The molar mass of a polymer was determined by measuring the...

The molar mass of a polymer was determined by measuring the osmotic pressure, $7.6 \mathrm{~mm} \mathrm{Hg}$, of a solution containing $5.0 \mathrm{~g}$ of the polymer dissolved in $1.0 \mathrm{~L}$. benzene. What is the molar mass of the polymer? Assume a temperature of $298.15 \mathrm{~K}$

Key Concepts

Osmotic Pressure

Osmotic pressure is a colligative property that represents the pressure required to halt the net flow of a solvent across a semipermeable membrane from a pure solvent into a solution. It is directly related to the concentration of solute particles present.

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of solute particles, rather than their identity. They include phenomena such as boiling point elevation, freezing point depression, and osmotic pressure, and are essential for understanding how solute-solvent interactions affect solution behavior.

Van’t Hoff Equation

The van’t Hoff equation (? = cRT) establishes a relationship between osmotic pressure (?), the concentration in moles per liter (c), the ideal gas constant (R), and the temperature (T). This equation is a key tool for connecting measured osmotic pressures to the number of moles of solute in a solution, and it underpins many calculations in colligative property studies.

Molar Mass Determination

Molar mass determination via osmotic pressure involves dissolving a known mass of solute in a given volume of solvent and measuring the resulting osmotic pressure. By applying the van’t Hoff equation, one can determine the molar concentration of the solute, which in turn allows for the calculation of its molar mass. This method is particularly useful for high-molecular-weight compounds like polymers.

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