The unit cell of a compound containing Co and O has a unit cell shown below. The Co atoms are on the corners, and the O atoms are completely within the unit cell. What is the empirical formula of this compound? What is the oxidation state of the metal?

Verified step by step guidance

1. Identify the number of Co atoms in the unit cell. Since Co atoms are located at the corners of the unit cell, and each corner atom is shared by 8 adjacent unit cells, each corner contributes 1/8 of an atom to the unit cell. There are 8 corners, so the total number of Co atoms in the unit cell is 8 * (1/8) = 1 Co atom.
2. Identify the number of O atoms in the unit cell. The O atoms are completely within the unit cell, and there are 6 O atoms present.
3. Determine the empirical formula by comparing the ratio of Co atoms to O atoms. Since there is 1 Co atom and 6 O atoms, the empirical formula is CoO6.
4. To find the oxidation state of Co, assume the oxidation state of O is -2 (as it typically is in compounds). Let the oxidation state of Co be x.
5. Set up the equation based on the charge balance: x + 6(-2) = 0. Solve for x to find the oxidation state of Co.

Key Concepts

Unit Cell Structure

A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal. In this case, the cobalt (Co) atoms are located at the corners of the unit cell, while the oxygen (O) atoms are positioned entirely within the cell. Understanding the arrangement of atoms in the unit cell is crucial for determining the empirical formula of the compound.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. To derive the empirical formula from the unit cell, one must count the number of each type of atom within the unit cell. For this compound, knowing the positions of Co and O atoms allows for the calculation of their ratio, which leads to the empirical formula.

Oxidation State

The oxidation state of an element in a compound indicates the degree of oxidation (loss of electrons) of that element. In this case, determining the oxidation state of cobalt involves analyzing its bonding with oxygen, which typically has an oxidation state of -2. By balancing the charges based on the number of Co and O atoms in the empirical formula, one can deduce the oxidation state of cobalt.