A 0.500 -g sample of a compound is dissolved in enough water...

A 0.500 -g sample of a compound is dissolved in enough water to form $100.0 \mathrm{mL}$ of solution. This solution has an osmotic pressure of 2.50 atm at $25^{\circ} \mathrm{C}$. If each molecule of the solute dissociates into two particles (in this solvent), what is the molar mass of this solute?

Key Concepts

Molar Mass Determination

Determining the molar mass through osmotic pressure involves measuring the osmotic pressure to find the molarity of the solution, then calculating the number of moles of solute present using the solution volume, and finally dividing the mass of the solute by the number of moles. This method links experimental colligative property measurements to a fundamental property of the compound.

Relationship Between Osmotic Pressure and Molarity

The relationship is defined by the equation ? = iMRT, where ? represents osmotic pressure, M is molarity, R is the universal gas constant, T is the temperature in Kelvin, and i is the van't Hoff factor. This equation allows one to calculate the molar concentration of solute particles, which can then be used to determine the molar mass of a substance.

Osmotic Pressure

Osmotic pressure is a colligative property that reflects the pressure required to stop the net movement of water across a semipermeable membrane, and it is directly proportional to the molar concentration of solute particles in a solution. This concept is central to determining molar mass when using experimental measurements of osmotic pressure.

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number, not the type, of solute particles present. They include osmotic pressure, boiling point elevation, freezing point depression, and vapor pressure lowering, and are used to infer molecular weights and molecular behavior in solutions.

van't Hoff Factor

The van't Hoff factor (i) quantifies the number of particles formed in a solution as a result of solute dissociation. This factor is crucial when applying colligative property equations because it adjusts the effective concentration of solute particles, impacting properties like osmotic pressure.

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