Question

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving \(2.35 \mathrm{~g}\) of the compound in water to form \(0.250 \mathrm{~L}\) solution. The resulting solution has an osmotic pressure of \(0.605 \mathrm{~atm}\) at \(25^{\circ} \mathrm{C}\). Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

Short answer

The molar mass of the organic compound is \(38.3\mathrm{~g/mol}\).

Step-by-step solution

Calculate Temperature in Kelvin

Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius value: \(T = 25 + 273.15 = 298.15\mathrm{~K}\)

Calculate Molarity of the Solution

Use the osmotic pressure formula (π = MRT) to calculate the molarity (M) by rearranging it: \(M = \frac{π}{RT}\) Substitute the given values of π, R, and T into the formula to calculate the molarity: \(M = \frac{0.605\mathrm{~atm}}{(0.0821\mathrm{~L~atm/mol~K}) (298.15\mathrm{~K})} = 0.0247 \mathrm{~mol/L}\)

Calculate Grams per Mole

Use the formula to calculate grams per mole: \[M₂ = \frac{m}{MV}\] Substitute the mass (m), molarity (M), and volume (V) into the formula to calculate the molar mass: \(M₂ = \frac{2.35\mathrm{~g}}{(0.0247\mathrm{~mol/L})(0.250\mathrm{~L})} = 38.3\mathrm{~g/mol}\) Therefore, the molar mass of the organic compound is 38.3 g/mol.