Calculate the Molar Mass (g/mol) of an unknown nonelectrolyte if the osmotic pressure exerted by dissolving 44.2 mg of it in 358 mL of solution at 25.0 oC is 12.7 torr. a) 104 b) 181 c) 203 d) 78.6 e) 167 f) 283 g

b) 181

Explanation:

T = 25 + 273 = 298K (Upon converting to Kelvin Temperature)

Osmotic pressure, π = 12.7 torr = 0.0167 atm ( converting to atm by dividing the pressure value by 760 )

The equation relating these variables is given as;

π = MRT

M = π / RT

R = gas constant = 0.0821 L atm/mol K

Upon solving for M;

M = 0.0167 / ( 0.0821 * 298)

M = 0.0167 / 24.47

M = 0.000682 M

The mass concentration = Mass / Volume

Mass conc = 44.2 mg / 358

Mass conc = 0.1235g/l

The relationship between the molar concentration and mass concentration is;

Molar mass = Mass conc / Molar conc

Upon substituting the values we have;

Molar mass = 0.1235 /  0.000682

Molar mass = 181.09 g/mol

The correct option is option B.