Vapour Pressure
Vapour Pressure
Vapour pressure is a fundamental concept in physical chemistry, particularly when discussing liquid solutions and phase transitions. It is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system.
Understanding Vapour Pressure
When a liquid is placed in a closed container, molecules from the liquid evaporate to form a vapor above the liquid. Over time, some of these vapor molecules will return to the liquid phase in a process called condensation. When the rate of evaporation equals the rate of condensation, the system reaches a dynamic equilibrium. The pressure exerted by the vapor at this point is known as the vapour pressure.
Factors Affecting Vapour Pressure
- Temperature: As temperature increases, the kinetic energy of the molecules increases, leading to a higher rate of evaporation and thus higher vapour pressure.
- Intermolecular Forces: Substances with weaker intermolecular forces have higher vapour pressures at a given temperature because their molecules can escape into the vapor phase more easily.
- Nature of the Liquid: Different liquids have different vapour pressures due to their unique molecular structures and intermolecular forces.
Vapour Pressure Formulas
The quantitative relationship between vapour pressure and temperature is described by the Clausius-Clapeyron equation:
$$ \ln\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R} \left(\frac{1}{T_2} - \frac{1}{T_1}\right) $$
where:
- $P_1$ and $P_2$ are the vapour pressures at temperatures $T_1$ and $T_2$ respectively,
- $\Delta H_{vap}$ is the enthalpy of vaporization,
- $R$ is the universal gas constant.
For small temperature ranges, the equation can be simplified to:
$$ \ln\left(\frac{P_2}{P_1}\right) \approx -\frac{\Delta H_{vap}}{R} \left(\frac{T_2 - T_1}{T_1 T_2}\right) $$
Raoult's Law
Raoult's law is a simplified way to calculate the vapour pressure of a solution. It states that the partial vapour pressure of each component in an ideal solution is directly proportional to its mole fraction in the solution:
$$ P_i = X_i \cdot P_i^* $$
where:
- $P_i$ is the partial vapour pressure of component $i$ in the solution,
- $X_i$ is the mole fraction of component $i$,
- $P_i^*$ is the vapour pressure of the pure component $i$.
Table of Differences and Important Points
| Property | Pure Liquid | Solution |
|---|---|---|
| Vapour Pressure | Equal to the liquid's inherent vapour pressure at a given temperature | Lower than the vapour pressure of the pure solvent due to the presence of solute particles |
| Dependence on Temperature | Follows Clausius-Clapeyron equation | Follows Raoult's law and is also affected by temperature |
| Dependence on Composition | Not applicable | Directly proportional to the mole fraction of the solvent |
Examples
Example 1: Temperature Dependence
Consider water at two different temperatures, 25°C and 50°C. The vapour pressure of water at 25°C is approximately 23.76 mmHg. Using the Clausius-Clapeyron equation, we can estimate the vapour pressure at 50°C if we know the enthalpy of vaporization for water.
Example 2: Raoult's Law
Suppose we have a solution of ethanol (C2H5OH) in water. The mole fraction of ethanol is 0.2, and the vapour pressure of pure ethanol at the given temperature is 45 mmHg. According to Raoult's law, the partial vapour pressure of ethanol in the solution would be:
$$ P_{\text{ethanol}} = X_{\text{ethanol}} \cdot P_{\text{ethanol}}^* = 0.2 \cdot 45 \text{ mmHg} = 9 \text{ mmHg} $$
The total vapour pressure of the solution would be the sum of the partial pressures of ethanol and water, each calculated using Raoult's law.
Understanding vapour pressure is crucial for predicting boiling points, understanding distillation processes, and explaining phenomena such as evaporation and condensation. It is a key concept in thermodynamics and plays a significant role in various industrial and scientific applications.