Question

The vapor pressure of liquid \(X\) is lower than that of liquid \(Y\) at \(20^{\circ} \mathrm{C}\), but higher at \(60^{\circ} \mathrm{C}\). What can you deduce about the relative magnitude of the molar heats of vaporization of \(X\) and \(Y ?\)

Short answer

The molar heat of vaporization of \(X\) is smaller than that of \(Y\).

Step-by-step solution

Understanding the Vapor Pressure and Molar Heat of Vaporization

The vapor pressure of a liquid increases with increasing temperature. The rate at which it increases depends on the molar heat of vaporization of the liquid: the larger the molar heat, the slower vapor pressure rises with an increase in temperature.

Relating Vapor Pressure and Molar Heat of Vaporization

If at \(20^{\circ} \mathrm{C}\) \(X\) has a lower vapor pressure than \(Y\), and at \(60^{\circ} \mathrm{C}\) \(X\) has a higher vapor pressure, this indicates that the vapor pressure of \(X\) increases more rapidly with temperature than does the vapor pressure of \(Y\).

Deduction

From the above information, it can be deduced that the molar heat of vaporization of \(X\) is lower than \(Y\), because a lower molar heat of vaporization results in a faster increase in vapor pressure with temperature.

Key concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. It is an important concept in understanding how liquids behave as they transition into gases. At any temperature, molecules in a liquid have various kinetic energies. Some possess enough energy to escape into the vapor phase, creating vapor pressure.

• High vapor pressure indicates a liquid that evaporates easily.
• Low vapor pressure suggests strong intermolecular forces holding the liquid together.

When the temperature rises, more molecules have sufficient energy to escape, so the vapor pressure increases. How rapidly this happens is influenced by the molar heat of vaporization, which is the energy needed to convert one mole of a liquid into a gas.

Thermodynamics

Thermodynamics explores the relationship between heat, work, and energy in physical systems. When we discuss molar heat of vaporization in thermodynamics, we're focusing on the energy required for a phase change from liquid to vapor.

• The heat of vaporization is a crucial component in determining how substances transition between phases.
• It provides insight into the strength of intermolecular forces.

In our example, understanding why one substance might have a higher vapor pressure at a particular temperature involves applying the concepts of energy balance and molecular interactions. Thermodynamics helps explain why a substance with a lower heat of vaporization will respond differently to temperature changes compared to one with a higher heat of vaporization.

Temperature Dependence

Temperature dependence refers to how certain properties of a substance change as the temperature varies. For liquids, a key temperature-dependent property is vapor pressure.

• As temperature increases, vapor pressure usually rises because more molecules gain the energy needed to escape the liquid.
• The rate of vapor pressure increase depends on the molar heat of vaporization.

In the given problem, liquid X initially has a lower vapor pressure compared to Y at 20°C, but surpasses it at 60°C. This is because X's vapor pressure increases more rapidly with temperature. Lower molar heat of vaporization means that X requires less energy for molecules to enter the vapor phase, leading to a faster increase in vapor pressure as temperature rises.