An aqueous solution containing 288 g of a non–volatile compound ...
Given:- Mass of nonvolatile compound = 288 g
- Mass of water = 90 g
- Boiling point of solution = 101.24 °C
- Pressure = 1 atm
- Kb(H2O) = 0.512 K kg mol^-1
To Find:Value of x in the stoichiometric composition CxH2xOx
Solution:1. Calculate the molality (m) of the solution:
Molality (m) is defined as the moles of solute per kilogram of solvent.
Molar mass of water (H2O) = 2 * 1 + 16 = 18 g/mol
Number of moles of water = Mass of water / Molar mass of water
= 90 g / 18 g/mol
= 5 mol
Molality (m) = (Number of moles of solute) / (Mass of solvent in kg)
= (288 g / Molar mass of solute) / (90 g / 1000)
= (288 / Molar mass of solute) / 0.09
= 3.2 / Molar mass of solute
2. Calculate the change in boiling point (∆Tb) of the solution:
∆Tb = Kb * m
= 0.512 K kg mol^-1 * (3.2 / Molar mass of solute)
3. Calculate the boiling point elevation (∆T) of the solution:
∆T = Boiling point of solution - Boiling point of pure solvent
= 101.24 °C - 100 °C
= 1.24 °C
4. Calculate the molar mass of the solute:
∆T = Kb * m
1.24 °C = 0.512 K kg mol^-1 * (3.2 / Molar mass of solute)
Molar mass of solute = (0.512 K kg mol^-1 * 3.2) / 1.24 °C
= 1.315 K kg mol^-1
Given:CxH2xOx has a stoichiometric composition
Molar mass of carbon (C) = 12 g/mol
Molar mass of hydrogen (H) = 1 g/mol
Molar mass of oxygen (O) = 16 g/mol
Molar mass of CxH2xOx = (12x + 1x + 16x) g/mol
= 29x g/mol
Molar mass of solute = 1.315 K kg mol^-1 = 29x g/mol
29x = 1.315 * 1000
x = 44
Therefore, the value of x in the stoichiometric composition CxH2xOx is 44.