation (10.15)]. 

The solid curve in Figure 16.1 shows the activity of the solvent in a solution as a function of the mole fraction of solvent. If the solution were ideal, Equations (14.6) and (16.1) would both be applicable over the whole range of mole fractions. Then, fli =Xi, which is a relationship indicated by the broken line in Figure 16.1. Also, because Equation (16.1) approaches Equation (14.6) in the limit as Xj 1 for the real solution, the solid curve approaches the ideal line asymptotically as Xj 1. 

In the limit of zero mole fraction of solute or unit mole fraction of solvent, the condition in which Henry s law is accurate as a limiting law. Equation (16.73) becomes... 

Tm = mole fraction of solvent that is coordinated to the metal [M]/[solvent] for dilute solutions ... 

Xi and X2 are the mole fractions of solvent and polymer, respectively g is the polymer-solvent interaction parameter... 

For ideal multicomponent systems, a simple linear relationship exists between the chemical potential fii) and the logarithm of the mole fraction of solvent and solute, respectively. 

Figure 13.23. Examples of vapor-liquid equilibria in presence of solvents, (a) Mixture of-octane and toluene in the presence of phenol, (b) Mixtures of chloroform and acetone in the presence of methylisobutylketone. The mole fraction of solvent is indicated, (c) Mixture of ethanol and water (a) without additive (b) with 10gCaCl2 in 100 mL of mix. (d) Mixture of acetone and methanol (a) in 2.3Af CaCl2 ip) salt-free, (e) Effect of solvent concentration on the activity coefficients and relative volatility of an equimolal mixture of acetone and water (Carlson and Stewart, in Weissbergers Technique of Organic Chemistry IV, Distillation, 1965). (f) Relative volatilities in the presence of acetonitrile. Compositions of hydrocarbons in liquid phase on solvent-free basis (1) 0.76 isopentane + 0.24 isoprene (2) 0.24 iC5 + 0.76 IP (3) 0.5 iC5 + 0.5 2-methylbutene-2 (4) 0.25-0.76 2MB2 + 0.75-0.24 IP [Ogorodnikov et al., Zh. Prikl. Kh. 34, 1096-1102 (1961)].

The vapor pressure of a solvent is reduced by the presence of a nonvolatile solute in an ideal solution, the vapor pressure of the solvent is proportional to the mole fraction of solvent. 

According to Raoult s law, the vapor pressure of the solution equals the vapor pressure of pure solvent times the mole fraction of the solvent in the solution. Thus, we have to find the numbers of moles of solvent and solute and then calculate the mole fraction of solvent. 

Figure 7.12 Trebal correlation for interfacial tension. XAB, mole fraction of raffinate dissolved in solvent XBA, mole fraction of solvent dissolved in raffinate XCA, mole fraction of solute dissolved in raffinate ...

For a solution containing just solvent and one solute, where xsoiute is the mole fraction of solute and xsoiVcnt is the mole fraction of solvent then (Frame 30, section 30.2, equation (30.6)) ... 

The further development of modern solution theory is connected with three persons, namely the French researcher Raoult (1830-1901) [28], the Dutch physical chemist van t Hoff (1852-1911) [5], and the Swedish scientist Arrhenius (1859-1927) [6]. Raoult systematically studied the effects of dissolved nonionic substances on the freezing and boiling point of liquids and noticed in 1886 that changing the solute/solvent ratio produces precise proportional changes in the physical properties of solutions. The observation that the vapour pressure of solvent above a solution is proportional to the mole fraction of solvent in the solution is today known as Raoult s law [28]. 

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