Question

According to Raoult's law, relative lowering of vapour pressure for a solution is equal to (a) mole fraction of the solute (b) mole fraction of a solvent (c) moles of a solute (d) moles of a solvent

Short answer

(a) mole fraction of the solute

Step-by-step solution

Understanding Raoult's Law

Raoult's Law states that the relative lowering of vapor pressure of a solvent is equal to the mole fraction of the solute in a solution. This means that the change in vapor pressure from the pure solvent to the solution is directly proportional to the concentration of the solute in the form of mole fraction.

Identifying the Right Option

Raoult's Law is expressed mathematically as \(P^o - P_s = P^o \cdot x_B\), where \(P^o\) is the vapor pressure of the pure solvent, \(P_s\) is the vapor pressure of the solution, and \(x_B\) is the mole fraction of the solute. Thus, the relative lowering of the vapor pressure \((P^o - P_s)/P^o\) simplifies to \(x_B\), the mole fraction of the solute.

Determining the Correct Answer

From the given options, the one that matches the condition stipulated by Raoult's Law, where relative lowering of vapor pressure is equal to, is 'mole fraction of the solute'. Therefore, the correct answer to the problem based on this understanding is (a) mole fraction of the solute.

Key concepts

Vapor Pressure and Its Role in Solutions

Vapor pressure is a fundamental concept in solution chemistry that refers to the pressure exerted by the vapor of a liquid in equilibrium with its liquid or solid phase at a given temperature. When a liquid is in a closed container, molecules at the surface can escape into the vapor phase. The pressure exerted by these molecules forms what we call vapor pressure.

In the context of solutions, vapor pressure can be affected by the presence of a solute. When a non-volatile solute is dissolved in a solvent, it occupies some of the surface space, effectively reducing the number of solvent molecules that can escape into the vapor phase. This leads to a decrease in vapor pressure, a phenomenon explained by Raoult’s Law. Understanding this helps explain why adding solute to a solution changes its physical properties, such as boiling and freezing points.

Understanding Mole Fraction of Solute

The mole fraction is a way to express the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles in the mixture. For a solute in a solution, the mole fraction is calculated as follows:\[ x_B = \frac{n_B}{n_A + n_B}\]where:

• \(n_B\) is the number of moles of the solute,
• \(n_A\) is the number of moles of the solvent.

The concept of mole fraction is crucial because it is directly used in Raoult's Law to determine the lowering of vapor pressure. By knowing the mole fraction of the solute, we can predict how much the solvent's vapor pressure will decrease when the solute is added. This makes the mole fraction a vital concept in practical applications, such as in the calculation of colligative properties.

Solution Chemistry and Raoult's Law

Solution chemistry is an area of chemistry that studies the processes involved when substances are mixed to form solutions. In this context, Raoult’s Law plays a critical role. This law provides a quantitative understanding of how the vapor pressure of a solution relates to the properties of the solute and solvent.

Raoult's Law states that the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.

• For solutions with non-volatile solutes, the law is simplified, describing how the relative lowering of vapor pressure is proportional to the mole fraction of the solute.
• This allows chemists to calculate the effects of adding solutes on physical properties like boiling and freezing points.

By exploring solution chemistry through Raoult's Law, students gain insight into the practical impacts of solute-solvent interactions, broadening their understanding of how compounds behave in mixtures.