Vapor Pressures of Solutions Liquid solutions have physical properties different from those of the pure solvent, which has great practical significance. Adding antifreeze to a car to prevent freezing in winter and boiling in summer. Melting ice on sidewalks and streets by adding salt. These work because of the solute’s effect on the solvent’s properties.

A dissolved nonvolatile (not readily evaporated) decreases the number of solvent molecules per unit volume. Proportionately lowers the escaping tendency of the solvent molecules. Solution = ½ nonvolatile solute molecules and ½ solvent molecules = vapor pressure ½ of pure solvent since only half as many molecules can escape The presence of a nonvolatile solute lowers the vapor pressure of a solvent.

His results are described by the equation known as Raoult’s law: Detailed studies of vapor pressures of solutions carried out by Francois Raoult. His results are described by the equation known as Raoult’s law: Vapor-Pressure Lowering P0solvent = vapor pressure of pure solvent Psoln = Xsolvent P0solvent Raoult’s law Xsolvent = mole fraction of the solvent Psoln = observed vapor pressure of the solution Solution = ½ solvent + ½ solute, Xsolvent is 0.5, so the vapor pressure of the solution is half that of the pure solvent. The idea is that the nonvolatile solute simply dilutes the solvent.

Vapor Pressure Lowering Can be used to determine molar masses. certain mass of solute is dissolved in solvent and the vapor pressure of solution is measured use Raoult’s law to determine moles of solute mass is known so molar mass can be calculated Can be used to characterize solutions. 1 mole of NaCl dissolved in water lowers the vapor pressure twice as much since NaCl has two ions per formula unit, which separate when it dissolves

Nonideal Solutions So far we have assumed that the solute is nonvolatile and does not contribute to vapor pressure over solution. In liquid-liquid solutions with two volatile components both contribute to vapor pressure. Use modified form of Raoult’s law: PTOTAL = PA + PB = XAP0A + XBP0B PTOTAL = vapor pressure of solution with A + B XA and XB = mole fractions of A and B P0A and P0B = vapor pressures of pure A and pure B PA and PB = partial pressures from molecules of A and of B in the vapor above the solution

Colligative Properties Depend only on the number, and not on the identity, of the solute particles in an ideal solution (solute is nonvolatile). Freezing Point Depression Boiling Point Elevation Osmotic Pressure

Boiling Point Elevation Normal boiling point = vapor pressure equal to 1 atm. Nonvolatile solute = lower vapor pressure of solvent. Therefore, such a solution must be heated to higher temperatures to reach a vapor pressure of 1 atm. A nonvolatile solute elevates the boiling point of the solvent.

More solute = higher boiling point. The magnitude of the boiling point elevation depends on the concentration of the solute. More solute = higher boiling point. Change in boiling point represented by the equation: Can be used to determine molar mass of the solute. ΔT = Kbmsolute ΔT = difference between the boiling point of the soln and that of the pure solvent Kb = molal boiling point elevation constant (characteristic of the solvent) msolute = molality of the solute in the solution

Sugar dissolved in water to make candy causes the boiling point to be elevated above 100oC.

Freezing Point Depression When a solute is dissolved in a solvent, the freezing point of the solution is lower than that of the pure solvent. Consider Figure (a): at 0oC, the vapor pressures of ice and liquid water are the same. Figure (b): Dissolve a solute in water. The presence of the solute lowers the rate at which molecules in the liquid return to the solid state.

For an aqueous solution, only the liquid state is found at 0oC. As solution is cooled, the rate at which the water molecules leave the solid ice decreases, until this rate and the formation of ice become equal and equilibrium is reached. This is the freezing point of the water in the solution.

Equation for freezing point depression: ΔT = Kfmsolute ΔT = difference between the freezing point of the pure solvent and that of the solution Kf = molal freezing point depression constant (characteristic of the solvent) msolute = molality of the solute Can also be used to determine molar mass of a solute.

The addition of salt on street prevents ice from forming in cold weather. The addition of antifreeze lowers the freezing point of water in a car’s radiator.

Osmotic Pressure A solution and pure solvent are separated by a semipermeable membrane, which allows solvent but not solute particles to pass through. As time passes, the volume of the solution increases and that of the solvent decreases. This flow of solvent into the solution is called osmosis. Eventually the liquid levels stop changing, indicating equilibrium. Liquid levels are different = greater pressure on the solution than on the pure solvent = excess pressure is osmotic pressure.

Equation for osmotic pressure (the pressure that must be applied to a solution to stop osmosis): Π = osmotic pressure in atmospheres M = molarity of the solution R = gas law constant T = Kelvin temperature Π = MRT

Colligative Properties of Electrolyte Solutions Electrolyte – dissolves in water to give solution that conducts electric current. Colligative Properties of Electrolyte Solutions A 0.10 m solution of glucose (nonelectrolyte) shows a freezing point depression of 0.186oC. A 0.10 m solution of NaCl (electrolyte) would show a freezing point depression of 0.37oC due to double the number of solute particles (010 m Na+ and 0.10 m Cl-). This relationship between moles of solute dissolved and moles of particles in solution is expressed using the van’t Hoff factor, i. i =

The expected value for i can be calculated for a salt by noting the number of ions per formula unit. For example, for NaCl, i is 2; for K2SO4, i is 3; and for Fe3(PO4)2, i is 5. Due to ion pairing the expected value for i is not always true. At a given instant, a small percentage of the ions may be paired.

The colligative properties of electrolyte solutions are described by including the van’t Hoff factor in the appropriate equation. Changes in freezing and boiling point: ΔT = imK K = freezing point depression or boiling point elevation constant for the solvent Osmotic pressure: Π = iMRT