Solutions of liquid in liquid

 

A(l) + B(l) à Solution

P⁰_A=Vapour pressure of A in Pure state.                                               

P⁰_B=Vapour pressure of B in Pure state.

Pure state means= only one component is present in container.

Vapour Pressure:-  It is defined as the pressure applied by vapours of liquid above liquid which are in equilibrium with the liquid at constant temperature.

Factors affecting vapour pressure:           1) Temperature                                2) Nature of Component

1)      Temperature: With increase in temperature the vapour pressure of liquid increases.

2)      Component having less force of attraction among its particle tend to have more vapour pressure.

What happens when two liquids are mixed?

When two liquids are mixed the vapour pressure of each component decreases.

P_A= vapour pressure of Component A in solution state

P_B= vapour pressure of Component B in solution state.

According to Raoult’s law:- A solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in the solution.

Mathematically:               P_A α x_A                  P_B α x_B

                                                                        P_A=P⁰_Ax_A                     P_B=P⁰_Bx_B

                P_S or P_T or P_sol = P_A + P_B

                P_S = P⁰_Ax_A + P⁰_Bx_B              …(1)                                       x_A + x_B = 1                            …(2)

                By substituting the value of (2) in (1)

                P_S = P⁰_A + (P⁰_B - P⁰_A ) x_B                   ….(3)

Following conclusion can be drawn from eq (3)

(i)                  Total vapour pressure of the solution can be related to the mole fraction of any one component.

(ii)                Total vapour pressure over the solution varies linearly with the mole fraction of component B.

(iii)               Depending on the vapour pressures of pure component A and B, total vapour pressure over the solution decreases or increases with the increase of mole fraction of component .  

Vapour pressure of Component in vapour phase:-

From the application of Dalton’s law of partial pressure:

                P_A= y_AP_S                                                                       P_B= y_BP_S

                        y_A= mole fraction of component A in vapour phase.

                    y_B= mole fraction of component B in vapour phase.

Numerical:

1)  Calculate the vapor pressure of a mixture containing  252 g of n-pentane (Mw = 72) and 1400 g of n-eptane (Mw = 100) at 20^oC. The vapor pressure of n-pentane and n-eptane are 420 mm Hg and 36 mm Hg respectively.

2)  Calculate the vapor pressure of a mixture containing  252 g of n-pentane  and 1400 g of n-butane at 20^oC. The vapor pressure of n-pentane and n-eptane are 420 mm Hg and 360 mm Hg respectively.

3) Calculate the vapor pressure of a mixture containing  25 g of n-propane  and 140 g of n-butane at 20^oC. The vapor pressure of n-pentane and n-eptane are 420 mm Hg and 360 mm Hg respectively.Also calculate mole fraction of component in vapour phase.

4) Calculate the mole fraction of n-propane  and n-butane at 20^oC. The vapor pressure of n-pentane and n-eptane are 420 mm Hg and 360 mm Hg respectively and the total vapour pressure is 400 mm Hg .Also calculate mole fraction of component in vapour phase.