An aqueous solution of a certain organic compound has a density of 1.063 g mL-1 , an osmotic pressure of 12.16 atm at 25 °C and a freezing point of 1.03 °C. What is the molar mass of the compound? - Chemistry

Exercise | Q 12 | Page 46

An aqueous solution of a certain organic compound has a density of 1.063 g mL-1 , osmotic pressure of 12.16 atm at 25 °C and a freezing point of 1.03 °C. What is the molar mass of the compound?

Solution


Given: Density of a solution = d = 1.063 g mL-1

Osmotic pressure of solution = π = 12.16 atm

Temperature = T = 25 °C = 298.15 K

Freezing point of solution = Tf = - 1.03 °C

To find: Molar mass of a compound

Formulae: 1. Tf=Kfm  

2. π = MRT

3. m = 1000W2M2W1  

Calculation: R = 0.08205 dm3 atm K-1 mol-1

Tf=Tf0-Tf = 0 °C - (- 1.03 °C) = 1.03 °C = 1.03 K

Kf of water = 1.86 K kg mol–1

Using formula (i),

Tf=Kfm

m = TfKf=1.03 K1.86K kg mol-1 = 0.554 mol kg-1 = 0.554 m

Using formula (ii),

π = MRT

M = πRT=12.16atm0.08205 dm3atm K-1mol-1×298.15K = 0.497 mol dm-3 = 0.497 M

Mass of solvent = 0.497 mol dm-30.554 mol kg-1×1 dm3 = 0.897 kg = 897 g units

Mass of solution = 1.063 g mL-1 × 1000 mL = 1063 g

Mass of solute = 1063 g – 897 g = 166 g

Now, using formula (iii),

m = 1000W2M2W1

∴ M2=1000W2mW1=1000g kg-1×166g0.554mol kg-1×897g 
= 334 g mol-1

The molar mass of the compound is 334 g mol-1.