Raoult's law is essential for understanding vapor pressure lowering, which refers to the decrease in vapor pressure of a solvent when a solute is added. Vapor pressure is defined as the pressure exerted by a gas in equilibrium with its liquid phase at a specific temperature within a closed system. It is crucial to note that vapor pressure is the pressure exerted by the gas at the surface of the liquid, where both condensation and vaporization occur at equal rates.
The formula for calculating vapor pressure lowering is given by:
\[P_{\text{solution}} = \chi_{\text{solvent}} \times P^{\circ}_{\text{solvent}}\]
In this equation, \(P_{\text{solution}}\) represents the vapor pressure of the solution, \(\chi_{\text{solvent}}\) is the mole fraction of the solvent, and \(P^{\circ}_{\text{solvent}}\) is the vapor pressure of the pure solvent, denoted with a degree symbol to indicate its purity.
To calculate the mole fraction of the solvent, the formula can be expressed as:
\[\chi_{\text{solvent}} = \frac{n_{\text{solvent}}}{n_{\text{solvent}} + i \cdot n_{\text{solute}}}\]
Here, \(n_{\text{solvent}}\) is the number of moles of the solvent, \(n_{\text{solute}}\) is the number of moles of the solute, and \(i\) is the van 't Hoff factor, which accounts for the number of particles the solute dissociates into in solution. This factor is crucial in colligative properties, as it influences the overall effect of the solute on the solution's properties.
It is important to remember that the addition of a solute always results in a vapor pressure that is lower than that of the pure solvent, meaning:
\[P_{\text{solution}} < P^{\circ}_{\text{solvent}}\]
This principle is fundamental when performing calculations related to vapor pressure lowering, as it highlights the impact of solute addition on the vapor pressure of a solution.
