Question

Cadmium sulfide, sometimes used as a yellow pigment by artists, crystallizes with cadmium, occupying one-half of the tetrahedral holes in a closest packed aligned of sulfide ions. What is the formula of cadmium sulfide? Explain your answer.

Short answer

The molecular formula of cadmium sulphide is CdS.

Step-by-step solution

Define the coordination number of a sphere

The coordination number of a sphere occupying tetrahedral hole is 4. Those 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.

Find the molecular formula by using provided statement

Assume \(x\) be the number of sulphide ions present in the lattice. Hence, the number of tetrahedral holes is 2x.

One-half of the tetrahedral holes are occupied by cadmium ions.

The mathematical representation is as follows: \(\frac{1}{2} \times 2x = x\)

The number of cadmium ions are \(x\) and sulphide ions are also \(x\). Hence, the molecular formula of cadmium sulphide is CdS.