The vapour pressure of a solution of two liquids, \(\mathrm{A}\left(P^{\circ}=80 \mathrm{~mm}, X=0.4\right)\) and \(\mathrm{B}\left(P^{\circ}=120 \mathrm{~mm}, X=0.6\right)\) is found to be \(100 \mathrm{~mm}\). It shows that the solution exhibits (a) negative deviation from ideal behaviour. \(\begin{array}{lll}\text { (b) positive } & \text { deviation } & \text { from } & \text { ideal }\end{array}\) behaviour. (c) ideal behaviour. (d) positive deviation at lower concentration

Raoult's law is a fundamental principle in physical chemistry that defines the relationship between vapor pressure and the concentration of a solution. It states that the partial vapor pressure of a component in a mixture is directly proportional to its mole fraction. Simply put, the more of a substance is present in a solution, the greater its contribution to the overall vapor pressure.

Raoult's law can be represented by the formula: \[ P_i = X_i \times P_i^{\text{o}} \]where \( P_i \) is the partial vapor pressure of component \( i \), \( X_i \) is the mole fraction of component \( i \) in the solution, and \( P_i^{\text{o}} \) is the vapor pressure of the pure component \( i \).In the context of the exercise, we apply Raoult's law to calculate the ideal vapor pressure of a solution by summing up the partial pressures, which are the products of each component's mole fraction and its pure vapor pressure. For instance, for component A with \(X_A = 0.4\) and for component B with \(X_B = 0.6\), their contributions are \(32 \text{ mm}\) and \(72 \text{ mm}\) respectively. Their sum, \(104 \text{ mm}\), represents the ideal vapor pressure as per Raoult's law.

An ideal solution is one that perfectly adheres to Raoult's law, meaning the intermolecular forces between the different components are similar to those within the pure components themselves. The vapor pressure and other properties of an ideal solution can be predicted accurately using the mole fractions of the respective components in the solution.

However, not all solutions behave ideally. There are two types of deviations from Raoult's law observed in non-ideal solutions: positive and negative deviations. If the actual vapor pressure of the solution is higher than the calculated ideal vapor pressure, it exhibits a positive deviation. This indicates weaker intermolecular forces in the mixture compared to the pure components. Conversely, if the actual vapor pressure is lower, as in our example exercise, this indicates a negative deviation. Stronger intermolecular forces in the mixture than in the pure components cause this. The exercise, showing an actual vapor pressure of \(100 \text{ mm}\), compared to the ideal \(104 \text{ mm}\), points to a negative deviation, implying increased interaction between the components of the solution.

The mole fraction is an expression of the concentration of a component in a mixture. It is the ratio of the number of moles of a particular component to the total number of moles of all components in the solution. Mathematically, the mole fraction \(X_i\) of a component \(i\) is given by:\[ X_i = \frac{n_i}{n_{total}} \]where \( n_i \) is the number of moles of component \( i \) and \( n_{total} \) is the total number of moles of all components in the mixture.

The mole fraction is a dimensionless number between 0 and 1 and is key when using Raoult's law to determine the partial pressures in a solution. In our textbook example, the mole fractions are given for components A and B as 0.4 and 0.6 respectively. This proportion helps in deriving the ideal vapor pressures which factor into determining if the solution behaves ideally or not.