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?
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.