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Chapter 12: Problem 59

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

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

Step by step solution

01

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)
02

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:
03

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.

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Most popular questions from this chapter

In their study of X-ray diffraction, William and Lawrence Bragg determined that the relationship among the wavelength of the radiation \((\lambda),\) the angle at which the radiation is diffracted \((\theta),\) and the distance between planes of atoms in the crystal that cause the diffraction \((d)\) is given by \(n \lambda=2 d \sin \theta .\) X-rays from a copper X-ray tube that have a wavelength of \(1.54 \AA\) are diffracted at an angle of 14.22 degrees by crystalline silicon. Using the Bragg equation, calculate the distance between the planes of atoms responsible for diffraction in this crystal, assuming \(n=1\) (first-order diffraction).

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