Correct Answer - Option 3 : Same boiling point and same freezing point
Concept:
Molality:
- Molality (m) is defined as the number of moles of the solute per kilogram (kg) of the solvent.
- It is independent of temperature.
- It is expressed as:
Molality (m) =Moles of solute/Mass of solvent in kg
Elevation in Boiling point:
- For dilute solutions, the elevation of boiling point (∆Tb) is directly proportional to the molal concentration of the solute in a solution.
\(\Delta {T_b} \propto \,m\)
\(\Delta {T_b} = {K_b}\,m\)
- Here m is the molality; Kb is called Boiling Point Elevation Constant or Molal Elevation Constant (Ebullioscopic Constant).
Depression in Freezing point:
- According to Raoult’s law, when a non-volatile solid is added to the solvent its vapor pressure decreases and now it would become equal to that of solid solvent at a lower temperature.
- Thus, the freezing point of the solvent decreases.
- Let \(T_f^0\) be the freezing point of pure solvent and \({T_f}\) be its freezing point when non-volatile the solute is dissolved in it.
- The decrease in freezing point \(\Delta {T_f} = T_f^0 - {T_f}\) is known as depression in freezing point.
- The depression of freezing point (\(\Delta {T_f}\)) for a dilute solution (ideal solution) is directly proportional to molality, m of the solution.
\(\Delta {T_f} \propto m\)
\(\Delta {T_f} = {K_f}\,m\)
Where the proportionality constant, Kf is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant.
Explanation:
We know that,\(\Delta {T_b} = {K_b}\,m\) and \(\Delta {T_f} = {K_f}\,m\)
Given: Two solutions are equimolar and solvents are the same.
- In an equimolar solution, the no. of moles of solute is the same.
- So the molality of both solutions will be the same.
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So, the boiling point ΔT and freezing point ΔTb will also be the same for different non-electrolytes.
Hence, Equimolar solutions of different non-volatile and non-ionic solutes in the same solvent have the same boiling point and same freezing point.
