Raoults law

Raoult's Law states that the partial vapor pressure of each volatile component in an ideal solution is equal to the product of the mole fraction of the component in the solution and the vapor pressure of the pure component at the same temperature. Mathematically, it can be expressed as:

$P_{i} = X_{i} \cdot P_{i}^{*}$

where:

$P_{i}$ is the partial vapor pressure of component $i$ in the solution.
$X_{i}$ is the mole fraction of component $i$ in the solution.
$P_{i}^{*}$ is the vapor pressure of the pure component $i$ at the same temperature.

For a solution with two components, A and B, the total vapor pressure ( $P_{t o t a l}$ ) of the solution is the sum of the partial pressures of the components:

$P_{t o t a l} = P_{A} + P_{B} = X_{A} \cdot P_{A}^{*} + X_{B} \cdot P_{B}^{*}$

Positive Deviation from Raoult's Law

A positive deviation from Raoult's Law occurs when the interactions between the molecules of the different components in a solution are weaker than the interactions between the molecules of each component in their pure state. This results in a higher vapor pressure than would be predicted by Raoult's Law because the molecules are more likely to escape into the vapor phase.

Example: Ethanol and Water

A classic example of positive deviation from Raoult's Law is a solution of ethanol (C₂H₅OH) and water (H₂O).

Ethanol (C₂H₅OH): Ethanol molecules interact with each other through hydrogen bonding.
Water (H₂O): Water molecules also interact with each other through hydrogen bonding.

When ethanol and water are mixed, the hydrogen bonds between ethanol molecules and between water molecules are disrupted. The new interactions between ethanol and water molecules are not as strong as the original hydrogen bonds in the pure substances. This results in increased escaping tendencies of both ethanol and water molecules, leading to a higher total vapor pressure than predicted by Raoult's Law.

In summary, the weaker interactions in the mixture compared to the pure substances cause the solution to have a higher vapor pressure, indicating a positive deviation from Raoult's Law.