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

Gallium's phase diagram might have a negative slope solid-liquid boundary, indicating pressure favors liquid over solid.

Step-by-step solution

Analyze Density Changes

When gallium transitions from solid to liquid, the density increases from \(5.91 \mathrm{~g} / \mathrm{cm}^{3}\) to \(6.1 \mathrm{~g} / \mathrm{cm}^{3}\). This is unusual because most substances expand and decrease in density when they melt.

Understanding Density Implications

Given that liquid gallium is denser than its solid form, it implies that solid gallium could float on liquid gallium. This density behavior is contrary to most substances, where the solid typically sinks in its liquid.

Predict the Phase Diagram Feature

In most phase diagrams, the solid-liquid boundary line has a positive slope, indicating that increasing pressure favors the solid state. However, for gallium, the increase in density upon melting suggests that increasing pressure might favor the liquid state, resulting in a negative slope of the solid-liquid boundary line.

Key concepts

Gallium

Gallium is a fascinating metal with unusual properties that make it stand out from most other elements. One of the most intriguing characteristics of gallium is its low melting point at just 29.8°C; this means you can melt it simply by holding it in your hand. Despite being solid at room temperature, this metal quickly transitions to a liquid state slightly above its melting point. Such unique behavior is mirrored by its appearance in phase diagrams.
Gallium is also known for its silvery-blue appearance and as a component in various high-tech applications like semiconductors and LEDs. It forms a critical part in producing gallium arsenide, a compound used in electronics that require high performance. Furthermore, gallium has a remarkable ability to remain non-toxic and harmless while being highly useful in modern technological advancements.

Density Changes

The density of a substance can significantly affect its properties and behavior during phase transitions. For gallium, the density increases when it melts—from 5.91 g/cm³ as a solid to 6.1 g/cm³ as a liquid.
This increase is quite unusual because typically when a solid melts to become a liquid, it expands and its density decreases. Most materials, such as ice becoming water, exhibit reduced density upon melting.
Gallium's increase in density during melting signifies that its atoms pack more closely together as a liquid, which can be attributed to changes in the structure of the molecules that allow them to occupy less volume despite being in a different state.

Solid-Liquid Transition

The transition of gallium from solid to liquid is distinctive because of its density anomaly. Normally, during a phase change from solid to liquid, a substance becomes less dense. With gallium, however, this phase change results in a denser liquid than the solid.
This peculiarity means that solid gallium will float on its liquid form. This behavior is contrary to materials like water, where ice, the solid form, floats on liquid water due to lower density.
Understanding such transitions is crucial in explaining gallium’s peculiar phase diagram, which involves a unique relationship between its solid and liquid states under changing conditions like temperature and pressure.

Pressure Effects

In typical phase diagrams, substances have a solid-liquid boundary line that slopes upwards, meaning that higher pressures promote the solid phase. However, for gallium, the phase diagram is different due to its peculiar density behavior.
Because liquid gallium is denser than solid gallium, increasing the pressure could actually encourage the transition from solid to liquid. This results in a solid-liquid boundary line with a negative slope.
This means that under higher pressure, gallium might preferentially become liquid, in contrast to most substances. Such effects where pressure impacts the state favorably towards liquid over solid can drastically influence the understanding and applications of gallium, particularly in technological industries or scenarios involving extreme environments.