## Solutions

The concepts of unsaturated, saturated, and supersaturated solutions are usually firmly entrenched in the minds of those who have studied general science or chemistry. The terms molar and molal, as described in Sec. 2.2, are not so well understood. Molal solutions are normally used when the physical properties of solutions, such as vapor pressure, freezing point, and boiling point, are involved. Molar concentrations are generally of interest for equilibrium calculations of various kinds. Normal solutions are commonly used for making analytical measurements and are described in Sec. 11.4.

### Vapor Pressure

The presence of a nonvolatile solute in a liquid always lowers the vapor pressure of the solution. Thus, when sugar, sodium chloride, or a similar substance is dissolved in water, the vapor pressure is decreased. This phenomenon is believed to be due to a physical blocking effect at the surface of the liquid where particles (ions or molecules) of the solute happen to be.

Raoult's Law

Raoult's law states: The vapor (partial) pressure (7>,) of a compound in a solution mixture of compounds is equal to the mole fraction of that compound (X,) in the mixture multiplied by its vapor pressure in pure form (P°):

Values of P" for many compounds can be found in standard reference books such as the Handbook of Chemistry and Physics} Mole fraction is a measure of the concentration of species i in the mixture, it is a dimensionless value that equals the ratio of the number of moles of species i (n,) present divided by the total number of moles of all species present {nfr.

Raoult's law is similar to Henry's law in that it relates the vapor pressure above a solution to the concentration in the solution. For ideal solutions, they are equivalent expressions. In practice and with the usual nonideal solutions, however, Henry's law is generally used when the concentration of species i in the mixture is low (for example, in dilute aqueous solution where the mole fraction of water approaches 1.0) while Raoult's law is generally applied when the concentration of species i in the mixture is high (for example, petroleum mixtures and mixtures of hazardous chemicals, i.e., chlorinated solvents). Deviations from ideal behavior are sometimes corrected through use of activity coefficients and fugacities as discussed in Sec. 2.12.

EXAMPLE 2,7 'D. 8. Lide (ed.): "Handbook of Chemistry and Physics," 82nd ed.; CRC Press, Boca Raton, FL, 2001. *R. P. Schwarzenbach, P. U. Gschwend, and D. M. Imboden, "Environmental Organic Chemistry," Wiley, New York, 1993.

Benzene, toluene, ethylbenzene, and xylene (BTEX) are common constituents of gaso-iine. 'Vapor: pressures ot' the ¿iure liquids :i»re, respectively, 0.126, 0.0380, 0.0126. and 0 0117 atm at 25°C.2 Assuming an equimolar mixture of these liquids obeys Raoult's law,

'D. 8. Lide (ed.): "Handbook of Chemistry and Physics," 82nd ed.; CRC Press, Boca Raton, FL, 2001. *R. P. Schwarzenbach, P. U. Gschwend, and D. M. Imboden, "Environmental Organic Chemistry," Wiley, New York, 1993.

It the mixture of B1EX given in Example 2 7 is in equilibrium with water, use Raoult's | EXAMPLE 2.8

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It the mixture of B1EX given in Example 2 7 is in equilibrium with water, use Raoult's | EXAMPLE 2.8

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Another use of Raoult's law is in understanding the effect that solutes have upon the freezing and boiling points of water and other solvents. Application of Raoult's law has shown that molal solutions of nonelectrolytes in water, such as sugar containing 6.02 X 1023 (Avogadro's number) molecules or particles, have their vapor pressures decreased to the same degree, and the boiling point is raised 0.52°C while the freezing point is depressed 1.86°C. A molal solution of an electrolyte such as NaCl, which yields two ions, produces nearly twice as great an effect because, after solution and ionization occur, the molal solution contains nearly two times Avogadro's number of particles.

Nearly all chemical reactions are reversible in some degree. When a reaction proceeds to a point where the combination of reactants to form products is just balanced by the reverse reaction of products combining to form reactants, then the reaction is said to have reached equilibrium. The concentration of the reactants and of the products is important in determining the final state of equilibrium. For a system in equilibrium as expressed by the classical equation an increase in either A or B will shift the equilibrium further to the right. Conversely, an increase of either C or D will shift the equilibrium to the left. The shifting of an equilibrium in response to a change of concentration is an example of the well-known principle of Le Chatelier, which states: A reaction, at equilibrium, will adjust itself in suck a way as to relieve any force, or stress, that disturbs the equilibrium.

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