Problem 20 - Chemistry: The Central Science

Question

Write electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cd}^{2+}\), (b) \(\mathrm{P}^{3-}\), (c) \(\mathrm{Zr}^{4+}\), (d) \(\mathrm{Ru}^{3+}\), (e) \(\mathrm{As}^{3-}\), (f) \(\mathrm{Ag}^{+}\).

Step-by-Step Solution

Answer

The ions with noble-gas configurations are: (a) \(\mathrm{Cd}^{2+}\): [Kr]4d¹⁰ (b) \(\mathrm{P}^{3-}\): [Ne] (c) \(\mathrm{Zr}^{4+}\): [Kr]4d² (e) \(\mathrm{As}^{3-}\): [Kr] (f) \(\mathrm{Ag}^{+}\): [Kr]4d¹⁰

Step 1: Identify Atomic Number and Number of Electrons in Each Ion

First, we must find the atomic number of each given element from the periodic table and calculate the number of electrons for each ion based on their charge: (a) Cadmium (Cd), Atomic Number = 48, Electrons in Cd2+ ion = 48 - 2 = 46 (b) Phosphorus (P), Atomic Number = 15, Electrons in P3- ion = 15 + 3 =18 (c) Zirconium (Zr), Atomic Number = 40, Electrons in Zr4+ ion = 40 - 4 = 36 (d) Ruthenium (Ru), Atomic Number = 44, Electrons in Ru3+ ion = 44 - 3 = 41 (e) Arsenic (As), Atomic Number = 33, Electrons in As3- ion = 33 + 3 = 36 (f) Silver (Ag), Atomic Number = 47, Electrons in Ag+ ion = 47 - 1 = 46

Step 2: Write Electron Configurations Using the Aufbau Principle

Using the Aufbau Principle, we will write electron configurations for each ion: (a) Cd2+: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ (b) P3-: 1s² 2s² 2p⁶ 3s² 3p⁶ (c) Zr4+: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d² (d) Ru3+: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d⁷ (e) As3-: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ (f) Ag+: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d¹⁰

Step 3: Compare with Electron Configurations of Noble Gases

Finally, let's compare the electron configurations of each ion with the electron configurations of noble gases to determine which ions have noble-gas configurations: (a) Cd2+: [Kr]4d¹⁰ (Kr stands for Krypton, a noble gas) (b) P3-: [Ne] (c) Zr4+: [Kr]4d² (d) Ru3+: Does not match any noble gas electron configuration (e) As3-: [Kr] (f) Ag+: [Kr]4d¹⁰

Step 4: Conclusion

The ions with noble-gas configurations are: (a) \(\mathrm{Cd}^{2+}\) (b) \(\mathrm{P}^{3-}\) (c) \(\mathrm{Zr}^{4+}\) (e) \(\mathrm{As}^{3-}\) (f) \(\mathrm{Ag}^{+}\)

Key Concepts

Understanding Ions

When discussing atoms, ions are a fundamental concept. An ion is simply an atom that has lost or gained electrons, which results in a net charge. There are two types of ions: cations and anions. Cations are positively charged ions that form when an atom loses one or more electrons. For instance,

• Cadmium ion Cd\(^{2+}\) results when Cadmium loses two electrons.
• Silver ion Ag\(^{+}\) is formed by losing one electron.

Anions, on the other hand, are negatively charged ions formed when an atom gains electrons. Examples include:

• Phosphorus ion P\(^{3-}\), which gains three electrons.
• Arsenic ion As\(^{3-}\), also gaining three electrons.

Understanding how atoms become ions is crucial, as it helps explain their electronic configurations and reactions. By calculating the difference between the protons and electrons, we determine the ionic charge of each atom.

Noble-Gas Configurations

Noble-gas configurations refer to the electron configuration that corresponds to that of a noble gas. Noble gases are elements in Group 18 of the periodic table, well known for their stability. This stability arises because their outermost electron shell is full. Atoms frequently gain, lose, or share electrons in chemical reactions to achieve this same stability.

• For example, Cd\(^{2+}\) with its electron configuration \([Kr] 4d^{10}\) matches that of Krypton, a noble gas.
• Similarly, P\(^{3-}\) has the configuration of Neon, \([Ne]\).
• Conversely, Ru\(^{3+}\) does not achieve any noble-gas configuration, indicating it doesn't achieve the same stable electron shell.

When an ion matches the electron configuration of a noble gas, it achieves lower energy and increased stability. This is why such configurations are often the 'goal' of ion formation in atoms.

Exploring the Periodic Table

The periodic table is a powerful tool that organizes all known elements based on their atomic number, electron configurations, and recurring chemical properties.

• The elements are arranged into periods (rows) and groups (columns).
• The recurring pattern of electron configurations shapes the layout of the table.
• Noble gases located in Group 18 play a crucial role in understanding the stability of electron configurations.

To write electron configurations, like those of ions in the exercise, we refer to this table, following the order set by the Aufbau principle. This principle dictates how electrons populate atomic orbitals, sequentially filling lower energy levels before moving to higher ones. Electrons fill orbitals in a specific order, typically observed as:

• 1s, 2s, 2p,
• 3s, 3p, 4s, 3d, 4p,
• 5s, 4d, 5p, etc.

By understanding the periodic table, one can predict the electron configurations of ions and whether they will share configurations with noble gases. This insight allows chemists to foresee the reactivity and bonding habits of various elements.