4. Solution containing volatile solute / solvents

Solution containing volatile solute / solvents

Mixture of 2 volatile liquids

Raoult's law ( for volatile Liq. Mixture )

Statement of Raoult's law ( for volatile liq. mixture ): In solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction.

p_A µ x_A   =>   p_A = x_AP_Aº

p_A = Partial vapour pressure of component A

x_A = Mole fraction of component ‘A’ in solution.

P_Aº = Vapour pressure of pure component ‘A’ at given temperature

Derivation of total pressure over solution using Raoult’s law and Dalton’s law:

Let A, B be to two volatite liquids in a closed container as shown.

  p_A = x_AP_Aº

Similarly, for liquid B we have,

  p_B = x_BP_Bº

Total pressure over the solution P_T , according to Dalton's law is

P_T = p_A + p_B = x_AP_A⁰ + x_BP_B⁰

Determining composition of vapour phase:       

Let,

y_A = mole fraction of A in vapour phase above the solution and

y_B = mole fraction of B in vapour phase above the solution

Now, we have, p_A = y_A P_T     .....Dalton's law of partial pressure for a gaseous mixture     

 p_A = x_AP_A^{º         ...........}Raoult's law

  Thus,    p_A =  y_A P_T  = x_A P_Aº

  Also,    p_B =  y_BP_T  =  x_BP_Bº

x_A + x_B = 1 =  ; Thus

Graphical Representation of Raoult's Law:

p_A= x_AP_Aº   &   p_B  = x_B P_Bº

P_T = x_AP_Aº + x_B P_Bº

P_T =  ( P_Aº – P_Bº ) x_A + P_B⁰                                            

P_T =  ( P_Bº – P_Aº ) x_B + P_A⁰         

This represents equation of straight line. P_T v.s. x

Note:  If P_A^º > P_B^º , A is more volatile than B. B.P. of A < B.P. of B. 

Limitations of Raoult’s Law: Raoult's Law only works for ideal solutions. Very dilute solutions obey Raoult's Law to a reasonable approximation.