Question

Express Raoult's law in words. Is Raoult's law valid for a solution of a volatile solute? Explain.

Short answer

Raoult's law states that the partial vapor pressure of each component in an ideal solution is proportional to its mole fraction. Raoult's law is valid for solutions of volatile solutes if the solution behaves ideally.

Step-by-step solution

Understand Raoult's Law

Raoult's law states that the partial vapor pressure of each component in an ideal solution is directly proportional to the mole fraction of that component in the solution. Mathematically, it is expressed as: \( P_i = X_i P_i^* \) where \(P_i\) is the partial vapor pressure of component \(i\), \(X_i\) is the mole fraction of component \(i\) in the solution, and \(P_i^*\) is the vapor pressure of the pure component \(i\).

Assess Validity for Volatile Solute

Raoult's law is valid for ideal solutions, meaning the solute and solvent must have similar intermolecular forces, and the solution must exhibit ideal behavior. For a volatile solute, Raoult’s law can still be valid if the solution behaves ideally. However, many real solutions deviate from ideal behavior due to differences in intermolecular forces between the solute and solvent.

Example Scenarios

In an ideal solution of a volatile solute and a solvent, both components follow Raoult's law. Both the solvent and the solute will contribute to the total vapor pressure based on their mole fractions. However, if the solution is non-ideal, interactions between solute and solvent molecules may lead to deviations from Raoult’s law.

Key concepts

Partial Vapor Pressure

The concept of partial vapor pressure is fundamental in understanding Raoult's law. The partial vapor pressure of a component in a solution is the pressure that component would exert if it were to occupy the entire volume of the mixture independently. In simple terms, it represents the 'share' of total vapor pressure contributed by a single component in a mixture.
For example, in a mixture of water and ethanol, the partial vapor pressure of water is the pressure exerted by water molecules in the vapor phase. It depends on both the mole fraction of water and its vapor pressure when pure. According to Raoult's law:
\( P_i = X_i P_i^* \) \(P_i\) is the partial vapor pressure, \(X_i\) is the mole fraction of the component, and \(P_i^*\) is the vapor pressure of the pure component.
This means that if water constitutes 0.5 of the mixture and its pure vapor pressure is 20 mmHg, the partial vapor pressure of water in the solution would be:
\( P_{\text{water}} = 0.5 \times 20 = 10 \text{ mmHg} \)
This principle helps predict how different components will behave when mixed.

Ideal Solution

For Raoult's law to hold true, the solution must behave ideally. An ideal solution is one where the intermolecular forces between the solute and solvent are similar to those in the pure solvent and solute.
In an ideal solution:

• The enthalpy of mixing is zero.
• The volumes are additive.
• The behavior follows Raoult’s law accurately.

Examples of nearly ideal solutions include hexane and heptane, where the molecules are similarly structured and interact in nearly the same way.
Ideal solution behavior is rare in real-world applications, as most solutions exhibit some degree of deviation due to differing molecular interactions. For instance, mixing ethanol and water leads to hydrogen bonding, which deviates from ideal behavior.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of the component to the total number of moles in the mixture.
Mathematically, it is represented as:
\( X_i = \frac{n_i}{n_{\text{total}}} \)
where \(n_i\) is the number of moles of the component and \(n_{\text{total}}\) is the total number of moles of all components in the solution.
For example, if a solution contains 2 moles of ethanol and 3 moles of water, the mole fraction of ethanol (\