Question

The substances \(\mathrm{NaF}\) and \(\mathrm{CaO}\) are isoelectronic (have the same number of valence electrons). (a) What are the charges on each of the cations in each compound? (b) What are the charges of each of the anions in each compound? (c) Without looking up lattice energies, which compound is predicted to have the larger lattice energy? (d) Using the lattice energies in Table \(8.1,\) predict the lattice energy of ScN.

Short answer

(a) The charges of the cations in each compound are: \(\mathrm{Na^{+}}\) (for \(\mathrm{NaF}\)) and \(\mathrm{Ca^{2+}}\) (for \(\mathrm{CaO}\)). (b) The charges of the anions in each compound are: \(\mathrm{F^{-}}\) (for \(\mathrm{NaF}\)) and \(\mathrm{O^{2-}}\) (for \(\mathrm{CaO}\)). (c) \(\mathrm{CaO}\) is predicted to have a larger lattice energy than \(\mathrm{NaF}\) since its cation and anion have higher charges. (d) The lattice energy of \(\mathrm{ScN}\) is expected to be larger than those of \(\mathrm{LiF}\) and \(\mathrm{LiBr}\) due to its higher charged cation (\(\mathrm{Sc^{3+}}\)) and anion (\(\mathrm{N^{3-}}\)).

Step-by-step solution

Identify valence electrons of elements

First, we need to find out the number of valence electrons for each element present in compounds \(\mathrm{NaF}\) and \(\mathrm{CaO}\). Sodium has 1 valence electron, Fluorine has 7 valence electrons, Calcium has 2 valence electrons, and Oxygen has 6 valence electrons.

Determine the charge of cations in compounds

To achieve a stable noble gas configuration, atoms lose or gain electrons. Sodium loses 1 electron and becomes a positively charged ion (cation) with a charge of +1. Calcium loses 2 electrons and becomes a cation with a charge of +2.

Determine the charge of anions in the compounds

Fluorine gains 1 electron to achieve a stable noble gas configuration and becomes negatively charged ion (anion) with a charge of -1. Oxygen gains 2 electrons and becomes an anion with a charge of -2.

Comparing the lattice energies of NaF and CaO without looking at the table

Lattice energy is directly proportional to the product of the charges of cations and anions and inversely proportional to the distance between them. Since \(\mathrm{Ca^{2+}}\) and \(\mathrm{O^{2-}}\) have higher charges than \(\mathrm{Na^{+}}\) and \(\mathrm{F^{-}}\), \(\mathrm{CaO}\) is expected to have a larger lattice energy.

Predicting the lattice energy of ScN

From the periodic table, Scandium has 3 valence electrons, and Nitrogen has 5 valence electrons. Scandium loses 3 electrons and forms a cation with a charge of +3. Nitrogen gains 3 electrons and forms an anion with a charge of -3. Using the lattice energies provided in Table 8.1, we can see that the lattice energy of \(\mathrm{LiF}\) is 1030 kJ/mol and \(\mathrm{LiBr}\) is 865 kJ/mol, for example. Since \(\mathrm{Sc^{3+}}\) and \(\mathrm{N^{3-}}\) have higher charges than \(\mathrm{Li^{+}}\) and \(\mathrm{F^{-}}\) or \(\mathrm{Li^{+}}\) and \(\mathrm{Br^{-}}\), we can expect the lattice energy of \(\mathrm{ScN}\) to be larger than the lattice energies given for \(\mathrm{LiF}\) and \(\mathrm{LiBr}\).

Key concepts

Isoelectronic Species

Isoelectronic species are atoms, ions, or molecules that have the same number of electrons, and thus the same electron configuration. This concept is particularly important when discussing ionic compounds, which are made up of positively charged cations and negatively charged anions. For example, in the exercise given, NaF and CaO are considered isoelectronic because they have the same number of valence electrons. Valence electrons play a significant role in chemical bonding, and having the same number of these electrons means that the species can have similar chemical properties.

However, the similarity in chemical properties does not necessarily imply similarity in physical properties. For instance, despite having the same number of valence electrons, the strength of bonds (quantified as lattice energy) between the ions in isoelectronic compounds can differ substantially due to differences in ionic charges and sizes of the ions involved. As learners delve deeper into chemistry, understanding the role of isoelectronic species is essential for predicting chemical reactions and properties of chemical compounds.

Cation and Anion Charges

Cations are positively charged ions, while anions are negatively charged ions. The charges result from the gain or loss of valence electrons to achieve a stable noble gas electron configuration. In the context of our exercise, Na in NaF loses one electron to become Na⁺, while Ca in CaO loses two electrons to become Ca²⁺. Correspondingly, F gains one electron to become F^- and O gains two to become O^2-.

The charges on these ions are not arbitrary but are dictated by the number of valence electrons an atom has and its desire to reach a state of electron configuration resembling that of the nearest noble gas. Understanding ion charges is essential for predicting the formulae of compounds formed and interpreting their chemical behavior.

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom that are involved in forming chemical bonds. They can be identified easily using the periodic table by looking at the group number for the main group elements. For instance, sodium (Na) is in group 1 and has 1 valence electron; fluorine (F) is in group 17 and has 7 valence electrons. During chemical reactions, atoms aim to achieve a full valence shell, typically resembling the nearest noble gas electron configuration. This can often involve the transfer or sharing of these electrons.

Understanding the concept of valence electrons is crucial as they determine the type and number of bonds an element can form. It directly influences the chemical properties and reactivity of an element. By grasping the role of valence electrons, students can predict the charge of ions and the formulas of compounds, as well as understand reactions involving electron transfer.

Periodic Table Trends

The periodic table is not just a tool for listing chemical elements; it showcases trends in the properties of elements, including atomic radius, electronegativity, ionization energy, and electron affinity. These trends can provide insights into the behavior of elements in chemical reactions and are essential for predicting properties such as lattice energy.

For example, as we move from left to right across a period, cations generally become smaller due to increased nuclear charge attracting electrons closer to the nucleus. Additionally, anions formed from elements on the right side of the periodic table are more stable because they are closer to noble gas configurations. Lattice energy is influenced by these trends as smaller ions with higher charges will have stronger attractions and thus higher lattice energies. When evaluating lattice energies in the absence of empirical data, understanding these periodic trends can be invaluable. For instance, in our exercise, ScN is predicted to have a higher lattice energy than LiF or LiBr simply by recognizing that Sc³⁺ ions and N^3- ions will have a stronger electrostatic attraction due to their higher charges, which are informed by their position on the periodic table.