The correct answer is option (1) Mole fraction.
Raoult's law describes the vapor pressure behavior of an ideal solution, which is a solution that obeys certain idealized assumptions. According to Raoult's law, the vapor pressure (\(P_i\)) of a component in an ideal solution is directly proportional to its mole fraction (\(x_i\)) in the solution. This law is particularly applicable to dilute solutions where intermolecular interactions between unlike molecules are assumed to be similar to those between like molecules.
Mathematically, Raoult's law is expressed as:
\[ P_i = x_i \cdot P_{i,\text{pure}} \]
where:
- \( P_i \) is the vapor pressure of component \(i\) in the solution,
- \( x_i \) is the mole fraction of component \(i\) in the solution,
- \( P_{i,\text{pure}} \) is the vapor pressure of pure component \(i\) in its pure state.
Here's a more detailed explanation:
1. Vapor Pressure:
Vapor pressure is the pressure exerted by the vapor (gaseous phase) of a substance in equilibrium with its liquid or solid phase.
In a solution, each component contributes to the overall vapor pressure.
2. Raoult's Law for Ideal Solutions:
For an ideal solution, Raoult's law assumes that the vapor pressure of each component is proportional to its mole fraction in the solution.
The total vapor pressure of the solution is the sum of the partial pressures of each component.
3. Mole Fraction:
The mole fraction (\(x_i\)) of a component \(i\) in a solution is the ratio of the moles of that component to the total moles of all components in the solution.
It is calculated as \( x_i = \frac{n_i}{n_{\text{total}}} \), where \(n_i\) is the moles of component \(i\) and \(n_{\text{total}}\) is the total moles in the solution.
4. Vapor Pressure Lowering and Raoult's Law Deviations:
Deviations from Raoult's law can occur in non-ideal solutions. These deviations can be positive or negative.
Positive deviations occur when the actual vapor pressure is higher than predicted by Raoult's law, often due to attractive interactions between unlike molecules.
Negative deviations occur when the actual vapor pressure is lower than predicted, often due to repulsive interactions between unlike molecules.
5. Applications:
Raoult's law is commonly used in the study of colligative properties such as vapor pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.
In summary, Raoult's law provides a useful approximation for the behavior of ideal solutions, where the vapor pressure of each component is directly proportional to its mole fraction in the solution. Deviations from Raoult's law can occur in non-ideal solutions, and these deviations are important in understanding the behavior of real-world solutions. |
