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 = T_f = - 1.03 °C

To find: Molar mass of a compound

Formulae: 1. ${\displaystyle △{\text{T}}_{\text{f}}={\text{K}}_{\text{f}}\text{m}}$  

2. π = MRT

3. m = ${\displaystyle \frac{1000{\text{W}}_2}{{\text{M}}_2{\text{W}}_1}}$  

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

${\displaystyle △{\text{T}}_{\text{f}}={\text{T}}_{\text{f}}^0-{\text{T}}_{\text{f}}}$ = 0 °C - (- 1.03 °C) = 1.03 °C = 1.03 K

K_f of water = 1.86 K kg mol^–1

Using formula (i),

${\displaystyle △{\text{T}}_{\text{f}}={\text{K}}_{\text{f}}\text{m}}$

m = ${\displaystyle \frac{△{\text{T}}_{\text{f}}}{{\text{K}}_{\text{f}}}=\frac{\text{1.03 K}}{1.86{\text{K kg mol}}^{-1}}}$ = 0.554 mol kg^-1 = 0.554 m

Using formula (ii),

π = MRT

M = ${\displaystyle \frac{\pi }{\text{RT}}=\frac{12.16\text{atm}}{0.08205 {\text{dm}}^3{\text{atm K}}^{-1}{\text{mol}}^{-1}\times 298.15\text{K}}}$ = 0.497 mol dm^-3 = 0.497 M

Mass of solvent = ${\displaystyle \frac{0.497 {\text{mol dm}}^{-3}}{0.554 {\text{mol kg}}^{-1}}\times 1 {\text{dm}}^3}$ = 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 = ${\displaystyle \frac{1000{\text{W}}_2}{{\text{M}}_2{\text{W}}_1}}$

∴ ${\displaystyle {\text{M}}_2=\frac{1000{\text{W}}_2}{\text{m}{\text{W}}_1}=\frac{1000{\text{g kg}}^{-1}\times 166\text{g}}{0.554{\text{mol kg}}^{-1}\times 897\text{g}}}$ 
= 334 g mol^-1

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