JEE Main & Advanced Chemistry Solutions / विलयन Lowering Of Vapour Pressure

The pressure exerted by the vapours above the liquid surface in equilibrium with the liquid at a given temperature is called vapour pressure of the liquid. The vapour pressure of a liquid depends on,

(1) Nature of liquid : Liquids, which have weak intermolecular forces, are volatile and have greater vapour pressure. For example, dimethyl ether has greater vapour pressure than ethyl alcohol.

(2) Temperature : Vapour pressure increases with increase in temperature. This is due to the reason that with increase in temperature more molecules of the liquid can go into vapour phase.

(3) Purity of liquid : Pure liquid always has a vapour pressure greater than  its solution.

Raoult’s law : When  a non-volatile substance is dissolved in a liquid, the vapour pressure of the liquid (solvent) is lowered. According to Raoult’s law (1887), at any given temperature the partial vapour pressure (p_A) of any component of a solution is equal to its mole fraction (X_A) multiplied by the vapour pressure of this component in the pure state \[(p_{A}^{0})\]. That is,   \[{{p}_{A}}=p_{A}^{0}\times {{X}_{A}}\]

The vapour pressure of the solution \[({{P}_{total}})\] is the sum of the partial pressures of the components, i.e., for the solution of two volatile liquids with vapour pressures \[{{p}_{A}}\] and \[{{p}_{B}}\].

\[{{P}_{total}}={{p}_{A}}+{{p}_{B}}=(p_{A}^{0}\times {{X}_{A}})+(p_{B}^{0}\times {{X}_{B}})\]

Alternatively, Raoult’s law may be stated as “the relative lowering of vapour pressure of a solution containing a non-volatile solute is equal to the mole fraction of the solute in the solution.”

Relative lowering of vapour pressure is defined as the ratio of lowering of vapour pressure to the vapour pressure of the pure solvent. It is determined by Ostwald-Walker method.

Thus according to Raoult’s law,

\[\frac{{{p}^{0}}-p}{{{p}^{0}}}=\frac{n}{n+N}=\frac{\frac{w}{m}}{\frac{w}{m}+\frac{W}{M}}\]

where, \[p=\] Vapour pressure of the solution

\[{{p}^{0}}=\]Vapour pressure of the pure solvent

\[n=\] Number of moles of the solute

 \[N=\] Number of moles of the solvent

\[w\] and \[m=\] weight and mol. wt. of solute

\[W\] and \[M=\] weight and mol. wt. of the solvent.

Limitations of Raoult’s law

• Raoult’s law is applicable only to very dilute solutions.
• Raoult’s law is applicable to solutions containing non-volatile solute only.
• Raoult’s law is not applicable to solutes which dissociate or associate in the particular solution.