A dilute aqueous solution (0.250 L) of an organic compund soluble in water is formed by dissolving 22.3 g of the organic compound in water. The solution formed has an osmotic pressure of 2.12 atm at 25 degrees celcius. Assuming that the organic compund is a non-electrolyte, what is its molar mass?
Osmotic pressure obeys the following formula:
`Pi V = nRT`
(sometimes the formula `Pi = iMRT` is also used where i is referred to as the van't Hoff factor, a dimensionless constant assumed to be equal to 1 for non-electrolytes, and M is the molarity or the ratio of moles solute per liter of solution.)
We know that number of moles is equal to the ratio of the mass and the molar mass: `n = m/(MW).`
`Pi V = m/(MW) RT rArr (MW) = (mRT)/(Pi V)`
`MW = (22.3*0.08206*(25 + 273))/(2.12*0.250) = 1028.909.`
Hence, the organic compound has molecular weight 1028.909 grams/mol.
Note: We had to convert temperature to the absolute scale (Kelvin), otherwise, we wouldn't get the correct answer.