An aqueous solution containing 28.4 g of non-volatile compound having ...
Given:
- Mass of non-volatile compound (CnH2nOn) = 28.4 g
- Mass of water = 100 g
- Boiling point of the solution = 101.24°C
- Boiling point of pure water = 100°C
- Kf (H2O) = 0.52 mol-1 kg
- Boiling point of pure water = 373 K
To Find:
The value of n in the stoichiometric composition CnH2nOn.
Solution:
We can use the equation for the boiling point elevation (ΔTb) to solve this problem. The equation is given by:
ΔTb = Kf * m
Where:
- ΔTb is the boiling point elevation
- Kf is the molal boiling point elevation constant
- m is the molality of the solution (moles of solute per kg of solvent)
Step 1: Calculate the molality of the solution.
Molality (m) is given by the equation:
m = (moles of solute) / (mass of solvent in kg)
We need to find the moles of solute in the solution. The molar mass of the compound CnH2nOn can be calculated as follows:
Molar mass = (12n + 2n + 16n)
Since the stoichiometric composition of the compound is CnH2nOn, the molar mass is equal to the mass of the compound (28.4 g).
Molar mass = 28.4 g/mol
Now, we can calculate the moles of solute using the given mass of the compound:
moles of solute = (mass of solute) / (molar mass)
moles of solute = 28.4 g / 28.4 g/mol
moles of solute = 1 mol
The mass of water is given as 100 g, which is equal to 0.1 kg.
Now, we can calculate the molality of the solution:
m = (moles of solute) / (mass of solvent in kg)
m = 1 mol / 0.1 kg
m = 10 mol/kg
Step 2: Calculate the boiling point elevation (ΔTb) using the equation ΔTb = Kf * m.
ΔTb = 0.52 mol-1 kg * 10 mol/kg
ΔTb = 5.2 K
Step 3: Calculate the boiling point of the solution.
The boiling point of the solution is equal to the boiling point of pure water (373 K) plus the boiling point elevation (ΔTb).
Boiling point of the solution = Boiling point of pure water + ΔTb
Boiling point of the solution = 373 K + 5.2 K
Boiling point of the solution = 378.2 K
Step 4: Convert the boiling point of the solution from Kelvin to Celsius.
The boiling point of the solution is 378.2 K, which is equal to 105.2°C.
Step 5: Compare the boiling point of the solution with the boiling point given in the question.