Colligative Properties

The mole fraction of an electrolytic solution depends on the degree to which the electrolyte dissociates, and 1 mol of a strong electrolyte produces more than 1 mole of solute particles in solution. The number of moles depends on the stoichiometry (quantitative relationships among different elements and substances) of the electrolyte. For example, NaCl produces 2 moles, and MgCl₂ produces 3 moles. Weak electrolytes, such as CH₃COOH, only partially dissociate, so the number of particles resulting from 1 mol of a weak electrolyte is more than 1 but less than the stoichiometric ratio.

Because colligative properties depend only on the number of particles in solution, electrolytes dissolved in water have a greater effect on the $\Delta T_f$ and $\Delta T_b$ than nonelectrolytes. This can be accounted for by including a factor i, called the van 't Hoff factor, in the equations for $\Delta T$: For nonelectrolyte solutions, such as acetone, $i=1$. For electrolytes, i is approximately equal to the number of moles produced by the dissociation of the electrolyte, depending on the concentration of the solution.
That the van 't Hoff factor depends on solution concentration may seem surprising, but it is because the motions of ions in solution are affected by one another. Ionic particles in solution are surrounded by particles with the opposite charge, so their mobility is reduced. Colligative properties depend on freely moving particles, so the effect of colligative properties is reduced in an ionic solution. The more dilute the solution, the more the ions are able to move, and the closer the van 't Hoff factor gets to its stoichiometric value.

Because chemical purification is often the goal in chemistry, it is sometimes desirable to separate solutions of two liquids. This can be accomplished by a process called fractional distillation, which is the separation of two liquids by boiling in stages. Raoult's law states that the partial pressure of a solute is proportional to its mole fraction in solution. The vapor pressures and liquid composition of a solution exist in an equilibrium that can be plotted as a function of the mole fraction. This is called a graph of the liquid-vapor equilibrium.

Simple distillation is separation by boiling a solution, collecting the vapor, and recondensing it. Salt water can be purified through this process. When it boils, the vapor pressure of water is so much lower than the vapor pressure of salt that the water boils off before the salt, and the resulting condensate is pure water.

Fractional distillation is used when the condensate from simple distillation is not pure, as in the case of a benzene-toluene mixture. The vapor pressures of benzene and toluene are close enough to each other that the vapor that is collected is a mixture of benzene and toluene vapors. However, because the P_vap values are not the same, the mole fraction of benzene in the vapor solution is higher than the $\chi_{\rm{B}}$ in the liquid solution. Thus, if this vapor solution is condensed and redistilled, the vapor will be even more concentrated in benzene. Pure benzene can be collected after multiple distillation stages, and pure toluene is left behind. Distillation is possible because the vapor pressure of a species is lowered when it is part of a solution. Osmosis also occurs because of the lowering of P_vap. Osmosis can be demonstrated using a U-shaped tube open to the atmosphere at both ends. The tube is divided into two sides by a semipermeable membrane, a barrier through which certain types of particles can pass but not others. In biological systems a semipermeable membrane may consist of a lipid (fat molecule) bilayer that restricts the flow of charged particles, but the membrane used in the osmosis demonstration is a simple film with microscopic holes restricting particles according to size. Sucrose (sugar) is poured into the water on one side of the tube, forming a sucrose solution. In osmosis, water (consisting of small molecules) can pass through the semipermeable membrane, but the sucrose (consisting of larger molecules) cannot. The vapor pressure over the pure water is higher than the vapor pressure over the sucrose solution because the P_vap of a solution is lower than the P_vap of a pure substance. This difference in P_vap causes a net force down on the pure water, which in turn causes the water molecules to pass through the semipermeable membrane into the sucrose solution until the mole fraction of water in the sucrose solution is enough to equalize the pressures. This flow of water can be stopped if an external pressure, perhaps in the form of a piston, presses on the sucrose solution. The pressure needed to stop the flow of water through a semipermeable membrane is the osmotic pressure ($\bold\pi$), another colligative property. Osmotic pressure can be calculated from the molarity of the solution (M), which is calculated from the number of moles—not the identity—of the solute and the gas constant, where n is the number of moles of the solute. Because it is a colligative property, osmotic pressure can be used to determine molar mass. Changes in osmotic pressure are far more drastic than ${\Delta T}$ in freezing point depression or boiling point elevation, so using osmotic pressure is a more accurate method.