Understanding the Vapour Pressure of a Sucrose Solution: A Thorough Analysis

Introduction

The vapour pressure of a solution is a crucial property that is influenced by the composition and temperature of the solution. This article delves into the specific case of a sucrose solution, where 80 grams of sucrose (C12H22O11) is dissolved in 100 ml of water at 25°C. We will calculate the expected vapour pressure of this solution and explore the underlying principles.

Vapour Pressure and Mole Fractions

The vapour pressure of a solution is proportional to the mole fractions of its volatile components. In this scenario, the water (H2O) is the volatile component. To determine the mole fractions, we must first calculate the number of moles of each component involved:

Moles of water:

100 grams of water corresponds to (frac{100}{18.01 , text{g/mol}} 5.55 , text{moles}).

Moles of sucrose (C12H22O11):

80 grams of sucrose corresponds to (frac{80}{342.31 , text{g/mol}} 0.234 , text{moles}).

Next, we calculate the mole fraction of water (χwater) and the mole fraction of sucrose (χsucrose):

Mole fraction of water:

(chi_{text{water}} frac{text{moles of water}}{text{moles of water moles of sucrose}} frac{5.55}{5.55 0.234}).

(chi_{text{water}} frac{5.55}{5.784} approx 0.960).

Mole fraction of sucrose:

(chi_{text{sucrose}} 1 - chi_{text{water}} 1 - 0.960 0.040).

The reduction in the vapour pressure of the solution compared to that of pure water is due to the fact that the sucrose disrupts the order of water molecules at the surface, leading to fewer water molecules evaporating from the solution.

Vapour pressure of the solution:

The vapour pressure of the solution is given by (chi_{text{water}} times text{vapour pressure of pure water}).

Given the vapour pressure of water at 25°C is approximately 23.76 torr (or 25 torr), and assuming the temperature is 25°C, the vapour pressure of the solution is:

0.960 × 23.76 torr ≈ 22.71 torr.

Conclusion

The calculated vapour pressure of the solution is significantly lower than that of pure water, as expected. This reduction in vapour pressure indicates a decrease in the evaporation rate of water molecules in the presence of sucrose, which raises the boiling point of the solution and lowers its freezing point. The exact temperature of 25°C is crucial in determining the precise vapour pressure, as it influences the equilibrium between liquid and vapour phases.

It's important to note that in practical applications, the vapour pressure of water at standard temperature can vary slightly, but the principle remains the same. The key takeaway is that as a solute (such as sucrose) is dissolved in a solvent (such as water), the vapour pressure of the solvent is reduced, leading to a lower boiling point and a higher freezing point of the solution.

Keywords

Vapour Pressure, Solution, Temperature