Question

For most substances, the solid is more dense than the liquid. Use Le Châtelier's principle to explain why the melting point of such substances should increase with increasing pressure. Sketch the phase diagram for such a substance, being sure to have the solid-liquid equilibrium line slope in the correct direction.

Short answer

The melting point of a substance whose solid phase is denser than its liquid phase increases with pressure due to Le Châtelier's principle. A phase diagram for such a substance will have the solid-liquid equilibrium line slope upwards to the right, showing higher melting points at higher pressures.

Step-by-step solution

Understanding Le Châtelier's Principle

Le Châtelier's Principle states that if a system at equilibrium is subjected to a change in pressure, temperature, or concentration, the equilibrium will shift to counteract the imposed change and a new equilibrium will be established. For substances where the solid is denser than the liquid, increasing pressure should lead to a favoring of the solid phase because more solid can fit into a given volume at a higher pressure, which means the equilibrium between solid and liquid will shift towards the solid phase.

Predicting the Effect on Melting Point

An increase in the external pressure will favor the phase that occupies less volume due to the principle of Le Châtelier. Since the solid phase is more dense, meaning it has a smaller volume for a given mass, increasing pressure will shift the equilibrium towards the formation of more solid. Therefore, the melting point of the substance will increase under higher pressure because more energy will be required to convert the solid into a liquid.

Sketching the Phase Diagram

A phase diagram shows the preferred states of matter of a substance at different temperatures and pressures. On such a diagram, the line that separates the solid and liquid phases is called the solid-liquid equilibrium line. For a substance where the solid is more dense than the liquid, this line will slope towards the liquid side as pressure increases. This means the line will slope upwards to the right, indicating that as pressure increases, the temperature at which the substance melts (melting point) also increases.

Key concepts

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It maps out which phase—solid, liquid, or gas—a substance will be in, at various temperatures and pressures. Phase diagrams typically feature regions that denote the solid, liquid, and gaseous states, separated by lines known as phase boundaries or equilibrium lines that indicate the conditions under which two phases can coexist. For substances where the solid is denser than the liquid, the slope of the solid-liquid equilibrium line in the phase diagram is negative, indicating an inverse relationship between pressure and temperature for the transition between these two phases. That is, as the pressure increases, the melting point of the substance also increases, and vice versa.

The significance of the phase diagram in understanding the properties of a substance is immense. By analyzing the diagram, one can predict the changes in phase that would occur with fluctuations in pressure and temperature, aiding in the study of materials and processes like crystallization, distillation, and more.

Melting Point

The melting point of a substance is the specific temperature at which it transitions from a solid to a liquid phase at atmospheric pressure. This is a characteristic property of a pure substance and is used to identify and classify materials. Understanding the melting point is crucial, as it influences various practical applications such as material selection in engineering and quality control in the manufacturing of various goods.

In the context of Le Châtelier's Principle, the melting point of a substance is not only dictated by the inherent properties of the substance but is also affected by the external pressure applied. If the solid form is denser than the liquid—implying it occupies less volume per unit mass—an increase in pressure would logically make the formation of the solid phase more favorable, thereby raising the melting point. Even a slight push in pressure requires the system to increase the energy input (in the form of temperature) for the solid to transition to its liquid form.

Solid-Liquid Equilibrium

Solid-liquid equilibrium refers to the state where solid and liquid phases of a substance coexist in balance, with no net change over time. At this point, the rates of melting and freezing (or crystallization) are equal, creating a dynamic but stable system. The temperature and pressure at which this equilibrium happens are depicted on the phase diagram as the solid-liquid equilibrium line. It’s key to recognize that this line doesn’t just represent a static situation but a responsive balance that can change with variations in environmental conditions.

Incorporating Le Châtelier's Principle, when external pressure is increased on a substance with a denser solid phase, the system adjusts by favoring the solid to reduce the effect of the applied pressure. In practical terms, for industrial processes like the forming of precious stones or metals, controlling these pressure conditions can significantly influence the quality and characteristics of the final product by manipulating the equilibrium.

Equilibrium Shift

An equilibrium shift occurs when a system that is in a state of equilibrium is disturbed by changes in external conditions such as pressure, temperature, or concentration. According to Le Châtelier's Principle, the system will respond to this disturbance by shifting its equilibrium to counteract the change and achieve a new state of balance. This concept is foundational in chemistry, as it predicts how a system will behave when subjected to stress.

For instance, in a solid-liquid system where the solid is denser, an increase in pressure results in a shift towards the solid to minimize the disturbance, effectively increasing the melting point. This principle is not just theoretical but can be applied in various real-world scenarios, such as adjusting the conditions to optimize chemical reactions in industrial processes or understanding the behavior of geological materials under the immense pressures found deep within the Earth.