Identify the concentration of the solution from following so that values of ,$$\Delta \mathrm{T}_{\mathrm{f}}$$ and $$\mathrm{K}_{\mathrm{f}}$$ are same.

Calculate the amount of solute dissolved in 160 gram solvent that boils at $$85^{\circ} \mathrm{C}$$, the molar mass of solute is $$120 \mathrm{~g} \mathrm{~mol}^{-1}$$. $$\left(\mathrm{K}_{\mathrm{b}}\right.$$ for solvent $$=2.7^{\circ} \mathrm{C} \mathrm{~kg} \mathrm{~mol}^{-1}$$ and boiling point of solvent $$=76^{\circ} \mathrm{C}$$)

The solution containing $$3 \mathrm{~g}$$ urea (molar mass 60 ) per $$\mathrm{dm}^3$$ of water and another solution containing $$4.5 \mathrm{~g}$$ of solute $$\mathrm{A}$$ per $$\mathrm{dm}^3$$ boils at same temperature, then what is molar mass of $$\mathrm{A}$$ ?

Vapour pressure of solution and of pure solvent are $$\mathrm{P}_1$$ and $$\mathrm{P}_1{ }^0$$ respectively. If $$\frac{P_1}{P_1^0}$$ is 0.15, find the mole fraction of solute.