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# Vapour pressure of binary solution of liquid in liquids

Now, let us consider a binary liquid solution formed by dissolving a liquid solute ‘A’ in a pure solvent ‘B’ in a closed vessel.

Vapour pressure of binary solution of liquid in liquids

Now, let us consider a binary liquid solution formed by dissolving a liquid solute ‘A’ in a pure solvent ‘B’ in a closed vessel. Both the components A and B present in the solution would evaporate and an equilibrium will be established between the liquid and vapour phases of the components A and B.

The French chemist Raoult, proposed a quantitative relationship between the partial pressures and the mole fractions of two components A & B, which is known as Raoult’s Law. This law states that “in the case of a solution of volatile liquids, the partial vapour pressure of each component (A & B) of the solution is directly proportional to its mole fraction”.

## According to Raoult’s law,

pAα xA (9.3)

pA = k xA

when xA = 1, k = p°A

where p°A is the vapour pressure of pure component ‘A’ at the same temperature.

Therefore,

pA = AXA  (9.4)

Similarly, for component ‘B’

pB= p°B x   (9.5)

xA and xB are the mole fraction of the components A and B respectively.

According to Dalton’s law of partial pressure the total pressure in a closed vessel will be equal to the sum of the partial pressures of the individual components.

Hence,

Ptotal = pA + pB (9.6)

Substituting the values of pA and pB from equations (9.4) and (9.5) in the above equation,

Ptotal = xAA + xBB (9.7)

We know that xA + xB = 1 or xA = 1 - xB

Therefore,

Ptotal = (1 - xB) p°A + xB p°B (9.8)

Ptotal= p°A + xB( p°B- p°A) (9.9)

The above equation is of the straight-line equation form y = mx+c. The plot of Ptotal versus xa will give a straight line with (pB°- pA°) as slope and pA° as the y intercept.

Let us consider the liquid solution containing toluene (solute) in benzene (solvent).

The variation of vapour pressure of pure benzene and toluene with its mole fraction is given in the graph. The vapour pressures of pure toluene and pure benzene are 22.3 and 74.7 mmHg, respectively. The above graph shows, the partial vapour pressure of the pure components increases linearly with the increase in the mole fraction of the respective components. The total pressure at any composition of the solute and solvent is given by the following straight line (represented as red line) equation. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
11th Chemistry : UNIT 9 : Solutions : Vapour pressure of binary solution of liquid in liquids |