Solutions
5.0 Raoult's law
5.0 Raoult's law
Vapour Pressure is the pressure exerted by vapours of a solution on lid of container, when rate of evaporation becomes equals to rate of condensation.
Consider, a binary solution of two volatile liquid components and heat it until the rate of evaporation becomes equal to rate of condensation, at this equilibrium, let the total pressure is ${P_{total}}$ and ${P_1}$ and ${P_2}$ be the partial vapour pressure of two components respectively.
Then,
According to Raoult's law, "for a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction".
For component $1$,
$${P_1} \propto {x_1}$$ $$ \Rightarrow {P_1} = {P^0}{x_1}$$
where, ${P^0}$ is vapour pressure of pure state of component at same temperature.
and by Dalton's law,
$${P_{total}} = {P_1} + {P_2}$$
$$ \to P{}_{total} = {x_1}P_1^0 + {x_2}P_2^0$$
and $${x_1} + {x_2} = 1$$
$$ \to {P_{total}} = P_1^0 + (P_2^0 - P_1^0){x_2}$$
Similarly,
$${P_{total}} = P_2^0 + (P_1^0 - P_2^0){x_1}$$
These equation can be compared to equation of line, the graph on the left is obtained, In this graph curve $a$ and $b$ represents the vapour pressure of ${1^{st}}$ and ${2^{nd}}$ components respectively, whereas line $c$ gives the total vapour pressure of solution.
