Question

Relative lowering of vapour pressure of a solution containing a nonvolatile solute is equal to the mole fraction of (a) solute (b) solvent (c) solvent minus solute (d) solvent plus solute

Short answer

The accurate answer is (a) solute.

Step-by-step solution

Understand the Raoult's Law

According to Raoult's law, the relative lowering of vapour pressure of a solution, which is the ratio of the decrease in vapour pressure to the original vapour pressure, is equal to the mole fraction of the solute. Mathematically, it can be expressed as \(\Delta P/P = x_{solute}\), where \(\Delta P\) is the decrease in vapour pressure, \(P\) is the original vapour pressure, and \(x_{solute}\) is the mole fraction of the solute.

Evaluate the Options

In this step, evaluate all options in accordance with the expression established in step 1. The expression \(x_{solute}\) refers to the mole fraction of the solute in the solution, so that the most accurate answer is the mole fraction of the solute.

Key concepts

Relative Lowering of Vapour Pressure

In solutions, the relative lowering of vapour pressure is a key concept tied directly to Raoult's Law. Raoult's Law states that the vapour pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent. However, the relative lowering of vapour pressure focuses on a specific aspect: how much the vapour pressure decreases when a nonvolatile solute is added to a pure solvent. This lowering is expressed as a fraction of the original vapour pressure and indicates how much less readily a solvent will evaporate due to the presence of a solute.

It can be mathematically expressed as \(\frac{\Delta P}{P} = x_{\text{solute}}\), where \(\Delta P\) is the decrease in vapour pressure, \(P\) is the original vapour pressure of the pure solvent, and \(x_{\text{solute}}\) is the mole fraction of the solute. By understanding this ratio, we can predict how the addition of solute will affect phenomena like boiling point, making it a crucial concept in chemistry.

• Lowering occurs because fewer solvent particles can escape into the vapour phase.
• It measures solute’s impact, not its specific quantity.
• Useful in calculating molecular weights and understanding colligative properties.

Mole Fraction

The mole fraction is a way to express a concentration of components in a solution. It is a dimensionless quantity and is defined as the number of moles of a component divided by the total number of moles of all components in the solution. This representation is mathematically given by:

\[ x_{\text{component}} = \frac{n_{\text{component}}}{n_{\text{total}}} \]
where \(x_{\text{component}}\) represents the mole fraction, \(n_{\text{component}}\) is the number of moles of the component (solute or solvent), and \(n_{\text{total}}\) represents the total moles in the mixture.

In the context of Raoult's Law and the relative lowering of vapour pressure, the mole fraction specifically refers to the proportion of moles of solute relative to the total moles in the solution. Understanding mole fraction allows chemists to accurately study and predict the behaviour of solutions, especially the changes in physical properties like vapour pressure, boiling point, and freezing point.

• Not dependent on the system's mass or volume.
• Helps in comparing compositions of different solutions.
• Vital in calculations using Raoult’s Law.

Nonvolatile Solute

A nonvolatile solute is one that does not evaporate readily and typically has a negligible vapour pressure. When a nonvolatile solute is dissolved in a solvent, it lowers the overall vapour pressure of the solution. This is because the solute particles occupy space at the surface of the liquid, thus reducing the number of solvent molecules that can escape into the vapour phase.

The presence of a nonvolatile solute is crucial in experiments dealing with colligative properties, which are properties that depend on the concentration of solute particles rather than their identity. A nonvolatile solute affects the solution's boiling point, freezing point, and osmotic pressure by altering the vapour pressure.

• Influences vapour pressure by decreasing it.
• Essential for studying solutions' phase changes.
• Does not contribute to the vapour phase itself.