Question

\(6.0 \mathrm{~g}\) of urea (molecular weight \(=60\) ) was dissolved in \(9.9\) moles of water. If the vapour pressure of pure water is \(P^{\circ}\), the vapour pressure of solution is: (a) \(0.10 P^{\circ}\) (b) \(1.10 P^{\circ}\) (c) \(0.90 P^{\circ}\) (d) \(0.99 P^{\circ}\)

Short answer

The vapour pressure of the solution is (d) \(0.99 P^{\circ}\).

Step-by-step solution

Calculate the number of moles of urea

To find the number of moles of urea, use the formula: \(\text{Number of moles} = \frac{\text{Mass of substance}}{\text{Molecular weight}}\). So, for urea: \( \text{Number of moles} = \frac{6.0 \text{ g}}{60 \frac{\text{g}}{\text{mol}}} = 0.1 \text{ mol} \).

Determine the total number of moles in solution

Combine the moles of urea and water to get the total number of moles in the solution: \(0.1 \text{ mol urea} + 9.9 \text{ mol water} = 10.0 \text{ mol total}\).

Calculate the mole fraction of water

The mole fraction of water is the ratio of the number of moles of water to the total number of moles in the solution: \( \text{Mole fraction of water} = \frac{9.9}{10.0} = 0.99 \).

Calculate the vapour pressure of the solution

Apply Raoult's Law, which states that the vapour pressure of a solution is proportionate to the mole fraction of the solvent: \( P_{\text{solution}} = \text{Mole fraction of water} \times P^{\circ} = 0.99 \times P^{\circ} \).

Key concepts

Raoult's Law

When diving into the understanding of solution chemistry, especially when it comes to vapor pressure, Raoult's Law serves as a foundational principle. It elegantly connects the macroscopic property of vapor pressure to the composition of a mixture on the molecular level. Simply put, Raoult's Law states that the partial vapor pressure of a solvent in a solution is directly proportional to the solvent's mole fraction in the solution.

In the exercise provided, we're applying Raoult's Law to determine the vapor pressure of an aqueous urea solution. The law formula can be expressed as: \[ P_{\text{solution}} = (\text{Mole fraction of the solvent}) \times P^{\circ} \], where \(P^{\circ}\) is the vapor pressure of the pure solvent (water, in this case). For the steps mentioned, after determining the mole fraction of water, we multiply it by the pure water's vapor pressure to arrive at the solution's vapor pressure.

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 one component to the total number of moles of all components in the mixture. The mole fraction is unitless and provides a measure of the proportion of a substance within a mixture.

Calculating the mole fraction is an essential step in the exercise. For example, the mole fraction of water in our urea solution is calculated by dividing the number of moles of water by the total number of moles in the solution (the sum of moles of water and urea). Understanding mole fraction is crucial not only for applications of Raoult's Law but also for many other calculations involving solutions, such as determining concentrations and colligative properties.

Colligative Properties

Colligative properties are properties of solutions that depend solely on the number of dissolved particles in the solution, not on the nature of the chemical species present. These properties include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure.

Understanding colligative properties helps us predict how a solution will behave compared to its pure solvent. In the context of vapor pressure, Raoult's Law describes how the presence of a solute (like urea) will lower the vapor pressure of the solvent (water). This lowering is a colligative property because it is directly related to the number of urea particles in the solution, regardless of their identity. The more solute particles present, the more the vapor pressure is lowered.

Solution Chemistry

Solution chemistry is an area of study that explores the interactions between solutes and solvents to form solutions. It encompasses understanding solubility, concentration measures (such as mole fraction), and the various colligative properties. In solution chemistry, the role of intermolecular forces is discussed to explain why substances dissolve and how the properties of the solution differ from those of the pure substances.

In our specific exercise, solution chemistry is at play when dissolving urea in water. The solute (urea) interacts with the solvent (water), affecting physical properties such as the vapor pressure. By studying solution chemistry, we can predict these changes and understand the underlying molecular interactions that drive them.