Problem 65 - Chemistry The Central Science

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) MgS, (b) \(\mathrm{MgF}_{2},(\mathbf{c}) \mathrm{MgO}\)

Step-by-Step Solution

Answer

The anion coordination numbers for the given compounds are: (a) MgS: 6, (b) MgF\(_2\): 12, and (c) MgO: 6.

Step 1: Identify the compounds and their formulas

We are given three compounds to find the anion coordination numbers for: (a) MgS (b) MgF\(_2\) (c) MgO

Step 2: Determine the anion coordination number for MgS

The compound MgS has a 1:1 ratio of Mg\(^{2+}\) to S\(^{2-}\) ions. Since we know that the coordination number of Mg\(^{2+}\) is 6, the anion coordination number will also be 6. This means that each Mg\(^{2+}\) ion is surrounded by 6 S\(^{2-}\) ions and vice versa.

Step 3: Determine the anion coordination number for MgF\(_2\)

The compound MgF\(_2\) has a 1:2 ratio of Mg\(^{2+}\) to F\(^-\) ions. Since the Mg\(^{2+}\) ion has a coordination number of 6, and there are two F\(^-\) ions for each Mg\(^{2+}\) ion, the anion coordination number will be 2 x 6 = 12. This means that each Mg\(^{2+}\) ion is surrounded by 12 F\(^-\) ions.

Step 4: Determine the anion coordination number for MgO

The compound MgO has a 1:1 ratio of Mg\(^{2+}\) to O\(^{2-}\) ions. Since the Mg\(^{2+}\) ion has a coordination number of 6, the anion coordination number will also be 6. This means that each Mg\(^{2+}\) ion is surrounded by 6 O\(^{2-}\) ions and vice versa. In summary, the anion coordination numbers for the given compounds are: (a) MgS: Anion coordination number = 6 (b) MgF\(_2\): Anion coordination number = 12 (c) MgO: Anion coordination number = 6

Key Concepts

MgS compound

Magnesium sulfide, abbreviated as MgS, is a compound forming a 1:1 stoichiometric ratio between magnesium ions \( \text{Mg}^{2+} \) and sulfide ions \( \text{S}^{2-} \). The concept of coordination number is critical here. In MgS, each magnesium ion is surrounded by six sulfide ions, and each sulfide ion is surrounded by six magnesium ions.
This balanced coordination gives us a clear structure where each ion plays a crucial role in maintaining the lattice stability and ensuring electrostatic equilibrium.
Understanding this, the coordination number for both the cation \( \text{Mg}^{2+} \) and the anion \( \text{S}^{2-} \) is indeed 6.

• This coordination creates an octahedral geometry around each ion.
• Such symmetric arrangements not only stabilize the compound but also explain its characteristic properties.

Being able to visualize these arrangements enhances comprehension of the basic principles governing ionic compounds.

MgF2 compound

Magnesium fluoride, known as MgFdata {2}, introduces us to a different composition where the ratio of ions is 1:2 between \( \text{Mg}^{2+} \) and \( \text{F}^{-} \). Despite each \( \text{Mg}^{2+} \) needing six neighbors to achieve stability, the anion, \( \text{F}^{-} \), bonds doubly.

• Given that we deal with two \( \text{F}^{-} \) ions for each \( \text{Mg}^{2+} \), these anions can achieve a larger coordination number.
• The coordination number for \( \text{F}^{-} \) is twice that of \( \text{Mg}^{2+} \), resulting in a total of 12.

The crystal structure can impact the physical properties significantly.
The high coordination number is the basis for MgFdata {2}'s utility in various optical applications, where it remains inert and stable under specific conditions.

MgO compound

Magnesium oxide, or MgO, shares a similar coordination dynamic as we saw in MgS. Both have a 1:1 ratio between magnesium \( \text{Mg}^{2+} \) and oxide \( \text{O}^{2-} \) ions. Therefore, the coordination number for each ion is 6.
In this compound:

• Every magnesium ion is surrounded octahedrally by six oxide ions.
• Likewise, every oxide ion is surrounded by six magnesium ions, creating a crystalline lattice that is both durable and reliable.

This tightly packed arrangement contributes to MgO's high melting point and thermal stability.
Magnesium oxide is widely used in construction, refractory materials, and other high-temperature applications, evidenced by the robust ion network maintained by its coordination.