State Raoult's law for solutions containing non-volatile solutes in volatile solvents. Derive a mathematical expression for the law.

Explanation

Raoult.s law. It states that at any temperature, partial vapour pressure of a volatile component of a solution is equal to the vapour pressure of that component and its mole fraction in solutions.
Let two volatile liquid components A and B of a solution has mole fractions `X_A and X_B` respectively.
Let `P_(A)^(@) =` V.P. of pure A in solution.
`P_(B)^@ = V.P.` of pure B in solution.
`P_(A)` = Partial V.P. of A in solution.
`P_B` = Partial V.P. of B in solution.
According to Raoult.s law,
`P_A = P_(A)^(@)X_A`
`P_B = P_(B )^(@) X_B`
Total V.P. of solution,
`P = P_A + P_B `
`P = P_(A)^(@) X_A +P_(B)^(@) X_B`
If the component B is a non-volatile solute.
`P_B = 0`
` therefore P = P_A = P_(A)^(@) X_ A`
`or (P_A)/(P_(A)^(@))=X_A`
`(P_A)/(P_(A)^(@))=1-X_B`
or ` 1-(P_A)/(P_(B) ^(@) )=X_B`
`(P_A^(@)-P_A)/(P_(A)^(@))=X_B`