Question

Which noble gas is isoelectronic with each of the following metal ions? (a) \(\mathrm{Sc}^{3+}\) (b) \(\mathrm{K}^{+}\) (c) \(\mathrm{Ti}^{4+}\) (d) \(\mathrm{Ba}^{2+}\)

Short answer

(a) 22week(ar): Ar; (b) 22week(ar): Ar; (c) 22week(ar): Ar; (d) 22week(xe): Xe.

Step-by-step solution

Understand Isoelectronic Species

Isoelectronic species are atoms and ions that have the same number of electrons. To find a noble gas that is isoelectronic with a given ion, determine the total number of electrons in the ion and find the noble gas with the same number of electrons.

Determine Electrons in Neutral Atoms

For each metal ion, first determine the number of electrons in its neutral atom. For example, a neutral Sc (atomic number 21) has 21 electrons, a neutral K (atomic number 19) has 19 electrons, Ti (atomic number 22) has 22 electrons, and Ba (atomic number 56) has 56 electrons.

Calculate Electrons in Ions

Subtract the charge of the ion from the number of electrons in the neutral atom to find the number of electrons in the ion. For Sc³⁺, subtract 3 electrons from Sc: 21 - 3 = 18 electrons. For K⁺, subtract 1 electron from K: 19 - 1 = 18 electrons. For Ti⁴⁺, subtract 4 electrons from Ti: 22 - 4 = 18 electrons. For Ba²⁺, subtract 2 electrons from Ba: 56 - 2 = 54 electrons.

Identify Isoelectronic Noble Gas

Using the electron counts from the previous step, find the noble gas with the same number of electrons. Sc³⁺, K⁺, and Ti⁴⁺ all have 18 electrons, which is the electron count of argon (22week(rlly)):Ar22week(rlly)(:22week(rlly)":Ar Ar390kation554ofBa²⁺withnewel(atdo)andth ofis53Ar38rhtajh 22week(rlly):Xe22week(rlly):54"

Key concepts

Noble Gases

Noble gases occupy Group 18 on the periodic table. These elements are renowned for their stability and non-reactivity due to their complete electron shells. For students learning chemistry, understanding noble gases provides essential insight into why certain atoms and ions strive to achieve similar configurations.

• Stability and Electron Configuration: Noble gases have full valence electron shells, either with eight electrons (octet rule) or, for helium, two electrons in the first shell. This configuration makes them stable and largely non-reactive, a condition other elements mimic when forming ions.
• Role in Chemical Bonds: Elements tend to lose, gain, or share electrons to reach a noble gas configuration, resulting in various ions and compounds. For instance, metals often lose electrons to achieve the electron count of a nearby noble gas.

Understanding noble gases is pivotal for comprehending why certain elements form specific ions. It anchors the concept of isoelectronic species, as ions with a similar electron count to noble gases exhibit concurrent stability.

Electron Count

Calculating the electron count in atoms and ions is a foundational skill in chemistry. This involves determining how changes in the electron configuration occur when atoms either gain or lose electrons, as seen with metal ions becoming isoelectronic with noble gases.

• Neutral Atoms: Each element, in its neutral state, has a specific number of electrons equal to its atomic number. For example, a neutral potassium atom (K) has 19 electrons.
• Forming Ions: When forming positive ions (cations), metals lose electrons. Scandium (Sc), with an atomic number of 21, becomes Sc³⁺ by losing 3 electrons, resulting in 18 electrons. This makes it isoelectronic with the noble gas argon.
• Isoelectronic Phenomenon: Ions like K⁺, when losing a single electron, also reach 18 electrons, showcasing that multiple elements can achieve isoelectronic states through different ionizations.

The concept of electron count is crucial in predicting and understanding atomic interactions, aiding in visualizing how and why different elements reach noble gas configurations.

Metal Ions

Metal ions play a significant role in chemistry, particularly when they lose electrons and form cations. Their tendency to achieve noble gas electron configurations explains much about their chemical reactivity and stability.

• Cation Formation: Metal atoms, which typically have few electrons in their outer shells, lose these electrons to form positively charged ions. For instance, barium (Ba) with its two valence electrons, forms Ba²⁺ by losing both, mimicking the electron configuration of xenon, a noble gas with 54 electrons.
• Reactivity and Associations: Metal ions readily participate in ionic bonding, crucial for the formation of salts and other compounds. The formation of these ions is driven by the pursuit of reduced energy states, like those of noble gases.
• Common Examples: Metal ions such as K⁺, Ti⁴⁺, or Ba²⁺ are paramount in various chemical reactions and are isoelectronic with noble gases—K⁺ with argon, Ti⁴⁺ with argon, and Ba²⁺ with xenon.

The transformation from neutral metal atoms to ions is key to understanding their behavior and interaction in chemical environments, extending beyond simple reactivity to structural and biological significance.