Question

In each of the following sets, which atom or ion has the smallest ionization energy? a. \(\mathrm{Ca}, \mathrm{Sr}, \mathrm{Ba}\) b. \(\mathrm{K}, \mathrm{Mn}, \mathrm{Ga}\) c. \(\mathrm{N}, \mathrm{O}, \mathrm{F}\) d. \(\mathrm{S}^{2-}, \mathrm{S}, \mathrm{S}^{2+}\) e. \(\mathrm{Cs}\), Ge, Ar

Short answer

The atoms or ions with the smallest ionization energy in each set are: a. \(Ba\) b. \(K\) c. \(N\) d. \(S^{2-}\) e. \(Cs\)

Step-by-step solution

a. Ca, Sr, Ba

All three elements belong to Group 2 (alkaline earth metals) on the periodic table. As we move down the group from calcium (Ca) to strontium (Sr) to barium (Ba), ionization energy generally decreases. Therefore, the element with the smallest ionization energy in this set is \(Ba\).

b. K, Mn, Ga

All three elements belong to different groups in the same period (Period 4) on the periodic table. As we move across a period from left to right, ionization energy generally increases. Since potassium (K) is the furthest to the left in Period 4, it will have the smallest ionization energy in this set.

c. N, O, F

All three elements belong to different groups in the same period (Period 2) on the periodic table. As we move across a period from left to right, ionization energy generally increases. Nitrogen (N) is the furthest to the left, so it will have the smallest ionization energy in this set.

d. S²⁻, S, S²⁺

All three species have sulfur (S) with different oxidation states. The negatively charged ion (\(S^{2-}\)) has gained electrons and will require less energy to remove an electron compared to the neutral atom (S). The positively charged ion (\(S^{2+}\)) has lost electrons, making it more difficult to remove another electron. Thus, the species with the smallest ionization energy in this set is \(S^{2-}\).

e. Cs, Ge, Ar

In this set, we have elements from three different groups on the periodic table. Cesium (Cs) is in Group 1 and is the furthest down the periodic table, which means it will have the lowest ionization energy due to the increased distance between the nucleus and the outer electrons. Germanium (Ge) is in Group 14, and Argon (Ar) is in Group 18 (a noble gas), both having higher ionization energies than Cs. Therefore, the element with the smallest ionization energy in this set is \(Cs\).

Key concepts

Periodic Table Trends

Understanding periodic table trends is key to predicting ionization energy, which is the energy required to remove an electron from an atom. Across the periodic table, ionization energy tends to increase as you move from left to right across a period. This happens because the atomic number increases, resulting in a greater positive charge in the nucleus.
The increase in nuclear charge pulls the electrons closer, making it harder to remove them. Meanwhile, as you move down a group, ionization energy decreases.
With each step down, another electron shell is added, increasing the distance between the outermost electrons and the nucleus. This greater distance, compounded by electron shielding, makes outer electrons easier to remove.

Alkaline Earth Metals

Alkaline earth metals belong to Group 2 on the periodic table. These elements include beryllium, magnesium, calcium, strontium, barium, and radium. They all share similar properties:

• They are all shiny, silvery-white metals.
• They have two electrons in their outermost shell.
• They readily lose these two electrons to achieve a full outer shell.

As you descend the group, elements tend to have lower ionization energies. Thus, barium has a lower ionization energy than strontium and calcium. The increasing atomic radius as you move down the group means the outer electrons are farther from the nucleus, reducing the energy required to remove an electron.

Oxidation States

Oxidation states indicate the degree of oxidation of an atom in a compound, essentially reflecting how many electrons are lost or gained. In simple ions, the oxidation state is the charge of the ion.
For example:

• The sulfur ion with a S^{2-} oxidation state has gained two electrons.
• Neutral sulfur, S, has no charge.
• The sulfur ion with a S^{2+} oxidation state has lost two electrons.

This change in electron configuration directly affects the ionization energy. Negatively charged ions, which have gained electrons, require less energy to remove an electron due to the extra electron-electron repulsion, while positively charged ions require more energy as their nuclear charge tightly holds the fewer remaining electrons.

Noble Gases

Noble gases, located in Group 18 of the periodic table, are unique for their full valence electron shell configurations. This full shell makes them extremely stable.

• Noble gases include helium, neon, argon, krypton, xenon, and radon.
• They are colorless, odorless, nonflammable gases at room temperature.
• Typically very inert, they usually do not form compounds.

The high stability implies these elements have high ionization energies since removing an electron would disrupt their stable electron configuration. Thus, compared to other elements in the same period, noble gases have the highest ionization energy, making them less likely to lose electrons.