Problem 45 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cu}^{2+}\) (b) \(\mathrm{Ca}^{2+},(\mathbf{c}) \mathrm{N}^{3-}\) (d) \(\mathrm{Ru}^{2+}\), (e) \(\mathrm{H}^{-}\).

Step-by-Step Solution

Answer

The electron configurations for the given ions are: (a) \(\mathrm{Cu}^{2+}\): [Ar] \(3d^9\) (b) \(\mathrm{Ca}^{2+}\): [Ar] (c) \(\mathrm{N}^{3-}\): [He] \(2s^2 2p^6\) (d) \(\mathrm{Ru}^{2+}\): [Kr] \(4d^6\) (e) \(\mathrm{H}^{-}\): \(1s^2\) The ions \(\mathrm{Ca}^{2+}\), \(\mathrm{N}^{3-}\), and \(\mathrm{H}^{-}\) have noble-gas configurations.

Step 1: Determine the atomic numbers

To write electron configurations, we need to find the atomic number of each element mentioned. Atomic numbers correspond to the number of protons in their nucleus, which also determines the number of electrons in the neutral atom. Here are the atomic numbers for the elements in question: Cu: 29 Ca: 20 N: 7 Ru: 44 H: 1 Next, we will use these atomic numbers to determine the electron configurations for each ion.

Step 2: Write electron configurations for each ion

To write electron configurations for these ions, we first need to know the number of electrons in each ion. We can determine this by referring to the atomic numbers and adding or subtracting the charge of each ion. (a) \(\mathrm{Cu}^{2+}\): 29 - 2 = 27 electrons (b) \(\mathrm{Ca}^{2+}\): 20 - 2 = 18 electrons (c) \(\mathrm{N}^{3-}\): 7 + 3 = 10 electrons (d) \(\mathrm{Ru}^{2+}\): 44 - 2 = 42 electrons (e) \(\mathrm{H}^{-}\): 1 + 1 = 2 electrons Now we can write electron configurations for each ion: (a) \(\mathrm{Cu}^{2+}\): [Ar] \(3d^9\) (b) \(\mathrm{Ca}^{2+}\): [Ar] (c) \(\mathrm{N}^{3-}\): [He] \(2s^2 2p^6\) (d) \(\mathrm{Ru}^{2+}\): [Kr] \(4d^6\) (e) \(\mathrm{H}^{-}\): \(1s^2\)

Step 3: Determine which ions have noble-gas configurations

We can now compare the electron configurations of each ion to the noble gases in order to determine which ions have noble-gas configurations. The noble gases are Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and Radon (Rn), and they possess completely filled electron shells. (a) \(\mathrm{Cu}^{2+}\): [Ar] \(3d^9\) - Not a noble-gas configuration (b) \(\mathrm{Ca}^{2+}\): [Ar] - Noble-gas configuration (Argon) (c) \(\mathrm{N}^{3-}\): [He] \(2s^2 2p^6\) - Noble-gas configuration (Neon) (d) \(\mathrm{Ru}^{2+}\): [Kr] \(4d^6\) - Not a noble-gas configuration (e) \(\mathrm{H}^{-}\): \(1s^2\) - Noble-gas configuration (Helium) The ions \(\mathrm{Ca}^{2+}\), \(\mathrm{N}^{3-}\), and \(\mathrm{H}^{-}\) have noble-gas configurations.

Key Concepts

Noble-Gas Configuration

A noble-gas configuration is a term used in chemistry to describe the electron arrangement of an atom or ion that has completely filled outer electron shells, similar to the noble gases. Noble gases such as Helium (He), Neon (Ne), and Argon (Ar) are extremely stable due to these full electron shells, making their configurations a desirable state for other elements to achieve through gaining, losing, or sharing electrons.

When writing electron configurations for ions, achieving a noble-gas configuration indicates that the ion has reached a very stable electronic state. This can often be seen in ions that either lose or gain electrons to have the same number of electrons as the nearest noble gas.

• For example, the \(\mathrm{Ca}^{2+}\) ion has a configuration of [Ar], indicating a noble-gas configuration due to its correspondence to Argon.
• The \(\mathrm{N}^{3-}\) ion, with a configuration of [He] \(2s^2 2p^6\), also illustrates a noble-gas configuration, echoing the electron arrangement of Neon.

Atomic Numbers

Atomic numbers serve as a fundamental feature in chemistry. They are unique to every element and correspond to the number of protons in the nucleus of an atom of the element. In a neutral atom, the atomic number also equals the number of electrons. Recognizing the atomic number is crucial when developing electron configurations, especially for ions that vary in their number of electrons due to their charge.

For instance, to find the electron configuration of an ion, you first identify the atom's atomic number, giving you the number of electrons in the neutral atom. Upon verifying the charge, adjustments are made to reflect the total number of electrons for the ion's state:

• For \(\mathrm{Cu}^{2+}\), with an atomic number of 29, the electron count becomes 27, accounting for the +2 charge.
• Conversely, \(\mathrm{N}^{3-}\), originally with 7 electrons, gains 3 more, resulting in 10 electrons total, echoing Neon’s electron configuration.

By tracking atomic numbers, you can accurately determine how many electrons are present and shape precise electron configurations for diverse ions.

Ions

Ions are atoms or molecules that have gained or lost one or more electrons, acquiring either a positive or negative charge. This process of losing or gaining electrons changes the overall electron count in the atom, differentiating them from their neutral states. The formation of ions helps elements achieve more stable electronic configurations, often reaching a noble-gas configuration.

Ions can be categorized as:

• Cations: Positively charged ions formed by losing electrons. This generally occurs with metals. For example, \(\mathrm{Ca}^{2+}\) loses two electrons to achieve a stable [Ar] configuration.
• Anions: Negatively charged ions resulting from electron gain. \(\mathrm{N}^{3-}\) becomes an anion by gaining three electrons, thus replicating a noble-gas configuration matching Neon.

Why are ions important?
Understanding ions and their configurations plays a key role in explaining many chemical reactions and bonding processes. Through ions, elements can form compounds, reach stability, and exhibit the diverse range of chemical behavior and properties seen in everyday materials and reactions.