Question

Show that relating lawing of vapour pressure of solution is equal to the mole fraction of solute

Answer 1

A colligative property is a property that depends only on the number of particles present in solution and not on the identity of those particles.

The relative lowering of vapor pressure is a colligative property as it depends only on the concentration of the solute and it is independent of its nature.

Let us consider a binary solution, consisting of non volatile solute in a volatile solvent. The vapor pressure of the solution (P) is equal to vapor pressure of solvent (P A ) in the solution, which in turn is directly proportional to its mole fraction in solvent.

P = P A

and P A ∝ χ A (mole fraction of solvent A)

Further, P = P A 0 . n A ...eq. 1 where n A = mole fraction of solvent.

If mole fraction of solute is n B then, n A + n B = 1

or, n A = 1-n B ... eq. 2

So, from eq. 1 and 2,

P A = P o A (1-n B ) = P o A -P o A .n B

Or, P o A - P A =P o A .n B

P o A - P A /P o A = n B

So, here term,( P o A - P A /P o A ) is the lowering r vapor pressure which depends on moles of solute only i.e. n B so, it is a colligative property.