Question

What is Raoult’s law? How can molar mass of a non-volatile solute be determined with its help?

Answer 1

Hint: Raoult’s law is only valid for ideal solutions. A non- volatile solute is a substance that does not readily evaporate into a gas under existing conditions. And a non-volatile solute exhibits a low vapor pressure and a high boiling point. For example sugar.

Complete step-by-step answer:
Raoult’s law states that the relative lowering of vapor pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution, it means that vapor pressure of a solution is dependent on the mole fraction of a solute added to the solution. And from the definition we can derive the formula of Raoult’s law:
${{P}_{solution}}={{X}_{solvent}}P_{solvent}^{0}$
Where, ${{P}_{solution}}$ is the vapor pressure of solution,
${{X}_{solvent}}$ is the mole fraction of solvent = moles of solvent / total number of moles
$=\dfrac{{{n}_{solvent}}}{{{n}_{totalmoles}}}$
$P_{solvent}^{0}$is the vapor pressure of pure solvent at a particular temperature.
The molar mass of a non-volatile solute can be determined by using following equation:

And here we know that
$\Delta P={{P}_{0}}-P$,
and ${{X}_{solute}}={{X}_{2}}=\dfrac{\tfrac{{{W}_{2}}}{{{M}_{2}}}}{\tfrac{{{W}_{1}}}{{{M}_{1}}}+\tfrac{{{W}_{2}}}{{{M}_{2}}}}$
By putting the value of ${{X}_{solute}}$ and $\Delta P$ and then rearranging the equation we get:

And here;
${{P}_{0}}$ = vapor pressure of pure solvent,
$P$ = vapor pressure of solution,
${{M}_{2}}$ = mass of solute,
${{W}_{2}}$ =molar mass of solute,
${{M}_{1}}$ = mass of solvent,
${{W}_{1}}$ = molar mass of solvent.
So, from this derivation we can find the molar mass of non-volatile solute (${{W}_{2}}$), if the other data is given.

Note: We should be care full about the units. And Raoult’s law is applicable for very dilute solutions and for solutions containing non-volatile solute only. Raoult’s law is not applicable to solutes which dissociate or associate in the particular solution.