Question

Consider the lattice energies of the following Group 2 \(\mathrm{A}\) compounds: \(\mathrm{Be} \mathrm{H}_{2}, 3205 \mathrm{kJ} / \mathrm{mol} ; \mathrm{MgH}_{2}, 2791 \mathrm{kJ} / \mathrm{mol}\) \(\mathrm{CaH}_{2}, 2410 \mathrm{kJ} / \mathrm{mol} ; \mathrm{SrH}_{2}, 2250 \mathrm{kJ} / \mathrm{mol} ; \mathrm{BaH}_{2}, 2121 \mathrm{kJ} / \mathrm{mol}\) (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 BeH \(_{2} .\) Does it require 3205 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 \(\mathrm{A}\) compounds, predict which Group 2 \(\mathrm{A}\) element is most similar in ionic radius to the \(\mathrm{Zn}^{2+}\) ion.

Short answer

The oxidation number of hydrogen in the given Group 2A hydrides is -1. BeH2 has the shortest cation-anion distance among the given compounds. Breaking one mole of solid BeH2 into its ions requires 3205 kJ of energy. The ionic radius of the Zn2+ ion is most similar to that of the Mg2+ ion among the Group 2A elements.

Step-by-step solution

(a) Oxidation number of hydrogen

To determine the oxidation number of hydrogen in these Group 2A hydrides, we need to remember that the oxidation number of an element is the hypothetical charge it would have if all its bonds were ionic. Group 2A elements (Be, Mg, Ca, Sr, and Ba) have oxidation numbers of +2 as they lose 2 electrons to attain a full electron configuration. Since the compounds given are hydrides (formed with hydrogen), the hydrogen must balance the charge. Therefore, the oxidation number of hydrogen in these compounds is -1.

(b) Shortest cation-anion distance

The shortest cation-anion distance in a lattice depends on the ionic radii of the cation and anion. For a fixed anion (in this case, hydrogen), the cation-anion distance decreases as the cation gets smaller. For Group 2A elements, the ionic radius decreases as we move up the group. Therefore, among the given compounds, BeH2 has the smallest cation (Be2+) and subsequently, the shortest cation-anion distance.

(c) Breaking one mole of solid BeH2

Lattice energy is defined as the energy required to break one mole of a solid ionic compound into isolated gaseous ions. Hence, breaking one mole of solid BeH2 into its ions requires 3205 kJ of energy, as given in the problem.

(d) Group 2A element similar to Zn2+ ion

To find the Group 2A element with an ionic radius most similar to the Zn2+ ion, we can compare the lattice energy values. A higher lattice energy value indicates a smaller ionic radius for the cation, as stronger ionic bonding leads to a more negative lattice enthalpy. Since the lattice energy of ZnH2 (2870 kJ/mol) lies between the lattice energy values of MgH2 (2791 kJ/mol) and BeH2 (3205 kJ/mol), we can predict that the ionic radius of the Zn2+ ion is most similar to that of the Mg2+ ion among the Group 2A elements.

Key concepts

Ionic Compounds

Ionic compounds are chemical compounds composed of ions held together by electrostatic forces termed ionic bonding. The positively charged ions are called cations, while the negatively charged ions are anions. These compounds are typically formed when a metal reacts with a nonmetal, resulting in the transfer of electrons from the metal to the nonmetal.

Understanding ionic compounds is crucial as it provides insight into their properties, such as high melting and boiling points, due to the strong ionic bond between the cations and anions. For example, in the given exercise, Group 2A elements like Be, Mg, Ca, Sr, and Ba form ionic compounds with hydrogen, known as hydrides. These hydrides exhibit significant differences in lattice energies primarily due to variations in the sizes of the cations, which affects the strength of the ionic bonds in the crystal lattice structure.

The lattice energy associated with these compounds directly correlates to the energy required to break apart the ionic bonds. The greater the lattice energy, the more stable the ionic compound and the more energy is needed to overcome these forces.

Cation-Anion Distance

The cation-anion distance in an ionic compound, also known as the bond length, is a determinant of the compound's lattice energy. It is the distance between the centers of the cation and anion in the crystal lattice. A key factor influencing this distance is the ionic radius of the interacting particles: the size of the ions forming the compound.

The size of an ion depends on the number of electrons, the effective nuclear charge, and the electronic configuration. In the Group 2A elements, as one moves up the group in the periodic table, the size of the ions decreases due to the increasing effective nuclear charge on the electrons. This means that beryllium (Be2+) has the smallest ionic radius in the given compound list, resulting in the shortest cation-anion distance in BeH2. A shorter cation-anion distance increases the electrostatic attraction between the ions, leading to a higher lattice energy, as seen in the exercise with the BeH2 lattice energy being the highest among the given hydrides.

Oxidation Number

The oxidation number or oxidation state is a concept that provides insight into the electron distribution within a compound. It signifies the charge that an atom would have if all its bonds to atoms of different elements were completely ionic. The oxidation state is instrumental in determining how electrons are shared in chemical reactions.

In the context of the given exercise with Group 2A hydrides, the oxidation number of hydrogen is typically +1. However, since these compounds are hydrides where hydrogen gains one electron, hydrogen's oxidation number is -1. This is because the Group 2A metals present in these hydrides (Be, Mg, Ca, Sr, Ba) have oxidation numbers of +2 due to the loss of two electrons to form stable ions, which is the key to maintaining electrical neutrality. The hydrides have overall neutral charges; hence, each hydrogen atom must have an oxidation number of -1 to counterbalance the +2 charged cation in each compound, perfectly illustrating the balancing act that oxidation states play in ionic compounds.