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# Assertion: Lowering of vapour pressure is directly proportional to osmotic pressure of the solution.

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Assertion: Lowering of vapour pressure is directly proportional to osmotic pressure of the solution.

Reason: Osmotic pressure is a colligative property.

(a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

(c) If Assertion is correct but Reason is incorrect.

(d) If both the Assertion and Reason are incorrect.

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(b) If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

Explanation:

Both assertion and reason are correct but reason is not the correct explanation of assertion. The relationship between lowering of vapour pressure and osmotic pressure can be derived as follows: Van’t Hoff equation for dilute solutions is

π = n/V RT    ....(i)

In case of a dilute solution, the volume of solution can be taken as equal to that of solvent. If N is the number of moles of solvent of molecular weight M and density ρ, the volume V is given by

V = NM/ρ      ......(ii)

or n/N = πM/ρ.R.T     .....(iii)

From Raoult’s law,

P° - P/P° = n/N     ......(iv)

P° - P/P° = πM/ρRT  [From (iii) and (iv)]

or (P° - P) = πM/ρRT x P°

The factor MP°/ρRT is constant at constant temperature.

∴ (P° - P) ∝ π

or lowering of V.P. ∝ osmotic pressure Thus assertion is correct.

Osmotic pressure is a colligative property is correct.

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