Question

At \(25^{\circ} \mathrm{C}\) gallium is a solid with a density of 5.91 \(\mathrm{g} / \mathrm{cm}^{3} .\) Its melting point, \(29.8^{\circ} \mathrm{C},\) is low enough that you can melt it by holding it in your hand. The density of liquid gallium just above the melting point is 6.1 \(\mathrm{g} / \mathrm{cm}^{3} .\) Based on this information, what unusual feature would you expect to find in the phase diagram of gallium?

Short answer

The unusual feature in the phase diagram of gallium is a negative slope in the solid-liquid equilibrium line. This is because the density of solid gallium is lower than the density of the liquid phase, which is not commonly observed in materials. Hence, as the temperature increases at constant pressure, solid gallium transforms to higher-density liquid gallium.

Step-by-step solution

Recall Common Density Relationships in Phase Diagrams

In most materials, the solid phase has a higher density than the liquid phase. This is because, in the solid state, particles are more closely packed together. However, in this case, the solid phase of gallium has a lower density compared to the liquid phase just above its melting point. This is an unusual behavior in phase diagrams.

Observe How Density Relationships Affect Phase Diagrams

In the phase diagram of most materials, the solid-liquid equilibrium line has a positive slope because the solid phase is denser than the liquid phase. However, in the case of gallium, since the solid has a lower density than the liquid phase, the solid-liquid equilibrium line will likely have a negative slope. This negative slope indicates that as temperature increases at constant pressure, solid gallium transforms to liquid gallium, which has a higher density.

Identify the Unusual Feature in Gallium's Phase Diagram

Based on the information given, the unusual feature we would expect to find in the phase diagram of gallium is a negative slope in the solid-liquid equilibrium line. This is because the solid phase of gallium has a lower density than the liquid phase, which is not commonly observed in materials. So, the solid-liquid equilibrium line will show solid gallium transforming to higher-density liquid gallium with increasing temperature at a constant pressure.

Key concepts

Density

Density is an essential concept in understanding phase diagrams. It refers to the mass per unit volume of a substance, and it often determines how different phases of a material behave when subjected to varying temperature and pressure. Generally, in most substances, the solid state is denser than the liquid state. That's because in solids, particles are tightly packed compared to the more loosely packed liquid phase.

However, gallium presents a curious case where its density behaves differently. At room temperature, gallium is a solid with a density of 5.91 g/cm³, but when it melts, the density increases to 6.1 g/cm³.

This implies that liquid gallium is actually more compact than solid gallium—a rarity among elements. Understanding this density anomaly is critical to grasping gallium's unique phase behavior and its impact on its phase diagram.

Solid-Liquid Equilibrium

The solid-liquid equilibrium line on a phase diagram demonstrates the conditions under which a material transitions between solid and liquid states. In most typical materials, the solid-liquid equilibrium line shows a positive slope. This positive slope indicates that, as temperature increases, the pressure required to keep the substance in a solid state must also increase because the solid is denser than the liquid.

However, for gallium, this equilibrium line behaves unusually. Due to gallium's solid having a lower density compared to its liquid, the equilibrium line displays a negative slope. This means that as the temperature goes up, increasing the energy that weakens intermolecular forces, gallium turns from solid to liquid without needing an increase in pressure.

Such a negative slope is a distinctive feature that signifies gallium's unique phase behavior. It suggests that under constant pressure, melting gallium will occupy less volume as it transforms into a denser liquid state.

Unusual Phase Behavior

Unusual phase behavior, as demonstrated by gallium, is fascinating for anyone studying phase diagrams. Most materials follow a regular pattern where solids are denser than liquids. However, gallium, with its density anomaly, offers an exception that leads to intriguing results in its phase behavior.

When gallium transitions from solid to liquid, the usual expectation that liquids are less dense is defied. Instead, the liquid phase is denser. This impacts the geometry of the phase diagram, especially the shape and slope of the solid-liquid equilibrium line, shifting it to a negative incline.

Recognizing such phase behavior challenges and broadens our understanding of material science. Gallium is a prime example of how not all elements conform to standard rules, prompting further study on how atomic structure and bonding might lead to such anomalies.