Textbook Question
Identify each of the following kinds of packing: (b)
Ch.12 - Solids and Solid-State Materials
Chapter 12, Problem 20
Titanium oxide crystallizes in the following cubic unit cell: 
(b) What is the formula of titanium oxide?
Verified step by step guidance1
Identify the positions of the titanium (Ti) and oxygen (O) atoms in the unit cell. In the given diagram, the blue spheres represent Zn atoms and the red spheres represent F atoms. For this problem, assume Zn represents Ti and F represents O.
Determine the number of Ti atoms in the unit cell. Ti atoms are located at the corners and the center of each face of the cubic unit cell. Each corner atom is shared by 8 unit cells, and each face-centered atom is shared by 2 unit cells.
Calculate the total contribution of Ti atoms in the unit cell. There are 8 corner atoms, each contributing 1/8 of an atom, and 6 face-centered atoms, each contributing 1/2 of an atom.
Determine the number of O atoms in the unit cell. O atoms are located entirely within the unit cell, so each O atom counts fully.
Calculate the total number of O atoms in the unit cell. There are 4 O atoms inside the unit cell. Combine the contributions of Ti and O atoms to determine the empirical formula of titanium oxide.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Cell Structure
A unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. In the case of titanium oxide, understanding the arrangement of atoms within the cubic unit cell is crucial for determining the stoichiometry and formula of the compound. The face-centered cubic structure indicates how atoms are positioned at the corners and the centers of the faces of the cube.
Recommended video:
Guided course
01:27
Simple Cubic Unit Cell
Stoichiometry
Stoichiometry involves the calculation of reactants and products in chemical reactions, based on the conservation of mass. For titanium oxide, knowing the ratio of titanium to oxygen atoms in the unit cell allows us to derive its chemical formula. This concept is essential for understanding how different elements combine in fixed ratios to form compounds.
Recommended video:
Guided course
01:16Stoichiometry Concept
Ionic Compounds
Ionic compounds are formed through the electrostatic attraction between positively and negatively charged ions. In the case of titanium oxide, titanium typically forms a cation (Ti^4+) while oxygen forms an anion (O^2-). The balance of these charges is critical in determining the empirical formula, which reflects the simplest whole-number ratio of the constituent ions.
Recommended video:
Guided course
02:11Ionic Compounds Naming
Related Practice
Textbook Question
Identify each of the following kinds of packing: (d)
1
views
Textbook Question
The following compound undergoes a phase transition from the solid to the smectic liquid crystal phase at 121 °C. Upon further heating, the compound undergoes another transition to liquid phase at 131 °C. (b) Which image represents the arrangement of molecules at 135 °C?
Textbook Question
The following diagrams show the electron populations of the bands of MO energy levels for four different materials: (a) Classify each material as an insulator, a semiconductor, or a conducting metal.
Textbook Question
The following diagrams show the electron populations of the bands of MO energy levels for four different materials:
. (c) Tell whether the conductivity of each material increases or decreases when the temperature increases.
Textbook Question
The following diagram represents the electron population ofthe bands of MO energy levels for elemental silicon:(a) Identify the valence band, conduction band, and band gap.