Skip to main content
Ch.12 - Solids and Solid-State Materials
McMurry - Chemistry 8th Edition
McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook
All textbooksMcMurry 8th EditionCh.12 - Solids and Solid-State MaterialsProblem 74
Chapter 12, Problem 74

Tungsten is hard and has a very high melting point (3422 °C), and gold is soft and has a relatively low melting point (1064 °C). Are these facts in better agreement with the electron-sea model or the MO model (band theory)? Explain.Table showing metals, their groups, and Mohs hardness values for chemistry study.

Verified step by step guidance
1
Step 1: Understand the electron-sea model and the MO model (band theory). The electron-sea model suggests that metal atoms release some of their electrons to form a 'sea' of electrons that are free to move throughout the metal lattice, which explains properties like electrical conductivity and malleability. The MO model (band theory) explains the bonding in metals by considering the overlap of atomic orbitals to form molecular orbitals, which are spread out over the entire metal lattice, creating energy bands.
Step 2: Compare the properties of tungsten and gold. Tungsten is hard and has a very high melting point (3422 °C), while gold is soft and has a relatively low melting point (1064 °C).
Step 3: Analyze the data in the provided table. The table shows the Mohs hardness values for various metals, indicating their relative hardness. Tungsten is not listed, but it is known to be very hard, similar to chromium (Cr) with a Mohs hardness of 8.5. Gold, on the other hand, is softer than copper (Cu) with a Mohs hardness of 3.
Step 4: Relate the properties of tungsten and gold to the electron-sea model and the MO model. The electron-sea model does not adequately explain the differences in hardness and melting points between tungsten and gold. The MO model (band theory) can better explain these differences by considering the different extents of orbital overlap and the resulting energy band structures in these metals.
Step 5: Conclude that the facts about tungsten and gold are in better agreement with the MO model (band theory) because it provides a more detailed explanation of the differences in their physical properties, such as hardness and melting points, based on their electronic structures.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
7m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electron-Sea Model

The electron-sea model describes metals as a lattice of positive ions surrounded by a 'sea' of delocalized electrons. This model explains many properties of metals, such as electrical conductivity and malleability, as the free-moving electrons can easily respond to applied forces. The strength of metallic bonds in this model is influenced by the number of delocalized electrons, which contributes to hardness and melting points.
Recommended video:
Guided course
02:43
Bohr Model of the Atom

Molecular Orbital (MO) Theory

Molecular Orbital (MO) theory, or band theory in the context of metals, describes how atomic orbitals combine to form molecular orbitals that can be occupied by electrons. In metals, these orbitals form bands that allow for the conduction of electricity. The energy gap between the valence band and the conduction band determines the electrical and thermal properties of the metal, influencing characteristics like hardness and melting point.
Recommended video:
Guided course
03:06
Molecular Orbital Theory

Melting Point and Hardness Correlation

The melting point and hardness of a metal are often correlated with its bonding characteristics. Metals with strong metallic bonds, such as tungsten, typically exhibit high melting points and hardness due to the strong attraction between the delocalized electrons and the metal ions. In contrast, metals with weaker bonding, like gold, tend to be softer and have lower melting points, reflecting the differences in their electronic structures and bonding interactions.
Recommended video:
Guided course
04:29
Boiling Point and Melting Point
Related Practice
Textbook Question
The melting points for the second-series transition elements increase from 1522 °C for yttrium to 2623 °C for molybdenum and then decrease to 321 °C for cadmium. Account for the trend using band theory.
Textbook Question
Tell what is meant by each of the following terms. (c) Band gap
Textbook Question
Explain why the enthalpy of vaporization of vanadium (460 kJ/mol) is much larger than that of zinc (114 kJ/mol).
Textbook Question
Draw the bands of MO energy levels and the electron population for: (a) A semiconductor (b) An electrical insulator Explain why a semiconductor has the higher electrical conductivity.

Textbook Question
State whether each of the following compounds is likely to have a liquid crystalline phase. Explain your reasoning. (a)

Textbook Question
Draw an MO energy-level diagram for beryllium metal, and show the population of the MOs for the following two cases. (a) The 2s and 2p bands are well separated in energy. (b) The 2s and 2p bands overlap in energy. Which diagram agrees with the fact that beryllium has a high electrical conductivity? Explain.