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Chapter 8: Problem 79

Consider the lattice energies of the following Group \(2 \mathrm{~A}\) compounds: $\mathrm{BeH}_{2}, 3205 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{MgH}_{2}, 2791 \mathrm{~kJ} / \mathrm{mol} ;\( \)\mathrm{CaH}_{2}, 2410 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{SrH}_{2}, 2250 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{BaH}_{2}, 2121 \mathrm{~kJ} / \mathrm{mol}$ (a) What is the oxidation number of H in these compounds? (b) Assuming that all of these compounds have the same three-dimensional arrangement of ions in the solid, which of these compounds has the shortest cation-anion distance? (c) Consider BeH \(_{2}\). Does it require \(3205 \mathrm{~kJ}\) of energy to break one mole of the solid into its ions, or does breaking up one mole of solid into its ions release \(3205 \mathrm{~kJ}\) of energy? (d) The lattice energy of \(\mathrm{ZnH}_{2}\) is \(2870 \mathrm{~kJ} / \mathrm{mol}\). Considering the trend in lattice enthalpies in the Group 2 compounds, predict which Group 2 element is most similar in ionic radius to the \(\mathrm{Zn}^{2+}\) ion.

Short Answer

Expert verified
(a) The oxidation number of H in these compounds is -1. (b) BeH₂ has the shortest cation-anion distance. (c) It requires 3205 kJ of energy to break one mole of solid BeH₂ into its ions. (d) Mg²⁺ is the Group 2 element ion with the most similar ionic radius to the Zn²⁺ ion.

Step by step solution

01

Identify the oxidation numbers of group 2A elements

Group 2A elements have a tendency to lose 2 electrons because they have two electrons in their outermost shell. They form cations with a +2 charge. Examples: Be → Be²⁺ + 2e⁻, so oxidation number of Be is +2 Mg → Mg²⁺ + 2e⁻, so oxidation number of Mg is +2
02

Determine the oxidation number of hydrogen in the compounds

Since the compounds are neutral, the sum of the oxidation numbers of the elements in the compound should be zero. So, we have to find an oxidation number for hydrogen which will make the overall charge of the compound neutral. For example, in BeH₂: (+2) + 2 × (oxidation number of H) = 0 Oxidation number of H = -1 The oxidation number of H in these compounds is -1. #b) Shortest cation-anion distance#
03

Identify factors affecting the cation-anion distance

Cation-anion distance depends on the atomic radii of the elements involved. Smaller the atomic radius, shorter will be the cation-anion distance. Consequently, the lattice energy is directly proportional to the cation-anion distance.
04

Find the compound with the shortest cation-anion distance

Since the lattice energy is directly proportional to the cation-anion distance, the compound with the highest lattice energy among given compounds will have the shortest cation-anion distance. From the given data, BeH₂ has the highest lattice energy (3205 kJ/mol), therefore, BeH₂ has the shortest cation-anion distance. #c) Energy requirement for breaking BeH₂#
05

Understand lattice energy and its sign

Lattice energy is the energy required to separate one mole of a solid ionic compound into its gaseous ions. The value of lattice energy is always positive because energy is needed to separate ions from their lattice.
06

Analyze the given data for BeH₂

The given lattice energy for BeH₂ is 3205 kJ/mol. This indicates that it requires 3205 kJ of energy to break one mole of solid BeH₂ into its ions. #d) Group 2 element with similar ionic radius to Zn²⁺ ion#
07

Compare lattice energy trends

The lattice energy generally decreases as the size of the cation in the group increases because the distance between the cation and anion increases. ZnH₂ has a lattice energy of 2870 kJ/mol. To find the Group 2 element with a similar ionic radius to Zn²⁺, we should look for a Group 2 compound with a lattice energy close to that of ZnH₂.
08

Predict the Group 2 element with similar ionic radius to Zn²⁺ ion

Based on the given lattice energies, MgH₂ (2791 kJ/mol) has the closest lattice energy to ZnH₂ (2870 kJ/mol). Hence, Mg²⁺ is the Group 2 element ion with the most similar ionic radius to the Zn²⁺ ion.

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Most popular questions from this chapter

(a) Use Lewis symbols to represent the reaction that occurs between Li and O atoms. (b) What is the chemical formula of the most likely product? (c) How many electrons are transferred? (d) Which atom loses electrons in the reaction?

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