Question

The elements xenon and gold both have solid-state structures with face- centered cubic unit cells, yet Xe melts at \(-112^{\circ} \mathrm{C}\) and gold melts at \(1064^{\circ} \mathrm{C}\). Account for these greatly different melting points.

Short answer

The melting points of xenon and gold differ greatly due to the differences in the types of forces holding their atoms in the solid state, despite both having face-centered cubic unit cell structures. Xenon has weak dispersion forces, resulting in a low melting point of \(-112^{\circ} \mathrm{C}\). In contrast, gold has strong metallic bonds, leading to a high melting point of \(1064^{\circ} \mathrm{C}\).

Step-by-step solution

Identify factors that affect the melting point

Melting points depend on the strength of the forces holding the atoms or molecules together in the solid-state structure. These forces can be ionic bonds, covalent bonds, metallic bonds, or intermolecular forces such as dispersion forces, dipole-dipole attractions, and hydrogen bonds. A higher force of attraction results in a higher melting point, while a lower force of attraction results in a lower melting point.

Determine the types of bonds or forces in xenon and gold

Xenon is a noble gas and exists in a pure state as individual Xe atoms. The only force acting between Xe atoms is dispersion forces, also known as van der Waals forces or London forces. These forces originate from the temporary imbalance of electron distribution in an atom or molecule, causing an instantaneous dipole that can induce dipoles in nearby atoms or molecules. Gold, on the other hand, is a metallic element. In the solid state, gold atoms form a metallic bond, where the atoms are arranged in a lattice structure and the electrons are delocalized, forming a "sea" of electrons around the positively charged gold ions.

Compare the strengths of the forces in xenon and gold

Dispersion forces between Xe atoms are relatively weak. This is because the temporary dipoles in Xe atoms are generally feeble, and the distance between Xe atoms (since they are in a gaseous state) is quite significant, making the force of attraction between them low. As a result, only a small amount of energy is needed to overcome these forces and melt xenon into a liquid. In contrast, metallic bonds in gold are much stronger. The delocalized electrons around gold ions create a strong attraction between the positive gold ions and the electron "sea". Due to this strong attraction, a lot of energy is required to overcome the metallic bonds and cause gold to melt.

Conclude the reason for different melting points

In summary, although xenon and gold both have face-centered cubic unit cell structures, their melting points differ greatly because the types of forces holding their atoms in the solid state are vastly different. Xenon has weak dispersion forces, which result in a low melting point of \(-112^{\circ} \mathrm{C}\), while gold has strong metallic bonds, causing it to have a high melting point of \(1064^{\circ} \mathrm{C}\).

Key concepts

Dispersion Forces

Dispersion forces, also known as London dispersion forces or van der Waals forces, are the weakest type of intermolecular attraction. These forces occur due to temporary fluctuations in electron distribution around an atom or molecule, creating an instantaneous dipole. This can induce temporary dipoles in neighboring atoms or molecules.

Despite their weakness, dispersion forces play a crucial role in the properties of gases and nonpolar molecules.

• They can become stronger with increased molecular size or mass, as larger atoms have more electrons that can create dipoles.
• Dispersion forces are present between all atoms and molecules, even noble gases like xenon.
• In solids like xenon at low temperatures, these weak attractions are enough to hold the atoms together.

For xenon, these forces are significant enough to cause it to form a solid at extremely low temperatures (-112°C). However, much less energy is needed to melt xenon compared to substances held together by stronger interactions.

Metallic Bonds

Metallic bonds are the force that holds metals together in the solid state. Unlike other forms of bonding, metallic bonds involve the delocalization of electrons.

In metals like gold, the electrons are not confined to individual atoms. Instead, they form a "sea" of electrons that flow around positively charged metal ions.

• This "sea" allows metals to conduct electricity and heat efficiently.
• It also gives metals their characteristic malleability and ductility.
• Metallic bonds are generally much stronger than dispersion forces.

Due to this strong attraction between the delocalized electrons and metal ions, it requires a significant amount of energy to melt a metal. Gold's melting point at 1064°C reflects the robust nature of metallic bonds, highlighting why it stays solid at high temperatures while xenon becomes a liquid with less heat.

Face-centered Cubic Structure

The face-centered cubic (FCC) structure is a common arrangement for atoms within a crystalline solid. In an FCC structure, atoms are packed closely in a cube-shaped lattice with additional atoms at the centers of each face.

This type of arrangement optimizes space, allowing for maximum attraction between atoms, which helps stabilize the structure.

• An FCC lattice is characterized by its high density and low coordination number.
• Common metals like gold exhibit this type of structure, benefiting from the strong interactions typical of metallic bonding.
• Although xenon atoms also adopt an FCC arrangement at low temperatures, their interactions are only dispersion forces.

Both xenon and gold have face-centered cubic structures, but their very different bonding types lead to vastly different melting points. For gold, the FCC arrangement aids the strength of already strong metallic bonds, whereas for xenon, it supports weaker dispersion forces.

Noble Gases

Noble gases, like xenon, are unique elements with full electron shells. This completeness renders them largely unreactive under standard conditions, hence their descriptor as "noble."

These gases exist as monatomic particles, meaning their intermolecular forces are limited to dispersion forces.

• Noble gases are known for their lack of chemical reactivity.
• They each have distinct, low boiling and melting points.
• Despite weak intermolecular forces, xenon can still form a solid under extremely low temperatures.

Xenon's melting point of -112°C is low compared to most elements, but typical for noble gases. Its melting behavior is dictated by the minimal force needed to separate its atoms, highlighting the contrast between the noble gas and more heavily bonded elements like gold.