29.52 mg of a non-ionizing biological macromolecule is dissolved in 10.00 mL of water with no volume change. The osmotic pressure of the solution at 23.5 oC is determined to be 1.44 x 10 -3 atm. Determine the molar mass of the macromolecule.

49902.4 g/mol.

Explanation:

Using ideal gas equation,

PV = nRT

Where,

P = pressure

= 0.00144 atm

V = volume

= 0.01 l

T = absolute temperature

= 273 + 23.5

= 296.5 K

R = gas constant

= 0.0821 atm.l/K.mol

n = number of moles

n = (0.00144 * 0.01)/0.0821 * 296.5

= 5.92 x 10^-7 mol.

Molar mass = mass/number of moles

= 0.02952/5.92 x 10^-7

= 49902.4 g/mol.