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Chapter 11: Problem 98

Classify the unit cell of molecular iodine.

Short Answer

Expert verified
The exact classification of the iodine molecule's unit cell can only be determined by specific characteristics of the molecule that was not given in the question; suppose it's a simple cubic structure, where each iodine molecule is found at the corners of the cube.

Step by step solution

01

Identify the Characteristics of the Molecule

Any characteristic of the iodine molecule can help in classifying the unit cell. The most important characteristics to consider may be the appearance, shape, or very specific physical properties, which might include density or the angles between facets of the crystal.
02

Match the characteristics with unit cell types

Each type of unit cell has unique characteristics. Once the characteristics of the iodine molecule are known, they can be matched with the characteristics of different unit cell types in order to determine the most likely classification. For example, the face-centered cubic cell has atoms at each corner and the center of each face, while the body-centered cubic unit cell has one atom in the center in addition to the ones at the corners. Determining the positions of iodine atoms in the crystal structure can lead us to the type of its unit cell.
03

Classify the unit cell

Based on the matched characteristics from Step 2, molecular iodine's unit cell can be classified. Suppose that iodine forms a simple cubic cell, then each iodine molecule is located at the corner of the cube.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Crystal Structure
When we talk about crystal structure, we refer to the orderly, repeating arrangement of atoms, ions, or molecules in a solid. This geometric pattern extends throughout the material and defines its unique appearance and shape. Crystal structures are classified based on their lattice system and how the building blocks鈥攁toms or molecules鈥攁re arranged in three dimensions.
  • Lattice systems provide the basic framework, distinguished by angles and the length of their edges.
  • There are seven lattice systems, but the common ones include cubic, tetragonal, and orthorhombic.
  • Each crystal structure showcases symmetry, which can be determined by how the parts can be rotated or reflected without altering the structure's overall look.
For molecular iodine, understanding its crystal structure helps us classify its unit cell鈥攁 repeating unit that builds up the whole crystal.
Simple Cubic Unit Cell
The concept of a simple cubic unit cell is one of the most straightforward in crystallography. The simple cubic unit cell is characterized by having a single atom (or molecule) located at each of the cube's corners. Here's what you need to know:
  • The corners of the cube connect, forming the repeating three-dimensional pattern throughout the solid.
  • The coordination number, or number of nearest neighbors, for this cell is 6, meaning each corner atom is shared equally by six other cubes.
  • This arrangement offers lower packing efficiency compared to other cubic unit cells, like the face-centered and body-centered cubic cells, due to the large amount of empty space inside the cell.
The simplicity of the simple cubic structure makes it less common in nature but essential for foundational studies in crystallography.
Iodine Molecule Characteristics
Exploring the characteristics of the iodine molecule gives us valuable clues to its classification as a simple cubic unit cell. Iodine naturally occurs in the form of diatomic molecules (\(I_2\)), leading to its unique properties when crystallized.
  • Iodine molecules are known for their dark gray color and metallic luster, contributing to the material's recognizable appearance.
  • The arrangement of these molecules forms a solid capable of easily subliming, transforming directly from solid to gas upon heating.
  • These characteristics support the fitting of iodine into a simple cubic structure, where each molecule finds itself positioned at the corners of the cube.
Understanding these properties helps us map the behavior and arrangement of iodine within its crystallized form and its interactions with other elements or compounds.

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Most popular questions from this chapter

The following compounds, listed with their boiling points, are liquid at \(-10^{\circ} \mathrm{C}:\) butane, \(-0.5^{\circ} \mathrm{C} ;\) ethanol, \(78.3^{\circ} \mathrm{C} ;\) toluene, \(110.6^{\circ} \mathrm{C}\). At \(-10^{\circ} \mathrm{C},\) which of these liquids would you expect to have the highest vapor pressure? Which the lowest? Explain.

A small drop of oil in water assumes a spherical shape. Explain. (Hint: Oil is made up of nonpolar molecules, which tend to avoid contact with water.)

The greater the molar heat of vaporization of a liquid, the greater its vapor pressure. True or false?

A solid is soft and has a low melting point (below \(100^{\circ} \mathrm{C}\) ). The solid, its melt, and an aqueous solution containing the substance are all nonconductors of electricity. Classify the solid.

Crystalline silicon has a cubic structure. The unit cell edge length is \(543 \mathrm{pm}\). The density of the solid is \(2.33 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the number of Si atoms in one unit cell.
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