Question

For each of the following pairs, indicate which element has the larger first ionization energy: (a) \(\mathrm{Ti}\), \(\mathrm{Ba}\); (b) \(\mathrm{Ag}\), \(\mathrm{Cu}\); (c) Ge, \(\mathrm{Cl}\); (d) \(\mathrm{Pb}\), Sb. (In each case use electron configuration and effective nuclear charge to explain your answer.)

Short answer

(a) Ti has a higher first ionization energy than Ba because its electrons are closer to the nucleus and experience a stronger effective nuclear charge. (b) Cu has a higher first ionization energy than Ag due to the increase in ionization energy across a period in the periodic table. (c) Cl has a higher first ionization energy than Ge because it is located further to the right in the periodic table and has a stronger effective nuclear charge. (d) Sb has a higher first ionization energy than Pb due to the trend of ionization energy decreasing down a group in the periodic table.

Step-by-step solution

(a) Titanium (Ti) and Barium (Ba)

First, let's consider the electron configurations of Ti and Ba: - Ti's electron configuration: [Ar] 4s² 3d² - Ba's electron configuration: [Xe] 6s² Since Ba is a larger atom and is in the same group as Ti (Group 2) but in a lower period, its electrons are further from the nucleus and experience weaker effective nuclear charge. This means that it is easier to remove an electron from Ba than from Ti. Therefore, Ti has a higher first ionization energy than Ba.

(b) Silver (Ag) and Copper (Cu)

Next, let's evaluate the electron configurations for Ag and Cu: - Ag's electron configuration: [Kr] 5s¹ 4d¹⁰ - Cu's electron configuration: [Ar] 4s¹ 3d¹⁰ Both Ag and Cu belong to the same group (Group 11), but Cu is in a higher period. As we move from left to right across a period, the ionization energy increases. Thus, Cu has a higher first ionization energy than Ag.

(c) Germanium (Ge) and Chlorine (Cl)

Now, let's find the electron configurations for Ge and Cl: - Ge's electron configuration: [Ar] 4s² 3d¹⁰ 4p² - Cl's electron configuration: [Ne] 3s² 3p⁵ Both elements are in the same period (Period 4) but Cl is located further to the right in the periodic table. This makes Cl's effective nuclear charge stronger and it is more difficult to remove an electron from Cl. Consequently, Cl has a higher first ionization energy than Ge.

(d) Lead (Pb) and Antimony (Sb)

Lastly, let's consider the electron configurations of Pb and Sb: - Pb's electron configuration: [Xe] 4f¹⁴ 5d¹⁰ 6s² 6p² - Sb's electron configuration: [Kr] 5s² 4d¹⁰ 5p³ Both elements belong to the same group (Group 15), but Pb is in a lower period. Since ionization energy decreases down the group, Sb will have a higher first ionization energy than Pb.

Key concepts

Electron Configuration

When we talk about electron configuration, we are referring to the distribution of electrons in an atom's orbitals. This configuration can significantly impact an atom's chemical properties, including its first ionization energy—the energy required to remove the most loosely held electron from an atom in its gaseous state.

Electrons reside in various shells and subshells around the nucleus, usually filled in a specific order according to the Aufbau principle. The configuration not only dictates the atom's stability but also its reactivity and the way it interacts with other atoms. For instance, the reason why the first ionization energy of Titanium (Ti) is higher than Barium (Ba) is closely linked to their electron configurations. Ti has its valence electrons in the 3d and 4s subshells, which are closer to the nucleus and more strongly bound compared to Ba's valence electrons in the 6s subshell, which are farther away and less tightly held due to additional shielding.

By understanding electron configurations, students can predict and explain why certain elements have higher or lower ionization energies based on the positioning of their valence electrons and the overall structure of their electron cloud.

Effective Nuclear Charge

The concept of effective nuclear charge is fundamental when discussing ionization energies. It describes the net positive charge experienced by an electron in a multi-electron atom. The actual nuclear charge is always positive due to protons in the nucleus, but not all of this positive charge effectively reaches an electron due to repulsion and shielding by other electrons.

As you move across a period in the periodic table, the effective nuclear charge increases. This is because protons are added to the nucleus, pulling electrons closer and increasing the energy required to remove an electron. For example, Chlorine (Cl) has a higher first ionization energy than Germanium (Ge), even though they're in the same period. Cl's valence electrons feel a stronger effective nuclear charge since it has more protons and fewer inner shell electrons to shield the valence electrons from the nucleus.

Understanding the concept of effective nuclear charge allows students to explain the periodic trends in ionization energies and rationalize why, within the same period, an element like Cl will have a higher ionization energy compared to elements like Ge, which are located on the left.

Periodic Trends

Periodic trends are patterns that are observed within the periodic table that illustrate various aspects of an element's characteristics. The first ionization energy trend is a key example of this, and it generally increases across a period and decreases down a group.

Across a period, the nuclear charge increases with each additional proton, and electrons are added to the same energy level without much increase in electron shielding. This results in a stronger attraction between the electrons and nucleus, hence a higher ionization energy. For instance, Copper (Cu) has a higher first ionization energy than Silver (Ag) because it lies to the left of Ag within the same period, enjoying an increasing nuclear charge without a substantial increase in shielding.

Down a group, the outermost electrons are farther from the nucleus due to an additional shell, which means more shielding and a decrease in the effective nuclear charge. Consequently, the ionization energy decreases. That's why Antimony (Sb) has a higher first ionization energy than Lead (Pb), as Sb lies above Pb in the group.

The understanding of periodic trends is immensely valuable for students as it allows them to predict and explain the behavior of elements simply based on their position in the periodic table.