**Problem : **

What is the vapor pressure of the pure solvent if the vapor pressure of a
solution of 10 g of sucrose
(C_{6}H_{12}O_{6}) in 100 g of ethanol
(C_{2}H_{6}O) is 55 mmHg?

To solve this problem, we will use Raoult's law:

Then rearrange the equation to solve for the pressure of the pure solvent,
P^{o}. After converting the gram amounts to moles we find that the mole
fraction of the solvent ethanol is 0.975. Therefore, the vapor pressure of
the solvent is 56.4 mmHg.

**Problem : **

What is the freezing point of a solution of 15.0 g of NaCl in 250 g of
water? The molal freezing
point constant, K_{f}, for water is 1.86 ^{o}C kg / mol.

ΔT_{f} = - i K_{f} m

For NaCl, i = 2. The concentration of the solution is 1.03 *m* in
NaCl. Therefore, the
*change* in the freezing point of the water is -3.8 ^{o}C.
The freezing point of the
solution is, therefore, -3.8 ^{o}C.

**Problem : **

A solution of 0.5 g of an unknown nonvolatile, nonelectrolyte solute is added to 100 mL of water and then placed across a semipermeable membrane from a volume of pure water. When the system reaches equilibrium, the solution compartment is elevated 5.6 cm above the solvent compartment. Assuming that the density of the solution is 1.0 g / mL, calculate the molecular mass of the unknown.

To solve this problem, we will rearrange the formula for osmotic pressure:

Then we can calculate the pressure from the pressure depth equation, then convert the units into atmospheres.

Next, we can calculate the molarity of the solution. Finally, we will use that molarity to calculate the molar mass of the unknown from the volume of the solution and the mass of the unknown.