212. State Raoult’s law for solutions where only solvent is volatile. Derive a mathematical exression for this law.

Answer:

Raoult's law states that for a solution of volatile liquid, the partial vapour pressure of each component in the solution is dirctly proportional to its mole fraction.

Thus if there is solution of two liquid component 1 and 2 then,

for component 1,

$$\begin{gathered} {\mathrm{p}}_1 \propto {\mathrm{x}}_1 \\ \mathrm{And} \\ {\mathrm{p}}_1 = {\mathrm{p}}_1^0 {\mathrm{x}}_1 \\ \mathrm{For} \mathrm{component} 2 , \\ {\mathrm{p}}_2 = {\mathrm{p}}_2^0 {\mathrm{x}}_2 \\ \mathrm{where} \\ {\mathrm{p}}_1 {\mathrm{p}}_2 = \mathrm{partial} \mathrm{vapour} \mathrm{pressure} \mathrm{of} \mathrm{two} \mathrm{volatile} \mathrm{component} \mathrm{in} \mathrm{solution}1 \mathrm{and} 2 \mathrm{of} \mathrm{the} \mathrm{solution} \\ {\mathrm{p}}_1^0 {\mathrm{p}}_2^0 = \mathrm{vapour} \mathrm{pressure} \mathrm{of} \mathrm{pure} \mathrm{component} 1\mathrm{and} 2 \\ {\mathrm{x}}_1 {\mathrm{x}}_2 = \mathrm{mole} \mathrm{fraction} \mathrm{of} \mathrm{component} \end{gathered}$$