Problem 61 - 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) \(\mathrm{MgS}_{\text {, }}\) (b) \(\mathrm{MgF}_{2}\), (c) \(\mathrm{MgO}\).

Step-by-Step Solution

Answer

The anion coordination numbers for the given compounds are: (a) In MgS, S2- has a coordination number of 6. (b) In MgF2, F- has a coordination number of 12. (c) In MgO, O2- has a coordination number of 6.

Step 1: Identify Cation and Anion in each compound

Here, the cation (positively charged ion) is Mg2+ in all the compounds, while the anions (negatively charged ions) are S2-, F-, and O2- in compounds MgS, MgF2, and MgO, respectively.

Step 2: Apply the relationship between cation and anion proportions

We can use the relationship between the charges of cations (Mg2+) and anions to find the anion coordination number. The general formula for this is cation:anion = cation charge/anion charge.

Step 3: Determine Anion Coordination Number in MgS

In MgS, the cation charge is 2+ and the anion charge is 2-. The proportion of Mg2+ to S2- can be expressed as: \( \frac{+2}{-2} = -1 \) Since the proportions should be positive, we take the absolute value: | -1 | = 1 Now, we use the given assumption that Mg2+ has a coordination number of 6. Then, the coordination number for S2- will be 6 * 1 = 6.

Step 4: Determine Anion Coordination Number in MgF2

In MgF2, the cation charge is 2+ and the anion charge is 1-. The proportion of Mg2+ to F- can be expressed as: \( \frac{+2}{-1} = -2 \) Taking the absolute value: | -2 | = 2 Given the assumption of Mg2+ having a coordination number of 6, the coordination number for F- will be 6 * 2 = 12.

Step 5: Determine Anion Coordination Number in MgO

In MgO, the cation charge is 2+ and the anion charge is 2-. The proportion of Mg2+ to O2- can be expressed as: \( \frac{+2}{-2} = -1 \) Taking the absolute value: | -1 | = 1 Given the assumption of Mg2+ having a coordination number of 6, the coordination number for O2- will be 6 * 1 = 6. So, the anion coordination numbers are: (a) For MgS, S2- has a coordination number of 6. (b) For MgF2, F- has a coordination number of 12. (c) For MgO, O2- has a coordination number of 6.

Key Concepts

Anion Coordination

In chemical compounds, the coordination number is a crucial concept that describes the number of atoms or ions immediately surrounding a central atom. When examining the anion coordination number, we focus on the negatively charged ions in a compound. For example, in the case of magnesium ions (Mg\(^{2+}\)) as investigated here, these are the counterpart ions that directly interact with positively charged ions.
Anions can vary in charge, often influencing their coordination environment. This is evident in compounds like MgS, MgF\(_2\), and MgO. Each anion, whether it be S\(^{2-}\), F\(^{-}\), or O\(^{2-}\), plays a significant role in determining how they 'coordinate' with the Mg\(^{2+}\) ions.

• In MgS, the anion S\(^{2-}\) directly interacts with Mg\(^{2+}\) with a coordination number of 6.
• In MgF\(_{2}\), each F\(^{-}\) accepts a higher coordination of 12 due to charge balancing requirements.
• For MgO, the interaction returns to S\(^{2-}\)-like conditions, maintaining a coordination number of 6.

Understanding these differences improves our grasp of the compound's structural blueprint.

Cation-Anion Relationship

The relationship between cations and anions in a compound is imperative for predicting the compound's physical and chemical behaviors. In all compounds discussed, Mg\(^{2+}\) serves as a cation while different anions are present, namely, S\(^{2-}\), F\(^{-}\), and O\(^{2-}\).
The key factor here is the balance of charges between cations and anions. This charge balance dictates how many anions can surround a cation, forming a stable structure. For instance:

• In MgS, the 2:2 ratio implies simple charge pairing with both ions having the same magnitude of charge, leading to a coordination number of 6 for S\(^{2-}\).
• MgF\(_2\) introduces a greater complexity, where the single-charge F\(^{-}\) needs to balance out the double-charge on Mg\(^{2+}\), increasing the coordination requirement to 12.
• In MgO, like MgS, a balanced 2:2 charge ratio ensures a straightforward coordination of 6 for O\(^{2-}\).

By evaluating these relationships, students gain insights into how ionic charges influence structural geometry.

Chemical Compounds Analysis

Analyzing chemical compounds involves understanding the composition and structure that influence their properties. The exercise with Mg-based compounds is a classic example of this analysis process. Initially, it was necessary to identify both the cations and anions present. With Mg\(^{2+}\) as the central cation in all cases, paired with varying anions such as S\(^{2-}\), F\(^{-}\), and O\(^{2-}\), each compound suggests different structural characteristics.
Each compound's analysis reveals:

• In MgS and MgO, symmetrical charge relationships (2:2 for Mg\(^{2+}\) and S\(^{2-}\) or O\(^{2-}\)) produce a uniform coordination environment.
• MgF\(_2\), with a more complex 2:1 charge ratio, demonstrates increased coordination numbers, reflecting its varied structural demands.

The deep dive into such compounds helps chemists and students alike predict not only the stability but also potential reactions and applications based on structural properties. This comprehensive understanding is essential for advanced studies in solid-state chemistry and material sciences.