Student can calculate molar mass using Freezing Point Depression and Osmotic Pressure.
Explains freezing point depression.
The freezing point is the temperature where the vapor pressure of a liquid equals the vapor pressure of its solid phase. When a non-volatile solute is added to a solvent, the vapor pressure drops. Because of this, the solution must be cooled to a lower temperature to freeze. This decrease in freezing point is called the freezing point depression ().
Calculates freezing point depression for ethylene glycol.
of ethylene glycol () is mixed with of water. Calculate (a) the freezing point depression and (b) the freezing point of the solution. ( for water is ).
Solves for molar mass of a solute in benzene.
In Example 1.10, 1.00 g of a non-electrolyte solute is dissolved in 50 g of benzene, lowering the freezing point by 0.40 K. The freezing point depression constant () of benzene is given as 5.12 K kg mol⁻¹.
To find the molar mass of the solute (), we use the rearranged equation 1.36: .
Substituting the values into the numerator gives us . For the denominator, we multiply the temperature change of K by the solvent mass of 50 g.
Solving this expression gives a final calculated molar mass of g mol⁻¹ for the unknown non-electrolyte solute.
Apparatus showing the pressure applied to stop osmosis.

This setup illustrates the measurement of osmotic pressure by identifying the exact external force required to counteract natural solvent migration.
Defines osmosis, osmotic pressure, and isotonic solutions.
When a semipermeable membrane (SPM) separates a solvent and a solution, solvent molecules naturally flow through the membrane. Crucially, they always flow from the pure solvent (or lower concentration) into the solution (higher concentration). This spontaneous flow is called osmosis.
Calculates the massive molar mass of a protein using osmotic pressure.
of an aqueous solution of a protein contains of the protein. The osmotic pressure of such a solution at is found to be . Calculate the molar mass of the protein.
Why Osmotic Pressure? This method is widely preferred for macromolecules like proteins and polymers. It is measured around room temperature (preventing heat degradation) and its magnitude is large and measurable even for very dilute solutions.
Explains reverse osmosis and its application in desalination.
The normal direction of osmosis can be reversed if a pressure larger than the osmotic pressure () is applied to the solution side.
When this happens, the pure solvent is forced out of the solution and pushed back through the semipermeable membrane. This phenomenon is called reverse osmosis.