Question

When non-zero volatile solute is dissolved in a solvent, the relative lowering of vapour pressure is equal to (a) molar fraction of solute (b) molar fraction of solvent (c) concentration of the solute in grams per liter (d) concentration of the solute in gram per \(100 \mathrm{~mL}\).

Short answer

(a) molar fraction of solute

Step-by-step solution

Identify the known principle

The exercise is about the relative lowering of vapour pressure when a non-zero volatile solute is dissolved. According to Raoult’s Law, the relative lowering of vapour pressure is equal to the mole fraction of the solute.

Recall the relevant formula

The formula for the relative lowering of vapour pressure ( PLow) is given by: \[\frac{\Delta P}{P_0} = x_B\]where \(\Delta P\) is the lowering of vapour pressure, \(P_0\) is the vapour pressure of pure solvent, and \(x_B\) is the mole fraction of the solute.

Evaluate options based on formula

Based on the formula, the correct relation for the relative lowering of vapour pressure corresponds to the mole fraction of the solute (\(x_B\)). This matches with option (a), molar fraction of solute.

Verify the correct answer

The solution confirms that the relative lowering of vapour pressure, according to Raoult's Law, is indeed equivalent to the mole fraction of the solite. Thus, choice (a) correctly explains this phenomenon.

Key concepts

Vapour Pressure Lowering

Vapour pressure lowering is an essential concept in chemistry that describes how the addition of a solute to a solvent decreases the overall vapour pressure of the solution. When a non-zero volatile solute is introduced, it occupies space at the surface of the liquid, reducing the number of solvent molecules that can escape into the gas phase. This results in a decrease in the overall vapour pressure.
Raoult's Law helps us understand this occurrence by relating the reduction in vapour pressure to the properties of the solute. It's important to remember that this phenomenon is observable in solutions where both the solute and solvent are volatile, meaning capable of evaporation.

Mole Fraction

The mole fraction is a way to express concentration and plays a crucial role in understanding vapour pressure lowering. It is the ratio of the number of moles of one component to the total number of moles in the solution. Mathematically, for a solute, it is expressed as:
\[ x_B = \frac{n_B}{n_A + n_B} \]
where \(n_B\) is the number of moles of the solute, and \(n_A\) is the number of moles of the solvent.
By using the mole fraction, we can establish a clear relationship between the concentration of the solute in the solution and the resulting effect on vapour pressure. This relationship is crucial for applying Raoult’s Law to determine the change in vapour pressure brought by adding a solute.

Volatile Solute

A volatile solute is a component in a solution that can easily evaporate, adding its own vapour to the pressure over the solution. Unlike non-volatile solutes, which do not evaporate, volatile solutes contribute significantly to the overall system's vapour pressure.
Understanding the volatility of a solute is essential when applying Raoult's Law, as it assumes both the solute and solvent play a role in determining the overall vapour pressure.
When a volatile solute is introduced, it can either increase or decrease the vapour pressure depending on its own intrinsic vapour pressure and how it interacts with the solvent molecules. This interaction is a key consideration in various practical settings, including distillation and chemical synthesis.

Chemistry Problem Solving

When tackling chemistry problems related to vapour pressure and Raoult’s Law, a structured approach can make complex solutions more accessible. Here are some steps to systematically solve these problems:

• **Identify the Known Concepts:** Start by understanding the core principles involved, such as vapour pressure and mole fraction. This provides a solid foundation.
• **Apply Mathematical Equations:** Use equations like \[\frac{\Delta P}{P_0} = x_B\] to relate mole fractions to changes in vapour pressure.
• **Evaluate Options or Variables:** Analyze the information given and how it fits into the known relationships. By assessing each option, you can determine which accurately reflects the physical conditions described.
• **Verification:** After solving, re-check each step and ensure the concluded answer fits logically with the theory and formulae.

This process not only builds understanding but also boosts confidence in handling chemistry problems involving vapour pressure and solute interactions.