Describe how you would use freezing-point depression and osmotic pressure measurements to determine the molar mass of a compound. Why are boiling-point elevation and vapor-pressure lowering normally not used for this purpose?

Freezing-point depression is a colligative property, meaning it depends on the number of solute particles and not their identity. To determine the molar mass of a compound using freezing-point depression, begin with dissolving a known amount of the compound in a solvent whose freezing point is known, and measure the depression of the freezing point. The depression in freezing point is given by the equation \( \Delta T_f = K_f \cdot m \) where \( \Delta T_f \) is the freezing point depression, \( K_f \) is the cryoscopic constant of the solvent, and m is the molality of the solution. Rearranging the equation to solve for molality gives \( m = \Delta T_f / K_f \). Then, determine the number of moles of the solute using \( moles = mass / molar mass \). Rearrange this equation to solve for molar mass: \( molar mass = mass / moles \). Since you have calculated the molality and you know the mass of the solute you used, molar mass can be calculated.

Like freezing-point depression, osmotic pressure depends only on the number of solute particles present, not their identity. Therefore, it can be used to determine molar mass. The osmotic pressure is given by the equation \( \Pi = MRT \), where \( \Pi \) is the osmotic pressure, \( M \) is the molarity of the solution, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin. Rearrange this equation to solve for molarity. Then use the definition of molarity to isolate molar mass. It's important to note that 'gel-like' or nonideal phenomena can complicate osmotic pressure measurements.

While these are also colligative properties, they are typically less used for this purpose. The elevation in boiling point or change in vapor pressure for solutions at room temperature tend to be small and hence are difficult to measure accurately. In addition, to measure vapor pressure lowering, a closed system must be used, and the methods for capturing and measuring vapor are more complex. Therefore, these methods are not usually the first choice for determining molar mass.