Is molality or molarity dependent on temperature? Explain your answer. Why is molality, and not molarity, used in the equations describing freezing-point depression and boiling-point elevation?

Molality (m) is defined as the number of moles of solute (solute particles) per kilogram of solvent (mass of solvent). It is written as: \[m = \frac{moles\, of\, solute}{kg\, of\, solvent}\] Molarity (M) is defined as the number of moles of solute per liter of solution. It is written as: \[M = \frac{moles\, of\, solute}{L\, of\, solution}\]

Molality depends only on the mass of the solute and solvent, and doesn't have any relation to volume or temperature. Thus, molality is independent of temperature. On the other hand, molarity depends on the volume of the solution, which might be affected by temperature since the volume of a liquid can change with temperature. Thus, molarity is dependent on temperature.

Freezing-point depression (∆Tf) and boiling-point elevation (∆Tb) depend on the concentration of the solute particles in the solution. These colligative properties can be described by the equations: \[\Delta Tf = K_f \cdot m \cdot i\] \[\Delta Tb = K_b \cdot m \cdot i\] Here, Kf and Kb are the cryoscopic and ebullioscopic constants for a particular solvent, m is the molality, and i is the van 't Hoff factor (the number of dissociated particles per formula unit in the solution). As the colligative properties depend only on the concentration of the solute particles and not on their chemical nature, it's important to use a concentration measure that is independent of temperature. This is because the colligative properties describe changes in properties of the solvent due to the presence of solute particles, and the dependence on temperature might affect the changes in these properties. Since molality is independent of temperature, it is used in these equations rather than molarity, which is dependent on temperature. Therefore, molality allows for the calculation of freezing-point depression and boiling-point elevation without any influence of temperature changes on the concentration of the solution.