Consider a two chamber vessel. An SPM Separates the two chambers into equal volume as shown A one-liter aqueous solution X (density = 1.6 g/mL) of a non-volatile solute is filled in one of the chamber

Question

Consider a two chamber vessel. An SPM Separates the two chambers into equal volume as shown

A one-liter aqueous solution X (density = 1.6 g/mL) of a non-volatile solute is filled in one of the chambers. Soon after, an equal volume of pure water (density = 1.0 g/mL) is filled in the other chamber. Very quickly, the solution surface is now covered with a capillary of 50 cm² cross-section. Pure water now starts flowing from the solvent towards the solution. At equilibrium, the level of the solution in the capillary is 30.4 cm. Find the osmotic pressure (in atm) of solution X. Assume $Δ V_{mi x} = 0$ .

Use: density of Hg = 13.4 g/mL, atmospheric pressure = 76 cm of Hg. (23.6 / 176 = 0.134)

TestHub · Accepted Answer

Let x cm = heights in the chamber ∵ Δ V mix ​ = 0 ⇒ Total initial volume = total final volume ⇒ 2000 = 100 x + 100 x + 50 × 30.4 ⇒ x = 2.4 cm Let C 1 ​ = initial concentration of the solution ' X '. & New concentration = C 2 ​ Also, density of the new solution is, d = 1760 1000 × 1.6 + 760 × 1 ​ = 1.34 g / ml ∴ π = 30.4 cm of final solution = 13.4 30.4 × 1.34 ​ = 3.04 cm Hg = 76 3.04 ​ = 0.04 atm 。 ⇒ π = 0.04 atm Also, π ∝ C ​ ⇒ C 1 ​ π 1 ​ ​ = C 2 ​ π 2 ​ ​ ​ π 1 ​ = π 2 ​ × C 2 ​ C 1 ​ ​ = 0.04 × 1760 C 1 ​ × 1000 ​ C 1 ​ ​ = 0.0704 atm ​

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