Explain depression in freezing point. How depression in freezing point can be used to find molar mass of a non-volatile solute

Explanation

Freezing point of a solvent is the temperature at which the solid and liquid forms of the solvent are in equilibrium i.e., the solid and the liquid forms of the solvent have same vapour pressure. As the addition of non- volatile solute to pure solvent lowers its vapour pressure, so the freeing point of a solution is expected to be less than that of pure solvent. This is known as depression in freezing point. This has been shown graphically in the figure. The depression in freezing point is represented as `Delta T_(f)` Mathematically

`Delta T_(f) = T_(f)^(@) - T_(f)`
where `T_(f)^(@)` is the freezing point of the pure solvent and `T_(f)` is the freezing point of the solution
The depression in freezing point `Delta T_(f)` has been found to be directly proportional to molar concentration
`Delta T_(f) = K_(f) xx m `
`m = (" No of moles of solute ")/(" Weight of solvent in kg") = (W_(B) xx 1000)/( M_(B) xx W_(A))`
`Delta T_(f) = (K_(f) xx w_(B) xx 1000)/( M_(B) xx w_(A))`
or `M_(B) = (K_(f) xx w_(B) xx 1000)/( Delta T_(f) xx W_(A))`
Where `K_(f)` is called molar depression constant