Problem 79 - Chemistry: The Central Science in SI Units, Global Edition

Question

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.

Step-by-Step Solution

Answer

(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 1: 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

Step 2: 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#

Step 1: 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.

Step 2: 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#

Step 1: 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.

Step 2: 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#

Step 1: 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.

Step 2: 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.

Key Concepts

Oxidation Number

Oxidation numbers are a way to keep track of electrons and identify the charge of atoms in a compound. They help chemists understand how electrons are distributed among elements in a molecule or compound. For group 2A elements like beryllium (Be), magnesium (Mg), and others, the oxidation number is often +2. This is because these elements tend to lose two electrons from their outer shell to form stable cations. In the case of hydrogen in metal hydrides such as BeH automatically assumed an oxidation state that balances the charge of the compound. Since each hydrogen generally gains an electron when forming an ionic bond with a group 2A metal, the oxidation number for hydrogen becomes -1. This means that in compounds like BeH₂, the sum of oxidation numbers for Be (+2) and for hydrogen (2 × -1) equals zero, resulting in a neutral compound. To find the oxidation number:

• Understand that Group 2A elements like Be will usually have an oxidation state of +2.
• In neutral compounds like BeH₂, the oxidation numbers of all atoms must add up to zero.
• Assign hydrogen an oxidation number of -1 to satisfy this balance.

Cation-Anion Distance

The cation-anion distance is a crucial factor in determining the properties of ionic compounds. It refers to the physical separation between positively charged cations and negatively charged anions in a crystal lattice structure. This distance significantly affects the lattice energy of a compound, which is the energy required to separate one mole of a solid ionic compound into gaseous ions. Lattice energy tends to be higher when cation-anion distance is shorter, due to the stronger electrostatic forces between the closely packed ions. Therefore, compounds like BeH₂, which have high lattice energies among Group 2 hydrides, imply a shorter cation-anion distance. Factors influencing cation-anion distances include:

• Ionic charge: Highly charged ions can lead to stronger attractions and shorter distances.
• Ionic size: Smaller ions allow for shorter distances, increasing lattice energy.

To identify the compound with the shortest cation-anion distance from a list:

• Look for the highest lattice energy value, as it suggests the strongest interactions and shortest distances.
• Recognize that in the given data, BeH₂ has the highest lattice energy, thus the shortest cation-anion distance.

Ionic Radius

The ionic radius is the effective distance from the nucleus of an ion to its outermost electron shell, often affecting how ions fit together in a lattice structure. This size is a critical factor in ionic bonding and determines the arrangement of ions in a solid. Assessing the ionic radius helps understand compound properties, such as lattice energies and chemical reactivity. In the Group 2A elements, ionic radii increase down the group because additional electron shells are added, increasing the size of the ions. When exploring the trends of lattice energies relative to ionic radii:

• Smaller ionic radii typically result in higher lattice energy values because the ions can pack more closely together.
• Lattice energy tends to decrease as ionic size increases, as seen in the order from BeH₂ to BaH₂ in Group 2A hydrides.

To predict which Group 2 element matches the ionic radius of Zn²⁺:

• Compare lattice energies of group 2 hydrides to ZnH₂, whose lattice energy is 2870 kJ/mol.
• Notice that MgH₂, with a lattice energy of 2791 kJ/mol, is closest to ZnH₂, suggesting Mg²⁺ has a similar ionic radius to Zn²⁺.