Historically certain colligativeproperties – freezing point depression, boiling

Question

Historically certain colligativeproperties – freezing point depression, boiling point

elevation, and osmotic pressure– have been used to determine molecular mass.

(Now there are instrumental methodsto determine this.) Of these three, osmotic

pressure is the most sensitive andgives the best results. Molecular mass can be

found according the followingequation:

Where: = osmotic pressure,

M = molarity ofsolution,

R = the ideal gas constant(L•atm/mol•K), and

T = Kelvin temperature.

At 23.6 degrees C, 0.500 L of asolution containing 0.302 grams of an antibiotic has an osmotic

pressure of 8.34 mmHg. What is itsmolecular mass?

Explanation / Answer

Formula:                        = MRT                      M = Number of moles / Volume of solution in L Number of moles = Mass in g / Molar mass in g /mol Data:                      T   = 23.6 0C                            =23.6 + 273.15 K                           = 296.75 K                       R = 0.0821 L .atm / mol .K                        = 8.34 mm Hg                          = (8.34 / 760 ) atm                          = 0.0109 atm                       m =0.302 g              Volume =0.500 L Upon substituting the data in the formula,      0.0109 atm = M * 0.0821 L.atm /mol.K * 296.75K                 M    = 4.5 * 10-4   mol/L                         =4.5 * 10-4   mol /L * 0.5 L                        = 2.252 * 10-4 mol   Molar mass    = 0.302 g/  2.252 * 10-4 mol                        = 1340.96 g / mol                         

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