The goal of this activity is to have students calculate the empirical formula of a compound given the contents of a unit cell.
A repeating building block, or unit cell, is used to represent extended structures since shifting a unit cell along its edges by the length of the edge will exactly replicate the extended structure.
In determining stoichiometry for an extended structure only the fraction of an atom within the unit cell counts. In three-dimensions atoms can be shared between unit cells on corners, on edges and on faces of the unit cell. Atoms on corners are shared by eight unit cells, atoms on edges are shared by four cells and atoms on faces are shared by two cells. Therefore only one-eighth of a corner atom, one-quarter of an edge atom and one-half of an atom on a face is in any one unit cell. The total number of atoms in a unit cell is given by:
For five solid state structures determine the empirical formula. Show your work by indicating how many spheres of each type have their centers located inside the unit cell, on faces, on edges, or on corners. (A given sphere only has one location: inside, face, edge, and corner locations are mutually exclusive.)
Students can determine the empirical formula from an extended solid state structure.
Students will be able to understand that a unit cell represents the contents of an extended solid.
A physical model kit such as the ICE Solid State Model Kit (see the related activities) could be used. With physical models students have to visualize the portion of each atom that is within the unit cell.
With the linked web resources for this activity students can use the "faces" option to shade the faces of the unit cell to help visualize the portion of each atom that is within the unit cell.
Both physical and virtual models are valuable learning tools. Either could be used separately depending on availability but they work together well.
Cubic unit cells are appropriate for an introductory course. The advanced unit cells include all crystal systems and centering options.
We have used a physical model kit to build solid state structures in class for many years. After building a few structures, students often want to try some more structures. These online models were created to allow continued study and practice out of class.
We provide a built solid state 3D physical model that the students had not previously seen as a quiz question where students are asked to show their work in calculating the stoichiometry.
See the evaluation questions and activity answer key in the faculty-only files.
Most students have been able to explain the empirical formula for any of these structures. They sometimes struggle with the difference between a corner, an edge, a face, and inside the unit cell. Students are generally able to determine the stoichiometry for an extended solid that they have not previously seen.