Question

State True or False.
The relative lowering of vapor pressure is equal to the mole fraction of the solute in the solution.
A.True
B.False

Answer 1

Hint: In a liquid, the molecules continue to collide with one another and also with the walls of the container. Thus, the liquid molecules are not associated with the same energy at the given temperature. These molecules at the surface of the liquid which acquire more energy overcome the attractive forces and change into a vapor.

Complete step by step answer:
Now we will discuss the given statement in detail.
According to Raoult’s law – The vapor pressure of solvent containing non-volatile solute is directly proportional to the mole fraction of the solvent at a given temperature.
 $ {p^s}\,\alpha \,{X_A}
  or {p^s} = \,{p^0}\, \times \,{X_A}$ where ${p^0}$ is Vapour pressure of the pure solvent
${p^s}$ is Vapour pressure of the solution
${X_A}$ is mole fraction of solvent
Now,
$\Rightarrow \,\,{p^s} = \,{p^0}\, \times \,{X_A}
 \Rightarrow \dfrac{{{p^s}}}{{{p^0}}}\, = \,{X_A} $
Now let us subtract from 1 on both sides,
 $ \Rightarrow 1 - \dfrac{{{p^s}}}{{{p^0}}} = 1 - {X_A} \
   \Rightarrow \dfrac{{{p^0} - {p^s}}}{{{p^0}}} = {X_{solute}} \
  \left( {{X_{solute}} + {X_A} = 1} \right) \ $
where $\dfrac{{{p^0} - {p^s}}}{{{p^0}}}$ is relative lowering in vapor pressure
${X_{solute}}$ is mole fraction of the solute.
After calculating we can say that the relative lowering in vapor pressure is equal to the mole fraction of the solute in the solution.
After discussing in detail we can say that the given statement is true.
Hence, the correct option is (A).

Note:
Factors affecting vapor pressure are:
Nature of the liquids: - Different liquids have different vapor pressures at a given temperature. The reason is that each liquid has a different magnitude of intermolecular forces of attraction. The volatile liquids (like ether, acetone, etc.) with low boiling points form more vapors at a given temperature. Such liquids have small intermolecular attractive forces and tend to evaporate. But liquids with low boiling points (water, glycol, etc.) have high intermolecular attractive forces and show low vapor pressure at a given temperature.
Temperature: - When the temperature of a liquid is raised the average kinetic energy of the molecule increases. Due to this, the intermolecular forces are easily overcome. Thus, the vapor pressure of a liquid increases with an increase in temperature.