Explain why molality is used for boiling-point elevation and freezing-point depression calculations and molarity is used in osmotic pressure calculations.

Molality, often represented by the symbol 'm', is a measure of the concentration of a solute in a solution. It's defined as the number of moles of solute per kilogram of solvent. Unlike molarity, molality does not change with temperature because it's based on the mass of the solvent rather than its volume.

This property makes molality especially useful for calculations involving temperature changes, such as boiling-point elevation and freezing-point depression. Because these properties are sensitive to temperature fluctuations, using a concentration measure that remains constant—regardless of whether the solution is heated or cooled—allows for more precise and reliable calculations.

Boiling-point elevation is a colligative property that describes how the boiling point of a liquid increases when a non-volatile solute is dissolved in it. The increase in boiling point is directly proportional to the molality of the solution. The formula to calculate this elevation is \( \Delta T_b = K_b \cdot m \) where \( \Delta T_b \) is the boiling-point elevation, \( K_b \) is the ebullioscopic constant, and \( m \) is the molality of the solution.

Since molality is used, this formula allows for accurate predictions irrespective of environmental conditions or the solution's volume, as it is independent of temperature.

Similarly to boiling-point elevation, freezing-point depression is another colligative property that explains why the freezing point of a solvent decreases when a solute is dissolved in it. The depression in freezing point is also proportional to the molality of the solution and can be expressed by the formula \( \Delta T_f = K_f \cdot m \) where \( \Delta T_f \) is the freezing-point depression, \( K_f \) is the cryoscopic constant, and \( m \) represents the molality of the solution.

Using molality for these calculations avoids errors that could result from the expansion or contraction of the solution's volume, which is common when temperatures drop toward a substance's freezing point.

Molarity, represented by 'M', is the number of moles of solute per liter of solution and is one of the most commonly used measures of solution concentration. The volumetric basis of molarity makes it sensitive to temperature changes since the solution’s volume can expand or contract with temperature fluctuations.

For processes occurring at constant or well-controlled temperatures, such as many laboratory reactions, molarity is a suitable concentration measure. Moreover, in the context of osmotic pressure, the volume of the solution is an integral factor, making molarity the more appropriate choice for calculations over molality.

Osmotic pressure is the pressure required to prevent the flow of a solvent into a solution through a semipermeable membrane. It is a colligative property that depends on the number of solute particles present in a given volume of solvent, which is why molarity is used in its calculation.

The formula for osmotic pressure is \( \Pi = MRT \) where \( \Pi \) represents osmotic pressure, \( M \) is the molarity of the solution, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvins. Osmotic pressure calculations based on molarity are critical in fields such as medicine and chemistry, where solutions are typically at or near biological or room temperatures.