Osmotic pressure and Raoult's law co-relation?

Consider two compartments A and B joined. A contains pure water. B contains brine (dilute). Consider the Vant Hoff factor ($i$).


Obviously pressure over B is less than over A.


We also know that the excess pressure if equal to $iC{\rm R}T$ (C is concentration of brine)


Thus it follows that pressure over B is p - icrt (p is vapour pressure of compartment A, which is pure water in this case).


But from Raoult's law we also know that pressure over compartment B is PX (x is mole fraction of water in brine).


That would mean


$$p - iC{\rm R}T= px$$


Is the equality correct?


