Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Ti}^{2+},(\mathbf{b})\) (d) \(\mathrm{PO}^{2-}\), (f) \(\mathrm{V}^{3+}\) \(\mathrm{Br}^{-}\) (c) \(\mathrm{Mg}^{2+}\) (e) \(\mathrm{Pt}^{2+}\)

The titanium ion has an atomic number of 22, but due to the charge (+2), it loses two electrons. Therefore, Ti²⁺ has 20 electrons. Its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s². This matches the electron configuration of calcium (Ca, atomic number 20) and is not a noble-gas configuration, as it is different from the nearest noble gas, Argon (Ar, atomic number 18).

The bromine ion has an atomic number of 35 and gains one electron due to its negative charge. Therefore, Br⁻ has 36 electrons. Its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶. This matches the electron configuration of the noble gas Krypton (Kr, atomic number 36); thus, Br⁻ has a noble-gas configuration.

The magnesium ion has an atomic number of 12 and loses two electrons due to the charge (+2). Mg²⁺ has 10 electrons. Its electron configuration is 1s² 2s² 2p⁶. This matches the electron configuration of the noble gas Neon (Ne, atomic number 10); thus, Mg²⁺ has a noble-gas configuration.

Phosphorous (P) has an atomic number of 15. However, due to the charge (-2), it gains two electrons. Thus, PO₂⁻ has 17 electrons. The electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁵. This does not match the electron configuration of the nearest noble gas, Argon (Ar, atomic number 18); hence, PO₂⁻ does not have a noble-gas configuration.

Platinum (Pt) has an atomic number of 78. Due to its charge (+2), it loses two electrons. Thus, Pt²⁺ has 76 electrons. Its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f¹⁴ 5s² 5p⁶ 5d⁹. This does not match the electron configuration of the nearest noble gas, Xenon (Xe, atomic number 54); hence, Pt²⁺ does not have a noble-gas configuration.

Vanadium (V) has an atomic number of 23. Due to its charge(+3), it loses three electrons. Thus, V³⁺ has 20 electrons. Its electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s². This matches the electron configuration of calcium (Ca, atomic number 20) and is not a noble-gas configuration, as it is different from the nearest noble gas, Argon (Ar, atomic number 18). To summarize: - \(\mathrm{Ti}^{2+}\) does not have a noble-gas configuration - \(\mathrm{Br}^{-}\) has a noble-gas configuration - \(\mathrm{Mg}^{2+}\) has a noble-gas configuration - \(\mathrm{PO}^{2-}\) does not have a noble-gas configuration - \(\mathrm{Pt}^{2+}\) does not have a noble-gas configuration - \(\mathrm{V}^{3+}\) does not have a noble-gas configuration