Relation between Raoults law and Daltons Law

Relation between Raoult’s Law and Dalton’s Law :-

If the mole fractions of solute(A) and solvent(B) in liquid phase are X_A and X_B , and their vapour pressures in pure state are P⁰_A and P⁰_B respectively. Vapour pressure of the solution is P.

 If the mole fractions of solute and solvent in Vapour Phase are Y_A and Y_B respectively than-

According to Raoult’s Law P_A = P⁰_A . X_A

And according to Dalton’s Law P_A = Y_A . P

Then                                      P⁰_A . X_A = Y_A . P   and  P⁰_B . X_B = Y_B . P

ð    Y_A = (P⁰_A . X_A )/P , similarly for B  Y_B = (P⁰_B . X_B )/P

Now using                           X_A + X_B = 1

Substituting X_A and X_B,

                                                (Y_A .P) / P⁰_A  + (Y_B .P) / P⁰_B   = 1

ð                                              Y_A/P⁰_A  + Y_B/P⁰_B  = 1/P

XII class

RAOULT'S LAW- The partial pressure of any volatile constituent of a solution at constant temperature is equal to the product of vapour pressure of pure constituent and its mole fraction.
i.e.
Where Pi = Vapoue pressure of solution, p*= V.P. of pure Constituent, xi = Mole fraction of Constituent
1. Raoult's law for binary solution of two volatile liquids:-  If A is solute and B is solvent then

Once the components in the solution have reached equilibrium, the total vapor pressure p of the solution is:

The figure shows the variation in V.P. with varying composition of the mixture.
2.Solid liquid solution containing non- volatile solute - 
The V.P. of a solution containing non- volatile solute is directly proportional to the mole fraction of the Solvent.
 Ps = p0 XB
 The vapour pressure of a pure solvent is always greater than the vapour pressure of solution contaning non- volatile solute.
Raoult's law is applicable only for dilute solution containing non volatile solute only.
Problem for practice-
Q. Benzene and Toluene form an Ideal solution. The vapour pressure of benzene and Toluene are 75mm and 22mm Hg respectively. If the mole fraction of benzene and toluene in vapour state are 0.63 and 0.37 respectively than calculate the vapour pressure of the ideal mixture.  (Ans- 39.68mm of Hg)

For XII

triple point

the triple point of a substance is the temperature and pressure at which three phases ( gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. 
Critical point or critical temperature is the temperature after which the gas can not be liquified by application of any amount of pressure.
below critical temperature the phase existing is vapour and above critical temperature the phase is called gas.
From the graph it can be observed that below critical temperature at high pressure liquid phase exists(the right side of the continuous green curve), above critical temperature gas can not be liquified so liquid phase does not exist whatever is the magnitude of pressure.