Question

prove mathematically that for a dilute solution, when the solute obeys Henry's law the solvent obeys Raoult's law

Answer 1

For a mixture of gas + Liquid

According to Raoult’s law, p = x p0. ...(i)

p = partial pressure of gas and x= mole fraction of gas in liquid

In the solution of a gas in a liquid, one of the components is so volatile that it exists as a gas and its solubility is given by

According to Henry’s law p = KH x ….......(ii)
If we compare the equations for Raoult’s law and Henry’s law, it can be seen that the partial pressure of the volatile component or gas is directly proportional to its mole fraction in solution. Only the
proportionality constant KH differs from p0.

Thus, Raoult’s law becomes a special case of Henry’s law in which KH becomes equal to p0