Molar mass of compound

Question

An aqueous solution of a soluble compound (a nonelectrolyte) is prepared by dissolving 33.2 g of the compound in sufficient water to form 250 mL of solution. The solution has an osmotic pressure of 1.2 atm at 25 °C. What is the molar mass (g/mole) of the compound?

Answer 1

π = iMRT

π = osmotic pressure = 1.2 atm

i = van't Hoff factor = 1 for a non-electrolyte

M = molarity = moles solute / liter solution = ?

R = gas constant = 0.0821 Latm / Kmol

T = temperature in Kelvin = 25ºC + 273 = 298K

Solve for M:

M = π / iRT = 1.2 atm / (1)(0.0821 Latm/Kmol)(298K)

M = 0.0490 moles / liter

Since we have 250 mls solution (0.250 L), we can find moles:

0.0490 mol / L x 0.250 L = 0.01226 moles

Molar mass = g / moles.

Molar mass = 33.2 g / 0.01226 moles

Molar mass = 2708 g / mole