Question

A solid cube of ammonia floats in liquid ammonia. Which is more dense: solid or liquid ammonia?

Short answer

Solid ammonia is less dense than liquid ammonia.

Step-by-step solution

Understanding the Problem

We are asked to determine the relative densities of solid and liquid ammonia when a solid cube of ammonia is floating in the liquid. Density is a measure of mass per unit volume.

Applying the Concept of Density

When an object floats in a fluid, the density of the object is less than or equal to the density of the fluid. In this case, the solid cube of ammonia is floating in liquid ammonia.

Analyzing the Floating Condition

Since the solid cube of ammonia floats, it indicates that the density of the solid is less than or equal to the density of the liquid. This is because an object that is less dense than the fluid will float.

Conclusion

Since the solid ammonia floats in liquid ammonia, we can conclude that solid ammonia is less dense than liquid ammonia.

Key concepts

Solid vs Liquid Ammonia

Ammonia exists in different states: as a solid and as a liquid, each exhibiting unique physical properties. The solid state of ammonia occurs at temperatures below its melting point of about -78°C (-108°F), while the liquid state is found above this temperature and below its boiling point of around -33°C (-28°F).

The change from solid to liquid ammonia involves the packing of ammonia molecules. In solid ammonia, molecules are closely packed in a structured, fixed arrangement. However, when melted into a liquid, these molecules are still relatively close but have more freedom to move around.

This structural difference plays a significant role in how each state behaves, especially concerning density. The transition from solid to liquid generally increases the ability of the molecules to rearrange more freely, resulting in slight changes in density.

Density Comparison

One essential property of materials is their density, which is defined as mass per unit volume, expressed mathematically as \( \rho = \frac{m}{V} \). The density provides insight into how closely packed the molecules of a substance are. Given this understanding, it's clear why attention is paid to the density of substances like ammonia.

When considering solid versus liquid ammonia:

• Solid ammonia possesses a crystalline structure, leading to a specific, often lower, density compared to its liquid state.
• Liquid ammonia, being denser, allows solid ammonia to float within it.

The knowledge that solid ammonia floats in liquid ammonia directly implies that the density of solid ammonia is less than that of liquid ammonia. This is a fascinating exception, as many materials become denser when solidified.

Floating and Density Principle

The principles of floating and density are foundational concepts in physics, particularly in the study of fluid mechanics. When examining why things float, it is crucial to understand the relationship between object density and the medium in which it is submerged. According to the buoyancy principle, an object will float if its density is less than or equal to the density of the fluid it is placed in.

Since the solid cube of ammonia floats on liquid ammonia, this indicates that the solid ammonia has a lower density than the liquid form.

• Floating occurs because the buoyant force, acting upwards, counteracts the gravitational force pulling the object downward.
• The fact that the solid is floating confirms that it displaces a weight of liquid ammonia equal to its own weight.

This classical principle not only explains why solid ammonia floats but also provides a basis for understanding similar behaviors in other materials and conditions.