The Rast method, one of the older techniques for finding the molecular mass of an unknown, measures the freezing point depression of solution in camphor. Camphor is used because its freezing point is very sensitive to added solution solute (It has highest `K_(f))`. A solution of `2.342 g` of an unknown substancein `49.88 g` of camphor freezes at `441.2 K`. If `K_(f)` for camphor is `40.0 Kg mol^(-1)`, calculate the molecular mass of the unknown.
Strategy: Find the molality of the solution from the freezing point of the pure camphor, the freezing point of the solution and the value of `K_(f)` by using the relationship `DeltaT_(f)=K_(f)m`. From the molality, find the no. of moles of solute in given mass of solvent. Finally find the molar mass (Melting point of pure camphar is 453.0 K)

Explanation

Step 1. Calculate the molality of the solution.
The freezing point (melting point) lowering is
`DeltaT_(f)=T_(f)^(0)-T_(f)=(453.0 K)-(441.2 K)`
`=11.8 K`
So the molality of the solution is
`m=(DeltaT_(f))/K_(f)=(11.8 K)/(40.0 K Kg mol^(-1))`
`=0.295 mol Kg^(-1)`
Step 2. Calculate the moles of the unknown compound that are dissolved in given mass of camphor.
The molality of solution is
`m=n_("solute")/g_("solv")xx(1000 g)/(kg)`
Hence, for the given solution,
`0.295 mol Kg^(-1)=n_("solute")/(49.88 g "camphor")xx(1000 g)/(kg)`
Rearranging this equation, we get
`n_(solute)=0.0147 mol` solute
Step 3. Calculate the molar mass of solute
`n_("solute")=("mass"_("solute"))/("molar mass"_("solute'))`
or `"molar mass solute"=("mass"_("solute"))/n_("solute")`
`=(2.342 g)/(0.0147 mol)`
`=159 g mol^(-1)`
Thus, the molecular mass of the unknown compound is `159 u`. Alternatively, we can directly use the equation `(2.70)` to get molecular mass