As you work through this section, if you find that you need a bit more background material to help you understand the topics at hand, you can consult “Chemistry: The Molecular Science” (5th ed. Moore and Stanitski) Sections 5-9 through 5-13, Sections 2-4 through 2-6, and Section 9-7, and/or Chapter 3.6-3.13 in the Additional Reading Materials section.

D5.1 Electron Configurations and Periodic Trends

The rules governing quantum numbers together with the relative energies of subshells give rise to electron configurations that repeat periodically. For example, each noble gas has a configuration s²p⁶, an octet, that results in low chemical reactivity. Each element that follows a noble gas in the building-up process has a single valence electron that is easily removed; elements in periodic group 1 (or IA) are highly reactive, easily forming positive ions. These periodic repetitions of electron configurations are the basis for the periodic table: elements with similar atomic electron configurations are in vertical columns in the periodic table. Their similar configurations result in similar chemical properties. In particular, elements in vertical columns in the table form compounds with similar formulas. For example, all elements in group 1 form chlorides, bromides, and iodides with formulas MCl, MBr, and MI, where M represents H, Li, Na, K, Rb, Cs, or Fr.

Electron configurations are related to a number of atomic properties as well as chemical formulas. Periodic trends in these atomic properties can be predicted by applying ideas about attraction of electrons to atomic nuclei and of repulsions among electrons:

• Electron-density distributions are in shells that increase in size as the principal quantum number, n, increases; electrons in larger shells are, on average, farther from the nucleus and less strongly attracted.
• Electrons repel other electrons, raising electrostatic potential energy. This partly counteracts the lowering of energy due to attraction of an electron by the nucleus. Electrons are said are said to screen or shield other electrons from nuclear charge.

Especially important is that electron density in inner shells mostly is closer to the nucleus than electron density in outer shells. Thus, electrons in the inner shells significantly counteract the effect of nuclear attraction. Consider a lithium atom, which has three protons in the nucleus and three electrons surrounding the nucleus. The electron configuration is 1s²2s¹. Because the 2s orbital is much larger than the 1s orbital, the 1s electron density is between the nucleus and the 2s electron much of the time. Thus, the two 1s electrons repel the 2s electron away from the nucleus, counteracting part of the 3+ charge of the three protons in the nucleus. (Move the slider at the bottom of Figure 1 halfway across to see how much of the 1s electron density lies between the nucleus and 2s electron density.)

To account for repulsion of electrons in outer shells by electrons in inner shells, we say that the effective nuclear charge is less than the actual nuclear charge because of electron repulsions. For a specific electron, effective nuclear charge is the positive nuclear charge (given by the atomic number) reduced by the repulsion of the electron by all the other electrons. In the case of the 2s electron in the lithium atom in the figure, the repulsion between the two 1s electrons and the 2s electron reduces nuclear charge by 1.72; that is, the effective nuclear charge for the 2s electron is 3 − 1.72 = 1.28. Had all the electron density of the 1s electrons been between the nucleus and the 2s electron, the nuclear charge would have been reduced by two units, to 1.

D5.2 Periodic Variation of Atomic Radius

It is often useful to think of atoms as if they were tiny spheres with nuclei at their centers. Then the size of an atom can be defined by the radius of a sphere. One way to determine atomic radii is to measure the distance between the nuclei of two atoms of the same element that are bonded to each other; the radius is half the internuclear distance. A second way is to measure the distance between the nuclei of two atoms in a solid metal, where each atom touches several nearest neighbors. Once a set of atomic radii has been determined, the radii can be used to predict the lengths of bonds that have not yet been measured. A table of atomic radii is in the appendix.

D5.3 Periodic Variation of Ionic Radii

Ionic radius  is the radius of a sphere that represents a positive or negative ion. (There is an ionic radius table in an appendix.)

A cation has fewer electrons and the same number of protons as the parent atom; there are fewer electron-electron repulsions but the same nuclear attraction, so cations are smaller than the atoms from which they are derived. For example, the atomic radius of Al (1s²2s²2p⁶3s²3p¹) is 143 pm, whereas the ionic radius of Al³⁺ (1s²2s²2p⁶), with only core electrons remaining, is 68 pm. Cations with higher positive charges are smaller than cations with lower charges; for example, V²⁺ has an ionic radius of 93 pm, while that of V³⁺ is 78 pm. Proceeding down the groups of the periodic table, we find that cations of successive elements with the same charge generally have larger radii, corresponding to an increase in the principal quantum number, n.

An anion is formed by adding one or more electrons to the valence shell of an atom. There is greater repulsion among the electrons and a decrease in effective nuclear charge for the outermost electrons. This causes anion radii to be larger than for the parent atom. For example, the atomic radius of S ([Ne]3s²3p⁴) is 104 pm, whereas the ionic radius of  S^2- ([Ne]3s²3p⁶) is 170 pm. Going down any periodic group row by row, anions of the same charge have larger principal quantum numbers and, thus, larger radii.

Earlier we defined atoms and ions that have the same electron configuration as isoelectronic. An example of isoelectronic species are N^3–, O^2–, F^–, Ne, Na⁺, Mg²⁺, and Al³⁺ (all 1s²2s²2p⁶). For isoelectronic atoms or ions, the greater the nuclear charge (number of protons), the smaller the ionic radius. This implies that isoelectronic anions are larger than cations. Indeed, anions are usually larger than cations even if they are not isoelectronic.

D5.4 Periodic Variation of Ionization Energies

The quantity of energy required to remove an electron from an atom is called ionization energy. Because most atoms contain more than a single electron, there are successive ionization energies: the first ionization energy is for removing the least tightly bound electron; the second ionization energy is for removing an electron from a 1+ cation (the second easiest electron to remove); the third ionization energy is for removing a third electron and so forth. The first ionization energy, IE₁, corresponds to this equation,

and the second ionization energy, IE₂, to this one,

Energy is always required to remove electrons from atoms or ions, so ionization is endothermic and IE values are always positive.

In Activity 5 you developed a general rule that across a period, IE₁ increases with increasing atomic number, Z; down a group, IE₁ decreases with increasing Z. There are some systematic deviations from this trend, four of which occur in periods 1, 2, and 3. Look at Figure 3 again, locate the deviations in the first three periods, and click on each one.

Another deviation from the trend of increasing IE across a period occurs when a subshell becomes more than half filled. The first ionization energy for oxygen is slightly less than that for nitrogen. The orbital box diagram of oxygen shows that the last electron added is forced to pair because the p subshell is more than half full. Loss of one electron reduces electron–electron repulsion because there are no longer two electrons in the same region (orbital). The same explanation applies to the dip for sulfur after phosphorus in Figure 2.

Ionization energies help confirm the idea that valence electrons are important for chemical combination. The second ionization energy is always larger than the first, the third larger than the second, and so forth because of the greater electrostatic attraction by 1+ and 2+ ions. Successive ionization energies always increase but sometimes the increase is larger than expected. Some data are in Table 1.

D5.5 Periodic Variation of Electron Affinities

We define electron affinity (EA) as the energy change when an electron is added to an atom to form a negative ion (anion). A table of electron affinity values is in the appendix. The first EA corresponds to adding a single electron to an atom, as shown in this equation:

Many elements have negative EA_1, which means that the energy of the 1− anion is lower than the energy of the atom to which the electron was added; that is, the anion is more stable than the atom. For other elements, EA₁ is positive, meaning that the anion is less stable than the parent atom.

The properties discussed thus far (size of atoms and ions, effective nuclear charge, ionization energies, and electron affinities) are central to understanding chemical reactivity. For example, because atoms of elements in periodic group 17 (7A) have large ionization energies and large negative electron affinities, it is much easier to form anions than cations. Atoms of elements in periodic groups 1 and 2 (1A and 2A) have very small ionization energies, which means that they can lose electrons relatively easily to form cations. Thus, compounds can be formed when atoms of elements in periodic groups on the left of the table transfer electrons to atoms of elements in groups on the right (except the noble gases). The cations and anions formed this way attract and an ionic compound results.

Metallic substances, which have properties such as high electric conductivity and malleability (the ability to be formed into sheets), are made of atoms whose electrons that can be removed easily; that is, atoms with small ionization energies. Thus, metallic character decreases across a period and increases down a group.

D5.6 Ionic Compounds

When an atom that can lose electrons relatively easily interacts with an atom that readily gain electrons , transfer of one or more electrons can occur, producing an anion and a cation. Atoms that can lose electrons are those with low ionization energy; that is, metals (left side of the periodic table). Atoms that readily gain electrons are those with large negative electron affinities; that is, nonmetals, (right side of the periodic table, except for noble gases).
Lewis diagrams can be used to illustrate the transfer of electrons during the formation of ionic compounds, as shown in Figure 4.

According to Coulomb’s law, anions and cations attract, cations and cations repel, and anions and anions repel. When one anion and one cation form they are attracted and form an ion pair. When a large number of ions form, they combine to form a solid crystal lattice in which anions and cations are arranged so that attractions predominate over repulsions. A compound made up of anions and cations is called an ionic compound and the overall attraction holding it together is called ionic bonding.

For example, when each sodium atom in a sample of sodium metal (group 1 or 1A) gives up one electron to form a sodium cation, Na⁺, and each bromine atom in a sample of liquid bromine (group 17 or 7A) accepts one electron to form a bromide anion, Br⁻, the crystal lattice of the compound sodium bromide, which is shown in Figure 4, contains one Na⁺ ion (green) for each Br⁻ ion (violet). The chemical formula representing the part of the lattice shown in Figure 4 is Na₇₅Br₇₅ because there are 75 Na⁺ and 75 Br⁻ ions. The actual crystal is much larger so the subscripts in the formula of a real crystal would be huge. A formula unit is a group of chemical symbols that indicates the smallest whole number ratio of ions of each kind that make up the substance. Thus, the formula unit of sodium bromide is NaBr and we say that the formula for sodium bromide is NaBr.

The properties of an ionic compound are determined by the ions the compound is made of and are quite different from the properties of the elements from which the ionic compound was made. For example, both sodium and bromine react with water, but sodium bromide dissolves in water without reacting. Sodium ions and bromide ions do not react with water, but sodium atoms and Br₂ molecules do.

Some ions consist of a group of atoms with an overall charge. Examples are sulfate ion, SO₄²⁻, dihydrogen phosphate ion, H₂PO₄⁻, and ammonium ion, NH₄⁺. It is important to be able to recognize such polyatomic ions and know their charges. A table of polyatomic ions is in the appendix.

Ionic compounds contain cations of metals from the left side of the periodic table and anions of nonmetals from the right side of the periodic table. If a compound’s chemical formula contains a polyatomic ion, then the compound is an ionic compound.

All chemical substances must have zero overall electric charge. Thus, in every ionic compound, the total number of positive charges of all cations equals the total number of negative charges of all anions. The subscripts in a formula unit of any ionic compound must result in equal quantities of positive and negative charge. If we know the charges of the ions, then we can write the formula.

It is useful to be able to identify ionic compounds from their chemical formulas because all ionic compounds have similar properties. These properties are like the properties of table salt, NaCl and ionic compounds are often referred to as “salts”.

• Ionic compounds have high melting points and boiling points; thus, they are solids at room temperature.
• Ionic compounds are crystalline, have distinct crystal shapes, and are easily cleaved (that is, they break along smooth planes).
• ionic compounds conduct electricity when molten (liquid) but do not conduct when solid. (Click here to see a molten salt conduct.)
• When an ionic compound dissolves in water the solution conducts electricity much better than pure water.

D5.7 Energy, Ions, and Ionic Compounds

Think about the energy changes involved in ionic bonding. As an example consider transfer of an electron from a Li atom to a F atom to form an ion pair, Li⁺F^–, which has lower total energy than the two atoms from which it formed. (The ion pair is more stable than the two atoms.) We can break ion-pair formation into three simpler steps and consider the energy change involved in each:

1. Remove the 2s electron from a Li atom to form a Li⁺ ion.
2. Add that same electron to a F atom to form a F^– ion.
3. Bring the Li⁺ ion close to the F^– ion to form an ion pair.

When an ionic crystal lattice (Figure 5) forms energy is lowered even more than for an ion pair because more ions are close together in a structure where attractive forces predominate over repulsive forces. Thus, the calculation in Activity 10 is an underestimate of the stability of a crystal of LiF compared a large number of individual Li and F atoms. The energy of an ionic crystal lattice is lower than for the separated ions by a quantity known as the lattice energy. Lattice energies of ionic compounds can be calculated using a modified form of Coulomb’s law; Table 2 shows results of such calculations.

To summarize the results of Activities 11 and 12, lattice energies are highest for substances with small, highly charged ions. Also, lattice energies can affect physical properties of ionic crystals, such as solubility, melting and boiling points, and hardness.