Q. 56

# Using Raoult’s la

Answer :

1. Raoult’s law states that ‘for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in solution.’ This means that the vapour pressure of the solvent above the solution is equal to the vapour pressure of the pure solvent at the same temperature regulated by the mole fraction of the solvent present. Thus for one of the two components of a binary solution,

p1 x1

and, p1 = p10 x1

Where p1 is the partial vapour pressure of component 1 and p10 is the vapour pressure of the pure solvent at the same temperature, and x1 is the mole fraction of component 1.

Similarly, for component 2, its partial vapour pressure is denoted as

p2 = p20 x2

2. Consider CHCl3 and CH2Cl2, chloroform and dichloromethane, both being volatile liquids, chloroform being non-polar and dichloromethane being lightly polar yet miscible with chloroform forming a binary solution, the total pressure will be the sum of the partial vapour pressures of the two volatile components,

ptotal = p1 + p2

= p10 x1 + p20 x2

= (1-x2)p10 + x2 p20

= p10 + (p20 – p10)x2

And similarly, p20 + (p10 – p20)x1.

(i) This equation explains the Dalton’s law of partial pressures - the total pressure (ptotal) exerted by the gases over the solution phase in a container will be the sum of the partial pressures of the components of the gas. In this case, it will be the sum of the volatile components exerting vapour pressure on the binary solution. This equation also explains the relation between the vapour pressure of the components and the mole fraction.

(ii) The vapour pressure over the solution can be related to the mole fraction of either of the component, CHCl3 or CH2Cl2. The total vapour pressure of the solution depends on the mole fraction of both the components in their pure state and the mole fraction of the second component in solution.

(iii) If the equation were plotted for an ideal solution, it would be a straight line in the equation form of y = mx + c [ptotal = (p20 – p10)x2], where the line is between ptotal and x2 whose slope is given by (p2o-p1o) and the y-intercept is equal to p1o.

3. For NaCl(s) and H2O(l), a solution contains a non-volatile solute in the form of NaCl. Both are polar molecules and with the principle “like dissolves like”, NaCl dissolves in water and exists in ionic form. The fraction of the liquid solvent molecules on the surface of the liquid gets replaced by dissolved solute molecules, reducing the solvent molecules escaping the surface, reducing the vapour pressure of the solution. Raoult’s law is applicable only to vapourisable component, H2O (component 1), and total vapour pressure is written as

ptotal = p1 = x1p10. The plot between the vapour pressure and the mole fraction is linear in this case.

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