Problem 46 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

(a) Ba, because its valence electrons are farther from the nucleus and experience less attraction, resulting in a smaller ionization energy. (b) Ag, due to similar electron configurations but higher effective nuclear charge for Ag and its valence electron being farther from the nucleus. (c) Ge, because it has a higher effective nuclear charge, more shielding electrons, and Cl having more stability due to an incomplete 3p subshell. (d) Pb, as it has a higher effective nuclear charge, but its valence electrons are farther from the nucleus and experience the shielding effect of 4f¹⁴ and 5d¹⁰ subshells.

Step 1: (a) Compare Ti and Ba

Electron Configuration: Ti: [Ar] 4s² 3d² Ba: [Xe] 6s² Effective Nuclear Charge: Ti: Z = 22 Ba: Z = 56 Although Ba has a higher effective nuclear charge, its electrons are farther from the nucleus (6th energy level) compared to Ti (4th energy level). Thus we can say that Ba has a smaller first ionization energy than Ti.

Step 2: (b) Compare Ag and Cu

Electron Configuration: Ag: [Kr] 5s¹ 4d¹⁰ Cu: [Ar] 4s¹ 3d¹⁰ Effective Nuclear Charge: Ag: Z = 47 Cu: Z = 29 Ag and Cu have similar electron configurations, but Ag has a higher effective nuclear charge and its valence electron is farther from the nucleus (5th energy level) compared to Cu (4th energy level). Thus we can say that Ag has a smaller first ionization energy than Cu.

Step 3: (c) Compare Ge and Cl

Electron Configuration: Ge: [Ar] 4s² 3d¹⁰ 4p² Cl: [Ne] 3s² 3p⁵ Effective Nuclear Charge: Ge: Z = 32 Cl: Z = 17 Ge has a higher effective nuclear charge and has more shielding electrons in the completely filled 3d subshell. On the other hand, Cl has one electron less than a complete 3p subshell, which gives it more stability. Thus we can say that Ge has a smaller first ionization energy than Cl.

Step 4: (d) Compare Pb and Sb

Electron Configuration: Pb: [Xe] 4f¹⁴ 5d¹⁰ 6s² 6p² Sb: [Kr] 4d¹⁰ 5s² 5p³ Effective Nuclear Charge: Pb: Z = 82 Sb: Z = 51 Pb has a higher effective nuclear charge, but its valence electrons are farther from the nucleus (6th energy level) compared to Sb (5th energy level), and it has the shielding effect of 4f¹⁴ and 5d¹⁰ subshells. Thus we can say that Pb has a smaller first ionization energy than Sb.

Key Concepts

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom's orbital. Every element has its unique electron configuration that tells us where its electrons reside in different energy levels or shells.
Understanding electron configuration helps us determine the behavior of an element during chemical reactions, including its ionization energy. In general:

• The lower the energy level (or shell), the closer the electrons are to the nucleus.
• The presence of electrons in an inner shell can block or shield outer electrons, affecting how tightly the outermost (valence) electrons are held.

For example, in the elements like Titanium (Ti) and Barium (Ba), their electron configurations are written as:

• Ti: [Ar] 4s² 3d²
• Ba: [Xe] 6s²

Analyzing these, we find that titanium's valence electrons are in the 4th energy level, whereas barium's electrons are further out in the 6th level, affecting their ionization energy. Essentially, the setup of electron configuration allows us to predict elemental properties based on which electrons are more available to interact or react. By examining the configuration, we can infer trends in the periodic table and understand differences in elements.

Effective Nuclear Charge

Effective nuclear charge (Z_{eff}) is a concept that describes the net positive charge experienced by valence electrons. It accounts for the actual nuclear charge (Z) minus the effect of electron shielding.The formula used is:\[Z_{eff} = Z - S\]Here:

• Z is the atomic number, indicating the number of protons in the nucleus.
• S is the shielding constant which reflects the screening or shielding by inner electrons.

The higher the effective nuclear charge,

• the more strongly the nucleus attracts its electrons, affecting properties like ionization energy.

For instance, comparing silver (Ag) and copper (Cu):

• Ag: Z_{eff} = 47
• Cu: Z_{eff} = 29

Although silver has a higher effective nuclear charge, its electrons are further away, leading to lower ionization energy compared to copper.Understanding effective nuclear charge helps clarify why electrons behave as they do. It’s a central idea that links the forces inside an atom to its chemical activity and trends observed across the periodic table.

Shielding Effect

The shielding effect refers to the reduction in effective nuclear charge on the electron cloud, due to the presence of other electrons closer to the nucleus. Electrons in inner shells repel outer electrons:

• This repulsion diminishes the nucleus's pull on the outer electrons.
• Results in easier removal of valence electrons, thus decreases ionization energy.

For example, when we look at lead (Pb) and antimony (Sb):

• Pb has its valence electrons in the 6th energy level, experiencing significant shielding from full inner shells like 4f ¹⁴ and 5d ¹⁰ .
• Sb has valence electrons in the 5th energy level, with slightly less shielding.

This increased shielding in lead means its outer electrons are less tightly held than those of antimony, hence the smaller ionization energy.
The concept of shielding is crucial in understanding many aspects of chemistry, particularly why certain atoms lose electrons more readily or have different trends in ionization energies. It ties directly into how we predict and rationalize chemical reactivity.