Question

The coordination number for \(\mathrm{Mg}^{2+}\) ion is usually six. Assuming this assumption holds, determine the anion coordination number in the following compounds: (a) \(\mathrm{MgS}\), (b) \(\mathrm{MgF}_{2}\), (c) \(\mathrm{MgO}\).

Short answer

The anion coordination numbers for the given compounds are 6 for MgS, 12 for MgF₂, and 6 for MgO.

Step-by-step solution

Consider the stoichiometric ratios of the compounds

Recall that the stoichiometric ratios of the compounds give us the proportion of each element within the compound. For the given compounds, the stoichiometric ratios are: (a) MgS: 1:1 (1 Mg²⁺ ion and 1 S²⁻ ion) (b) MgF₂: 1:2 (1 Mg²⁺ ion and 2 F⁻ ions) (c) MgO: 1:1 (1 Mg²⁺ ion and 1 O²⁻ ion)

Relate the coordination numbers to stoichiometric ratios

With the stoichiometric ratios, we can relate the cation (Mg²⁺) and anion coordination numbers while maintaining charge neutrality in the compound. To find the anion coordination number (ACN), we can use the following expression: ACN = (Coordination number of Mg²⁺ × Stoichiometric ratio of anion to Mg²⁺) / (Stoichiometric ratio of Mg²⁺) Given that the coordination number of Mg²⁺ is 6, we can find the anion coordination numbers for the three compounds:

Calculate the anion coordination numbers for each compound

(a) MgS: ACN = (6 × 1) / 1 = 6 The anion coordination number in MgS is 6. (b) MgF₂: ACN = (6 × 2) / 1 = 12 The anion coordination number in MgF₂ is 12. (c) MgO: ACN = (6 × 1) / 1 = 6 The anion coordination number in MgO is 6. So the anion coordination numbers in the given compounds are 6 for MgS, 12 for MgF₂, and 6 for MgO.

Key concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons to achieve stability. This typically involves a metal and a non-metal joining together. In an ionic compound, one atom gives up electrons to another, forming ions. These ions are atoms with an electric charge due to the loss or gain of electrons. For instance, magnesium in the form of

• a magnesium ion (\(\mathrm{Mg}^{2+}\)) loses two electrons.
• The sulfur in a sulfide ion (\(\mathrm{S}^{2-}\)) gains two electrons, making each ion stable and forming the compound magnesium sulfide (\(\mathrm{MgS}\)).

This transfer of electrons creates a strong attractive force that holds the ions together, known as ionic bonding. The forces responsible for ionic bonding are electrostatic forces that occur between oppositely charged particles.
These compounds generally form crystalline solids at room temperature, which are characterized by a regular three-dimensional arrangement of the ions.

Coordination Number

Coordination number refers to the number of atoms, ions, or molecules a central atom or ion can bind with in a molecular complex. In the context of the compounds discussed, it pertains to how many anions surround a given cation.
Take the \(\mathrm{Mg}^{2+}\) ion as an example – it usually binds with six anions. This arrangement forms a specific pattern, often forming a geometric shape like an octahedron. The coordination number gives insight into the compound’s stability and structure.
In coordination chemistry, the central metal ion's coordination number can affect the properties of the compound, such as its color, reactivity, and magnetic behavior. Understanding this concept is crucial for determining how compounds form and the variety of structures they can achieve when atoms bind in different ratios.

Stoichiometric Ratios

Stoichiometric ratios are vital in understanding the composition of a compound. These ratios tell us the proportion of each element within a chemical formula. For example, magnesium fluoride, \(\mathrm{MgF}_{2}\), has a stoichiometric ratio of 1:2, which means one \(\mathrm{Mg}^{2+}\) ion interacts with two \(\mathrm{F}^{-}\) ions.
These ratios arise from the need to balance charges, ensuring the compound is electrically neutral. When determining the anion coordination number, the stoichiometric ratio helps distribute how many anion interactions are possible for a fixed number of cations. In the case of \(\mathrm{MgF}_{2}\), it is observed that its anion coordination number is higher due to its greater number of fluoride ions relative to magnesium ions.
Stoichiometric ratios are foundational in the precise formulation of compounds, predicting their behavior, and understanding the massive diversity in chemical structures we observe.