Question

Rubidium iodide crystallizes with a cubic unit cell that contains iodide ions at the corners and a rubidium ion in the center. What is the formula of the compound?

Short answer

Molecular formula of rubidium iodide is Rbl.

Step-by-step solution

Define the coordination number of a sphere  

The coordination number of a sphere occupying a tetrahedral hole is 4 . They are smaller than cubic or octahedral holes. Face centred cubic arrangement has both tetrahedral (8) and octahedral holes (4). The example used to see a tetrahedral structure is methane. Here, the carbon atom is attached to four equidistance hydrogen atoms placed at the corners of tetrahedrons.

An octahedron is defined as a polyhedron with 8 regular triangles. It is made of one sphere surrounded by 6 equal spheres. By connecting 6 centres of the surrounding spheres, an octahedron can be generated. An example is sodium chloride. Here, octahedral holes are formed by chloride ions which are occupied by smaller sodium ions. In a face-centred cube, there are four octahedral holes as one octahedral hole per anion.

Find the molecular formula.  

Iodide is present at the eight corners of the cube, the number of atoms of iodine atoms in the cubic unit cell is $\frac{1}{8}\times 8=1$

The rubidium atom is present at the center of the cubic unit cell. Thus, the number of rubidium ions in the center of the cubic cell is one.

Hence, the ratio of cation rubidium and anion iodide ions is 1:1. Therefore, the molecular formula of rubidium iodide is Rbl.