A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 22.3 g of the compund in water to form 0.250 L solution. The solution formed has an osmotic pressure of 2.12 atm at 25 degrees celcius. Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

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Let the molar mass of the organic compound be M.

We know osmotic pressure of dilute solutions (of a nonelectrolyte) is a colligative property, given by π = c R T ----(i)

Where, π is the osmotic pressure in atmosphere units, c the molar concentration, R is the gas constant and T, its absolute temperature.

Here, π = 2.12 atmosphere,

22.3 g solute of molar mass M is dissolved in 0.25L solution.

therefore, molar concentration, c = 22.3*4/M moles per litre = 89.2/M molar.

T = 25ᵒC = 298 K

R = 0.08205 lit-atmos/K/mol

Putting these values in equation (i), we get,

2.12 = 89.2/M * 0.08205 * 298

Or, M = (89.2*0.08205*298)/2.12 = 1028.8

Hence molar mass of the organic compound is 1028.8.

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