by dalton law of partial pressure , derive Pa=(Pt)(Xa)

Raoult’s law → For a solution of volatile liquids, the partial vapour pressure of each component in
the solution is directly proportional to its mole fraction.

i.e.

Pa =P_a⁰Xa

also

P_b =P_b⁰X_b

P_total  =Pa+ P_b = P_a⁰Xa + P_b⁰X_b

or

so for a solution

Pa=P_total/X_a