Niobium oxide crystallizes in the following cubic unit cell:
What is the formula of niobium oxide, and what is the oxidationstate of niobium? (LO 12.5)(a) NbO, Nb = +2 (b) Nb2O, Nb = +2(c) NbO2, Nb = +4 (d) Nb2O3, Nb = +3

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Identify the type of cubic unit cell and the positions of the atoms within the unit cell. In this case, it is a face-centered cubic (FCC) unit cell.

Count the number of niobium (Nb) atoms in the unit cell. Each corner atom is shared by 8 unit cells, and each face-centered atom is shared by 2 unit cells.

Count the number of oxygen (O) atoms in the unit cell. Each face-centered atom is shared by 2 unit cells.

Determine the ratio of niobium to oxygen atoms in the unit cell to find the empirical formula of the compound.

Use the empirical formula to determine the oxidation state of niobium by balancing the charges of niobium and oxygen atoms.

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Key Concepts

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

Cubic Unit Cell Structure

A cubic unit cell is the smallest repeating unit in a crystal lattice that defines the structure of the material. In this case, the face-centered cubic (FCC) structure indicates that atoms are located at each corner and the centers of all the cube faces. Understanding this arrangement is crucial for determining the stoichiometry and coordination of the atoms in niobium oxide.

Oxidation States

The oxidation state of an element in a compound indicates the degree of oxidation (loss of electrons) of that element. For niobium oxide, determining the oxidation state of niobium involves balancing the total charge contributed by niobium and oxygen, which typically has an oxidation state of -2. This concept is essential for deducing the correct formula of the compound.

Stoichiometry in Ionic Compounds

Stoichiometry refers to the ratio of elements in a compound based on their oxidation states. In ionic compounds like niobium oxide, the total positive charge from niobium must balance the total negative charge from oxygen. This principle helps in deriving the correct empirical formula, which is critical for answering the question regarding the formula of niobium oxide and the oxidation state of niobium.

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