If 240 mL of an aqueous solution containing 1.67 g of an unknown covalent solid at 25oC gives rise to an osmotic pressure of 497 mmHg, what is the molar mass (g/mol) of the unknown?

Answer 1

Osmotic pressure (π) = iMRT

π = 497 mm Hg x 1 atm/760 mm Hg = 0.6539 atm

i = van't Hoff factor = 1 for a covalent compound that does not ionize

M = molarity = moles/liter = ?

R = gas constant = 0.0821 Latm/Kmol

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

Solving for M, we have...

M = π / (i)(R)(T) = 0.6539 atm / (1)(0.0821 Latm/Kmol)(298K)

M = 0.0267 moles/liter

Since there are only 0.240 L (240 ml), this equates to 0.0267 mol/L x 0.240 L = 0.00641 moles

molar mass = grams/moles = 1.67 g / 0.00641 moles

molar mass = 261 g/mole ( 3 sig. figs.)