Kaplan MCAT General Chemistry Review

When a nonvolatile solute is dissolved into a solvent to create a solution, the boiling point of the solution will be greater than that of the pure solvent. Earlier, we defined the boiling point as the temperature at which the vapor pressure of the liquid equals the ambient (external) pressure. We’ve just seen that adding solute to a solvent results in a decrease in the vapor pressure of the solvent in the solution at all temperatures. If the vapor pressure of a solution is lower than that of the pure solvent, then more energy (and consequently a higher temperature) will be required before its vapor pressure equals the ambient pressure. The extent to which the boiling point of a solution is raised relative to that of the pure solvent is given by the following formula:

T_b = iK_bm

where T_b is the boiling point elevation, K_b is a proportionality constant characteristic of a particular solvent (and will be given to you on Test Day), m is the molality of the solution [molality = moles of solute per kilogram of solvent (mol/kg); see Chapter 9, Solutions] and i is the van’t Hoff factor, which is the moles of particles dissolved into a solution per mole of solute molecules. For example, i = 2 for NaCl because each molecule of sodium chloride dissociates into two particles, a sodium ion and a chloride ion, when it dissolves.

FREEZING POINT DEPRESSION

The presence of solute particles in a solution interferes with the formation of the lattice arrangement of solvent molecules associated with the solid state. Thus, a greater amount of energy must be removed from the solution (resulting in a lower temperature) in order for the solution to solidify. For example, pure water freezes at 0°C, but for every mole of solute dissolved in 1 kg (1 liter) of water, the freezing point is lowered by 1.86°C. Therefore, the K_f for water is -1.86°C/m. As is the case for K_b, the values for K_f are unique to each solvent and will be given to you on Test Day. The formula for calculating the freezing point depression for a solution is

T_f = iK_fm

where T_f is the freezing point depression, K_f is the proportionality constant characteristic of a particular solvent, m is the molality of the solution, and i is the van’t Hoff factor.

If you’ve ever wondered why we salt roads in the winter, this is why: The salt mixes with the snow and ice and initially dissolves into the small amount of liquid water that is in equilibrium with the solid phase (the snow and ice). The solute in solution causes a disturbance to the equilibrium such that the rate of melting is unchanged (because the salt can’t interact with the solid water that is stabilized in a rigid lattice arrangement), but the rate of freezing is decreased (the solute displaces some of the water molecules from the solid-liquid interface and prevents liquid water from entering into the solid phase).

This imbalance causes more ice to melt than water to freeze. Melting is an endothermic process, so heat is initially absorbed from the liquid solution, causing the solution temperature to fall below the ambient temperature. Now, there is a temperature gradient and heat flows from the “warmer” air to the “cooler” aqueous solution; this additional heat facilitates more melting—even though the temperature of the solution is actually colder than it was before the solute was added! The more the ice melts into liquid water, the more the solute is dispersed through the liquid. The resulting salt solution, by virtue of the presence of the solute particles, has a lower freezing point than the pure water and remains in the liquid state even at temperatures that would normally cause pure water to freeze.

Could we use table sugar instead of salt? Absolutely—but sugar is more expensive. Could we use LiCl instead of NaCl? Absolutely—but NaCl is a lot easier and more economical. Besides, we’ve heard of manic drivers in need of a mood stabilizer, but manic roads? Could we use magical fairy dust? Absolutely—as long as magical fairy dust is soluble in water. In other words, it doesn’t matter what the solute is. Freezing point depression is a colligative property that depends only upon the concentration of particles, not upon their identity.

OSMOTIC PRESSURE