"Published in Newark, California, USA"
The osmotic pressure of a dilute aqueous ethyl alcohol solution at 25°C is 38 mm Hg. Calculate the boiling point elevation of this solution.
Solution:
Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in water by osmosis.
The osmotic pressure of any solution is given by the equation
where
Π = is the osmotic pressure of a solution
M = is the molarity of a solution
R = is the universal gas law constant
T = is the absolute temperature of a solution
The absolute temperature of a solution is
The universal gas law constant for grams, gmole, mm Hg, liters, and K is
. Hence, the molarity of ethyl alcohol solution is
The boiling point elevation is defined as the product of the boiling point constant of a solvent and the molality of a solution.
where m is the molality of a solution.
From the Table of Freezing and Boiling Information of Solvents, the boiling point constant of water is
.
Since the concentration of ethyl alcohol is in molarity, then we have to convert it into molality as follows
where ρ is the mass density of a solution.
By looking at the Table of Ethyl Alcohol - Water Mixtures, the density in kg/L is almost the same or similar to pure water which has a range from 0.9 to 1.0 kg/L although we increase the concentration of ethyl alcohol from 0 to 50% by weight. In this case, let's approximate that the density of ethyl alcohol solution is 1.00 kg/L.
Hence, the molality of ethyl alcohol solution is
The unit of molality must be gmoles of ethyl alcohol per kg. of water. The weight of ethyl alcohol in 1 liter of solution is
The weight of water in 1 liter of solution is
Since the weight of water is almost equal to the weight of solution, then the molality of ethyl alcohol is equal to
Therefore, the boiling point elevation of ethyl alcohol solution is
