Problem 79 - Chemistry The Central Science In Si Units

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 \(\mathrm{H}\) 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 \(\mathrm{BeH}_{2}\). 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) -1. (b) BeH2. (c) 3205 kJ is energy required. (d) Mg.

Step 1: Determine Oxidation Number of Hydrogen

In Group 2 hydrides ( ext{MH}_2), hydrogen is in the -1 oxidation state because Group 2 metals (Be, Mg, Ca, Sr, Ba) are in the +2 oxidation state. The total charge of the compound is zero, so for two hydrogens to balance the +2 charge from the metal, each hydrogen must be -1.

Step 2: Identify Compound with the Shortest Cation-Anion Distance

The shortest cation-anion distance in ionic compounds typically corresponds to the compound with the highest lattice energy, as smaller ions result in stronger attractive forces. Among the given compounds,  ext{BeH}_2 has the highest lattice energy of 3205 ext{ kJ/mol}, suggesting the shortest cation-anion distance.

Step 3: Interpret Lattice Energy for  ext{BeH}_2

Lattice energy is defined as the energy required to break one mole of a solid compound into its gaseous ions. Therefore, for  ext{BeH}_2, 3205 ext{ kJ/mol} of energy is required to separate one mole of the solid into its ions. It does not indicate energy released but energy absorbed.

Step 4: Predict Ionic Radius Similar to  ext{Zn}^{2+}

Comparing lattice energies,  ext{ZnH}_2 has a lattice energy of 2870 ext{ kJ/mol}, placing it between  ext{MgH}_2 (391 ext{ kJ/mol}) and  ext{CaH}_2 (2410 ext{ kJ/mol}). This suggests that the ionic radius of  ext{Zn}^{2+} is most similar to that of  ext{Mg}^{2+}, given the comparable lattice energy.

Key Concepts

Group 2 Compounds

Group 2 compounds are fascinating substances composed of elements found in the second column of the periodic table, often referred to as alkaline earth metals. These metals include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba). When these metals form compounds, they typically exhibit a +2 oxidation state due to their propensity to lose two electrons. This +2 charge is a hallmark of Group 2 metals, resulting in the formation of ionic compounds when combined with nonmetals like hydrogen.
In our exercise, the Group 2 compounds

• BeH dietxt₂,
• MgH dietxt₂,
• CaH dietxt₂,
• SrH dietxt₂, and
• BaH dietxt₂

are specifically noted. These substances are characterized by varying lattice energies, which reflect the strength of the ionic bonds within their structures. The stronger the lattice energy, the more stable the ionic compound because more energy is required to separate the ions.
The variation in these energies among the listed hydrides is mainly attributed to differences in the sizes of the cations (the Group 2 metal ions) within each compound.

Cation-Anion Distance

Cation-anion distance refers to the space between the positively charged metal ions (cations) and negatively charged ions, such as hydride ions (anions), in an ionic compound. This measurement is crucial because it influences the strength of the ionic bond and, consequently, the lattice energy of the compound.
Generally, a shorter cation-anion distance results in a stronger attractive force due to the closer proximity of opposite charges. In our exercise involving Group 2 hydrides,

• BeH dietxt₂ has the highest lattice energy at 3205 kJ/mol,
• suggesting it possesses the shortest cation-anion distance

among the compounds listed.
This is because beryllium ions are smaller compared to the other Group 2 metal ions mentioned. Smaller ions can be packed more closely together, thereby increasing the electrostatic forces between them. As a result, BeH dietxt₂'s strong ionic bonds are indicative of a tightly packed structure and high stability.

Oxidation Number

An oxidation number is a concept used to describe the degree of oxidation of an atom within a compound. In Group 2 hydrides, hydrogen atoms typically carry an oxidation number of -1. This is because they balance the +2 oxidation state of the Group 2 metal atoms, such as Be, Mg, and Ca, which are highly electropositive and readily donate electrons.
In our specific case, the compound formulas ( MH dietxt₂) ensure that each hydrogen, being less electronegative than the metal, must assume negative charges to maintain the overall neutral charge of the compound.
This uniform assignment of oxidation numbers is central to understanding how these atoms interact within the chemical structure of the compound, providing a fundamental basis for predicting chemical behavior and reactivity.

Ionic Radius

The ionic radius is the measure of an atom's ion in a crystal lattice, impacting how atoms pack within a solid. This concept is essential in understanding the size and spacing between ions in an ionic compound. For Group 2 metals, the ionic radius increases down the group because additional electron shells are added.
In our exercise, considering the lattice energy of ZnH dietxt₂ (2870 kJ/mol), we can predict the ionic radius of the Zn textsuperscript{2+} ion by comparing it to Group 2 metal hydrides. The lattice energy of ZnH dietxt₂ closely resembles that of MgH dietxt₂ (2791 kJ/mol), indicating Zn textsuperscript{2+} 's ionic radius is likely similar to Mg textsuperscript{2+} 's.
This is crucial because the similarity in ionic radius means that the packing of ions within ZnH dietxt₂'s lattice structure is similar in space to how Mg textsuperscript{2+} integrates into MgH dietxt₂. This comparison provides insight not only into ionic size but also into structural characteristics and reactivity in chemical processes.