Question

Osmotic pressure of a urea solution at 10°C is 500 mm Hg. Osmotic pressure of the solution become 105.3 mm Hg, when it is diluted and temperature is raised to 25°C. The extent of dilution is ____________.

Options

• 6 times

• 5 times

• 7 times

• 4 times

Answer 1

Osmotic pressure of a urea solution at 10°C is 500 mm Hg. Osmotic pressure of the solution become 105.3 mm Hg, when it is diluted and temperature is raised to 25°C. The extent of dilution is 5 times.

Explanation:

van't Hoff's equation is

πV = nRT

∴ π₁V₁ = nRT₁ and π₂V₂ = nRT₂

V₁ and V₂ are the initial and final volume of the solution respectively.

n = Number of moles

R = Ideal gas constant

T₁ = 10 + 273 = 283 K

T₂ = 25 + 273 = 298 K

π₁ = 500 mm Hg

π₂ = 105.3 mm Hg

`(π_1"V"_1)/(π_2"V"_2) = ("nRT"_1)/("nRT"_2)`

∴ `(500  "mm Hg" xx "V"_1)/(105.3  "mm Hg" xx "V"_2) = ("nR" xx 283  "K")/("nR" xx 298  "K"); "V"_1/"V"_2 = 1/5`

So, V₂ = 5V₁