Question

What is the electron configuration for the transition metal ion in each of the following compounds? a. \(K_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\) b. \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}\) c. \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{2}\) d. \(\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\right] \mathrm{I}\)

Short answer

The electron configurations for the transition metal ions in the given compounds are: a. Fe^3+: \(1s^22s^22p^63s^23p^63d^5\) b. Ag^+: \(1s^22s^22p^63s^23p^64s^23d^{10}4p^64d^{10}\) c. Ni^2+: \(1s^22s^22p^63s^23p^63d^7\) d. Cr^+: \(1s^22s^22p^63s^23p^63d^5\)

Step-by-step solution

Compound a: \(K_{3}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]\)

1. The central transition metal ion is Fe. 2. Since there are three potassium ions (K) with a charge of +1 each, the complex must have a -3 charge. The charge on the Fe ion is +3. 3. Iron (Fe) has an atomic number of 26. Its electron configuration is \(1s^22s^22p^63s^23p^64s^23d^6\). 4. Adjust the electron configuration for a +3 charge on the Fe ion: remove 3 electrons from the 4s and 3d orbitals. The electron configuration for Fe^3+ is \(1s^22s^22p^63s^23p^63d^5\).

Compound b: \(\left[\mathrm{Ag}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}\)

1. The central transition metal ion is Ag. 2. Since there is one chloride ion (Cl) with a charge of -1, the complex must have a +1 charge. The charge on the Ag ion is +1. 3. Silver (Ag) has an atomic number of 47. Its electron configuration is \(1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}\). 4. Adjust the electron configuration for a +1 charge on the Ag ion: remove 1 electron from the 5s orbital. The electron configuration for Ag^+ is \(1s^22s^22p^63s^23p^64s^23d^{10}4p^64d^{10}\).

Compound c: \(\left[\mathrm{Ni}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]\mathrm{Br}_{2}\)

1. The central transition metal ion is Ni. 2. Since there are two bromide ions (Br) with a charge of -1 each, the complex must have a +2 charge. The charge on the Ni ion is +2. 3. Nickel (Ni) has an atomic number of 28. Its electron configuration is \(1s^22s^22p^63s^23p^64s^23d^8\). 4. Adjust the electron configuration for a +2 charge on the Ni ion: remove 2 electrons from the 4s and 3d orbitals. The electron configuration for Ni^2+ is \(1s^22s^22p^63s^23p^63d^7\).

Compound d: $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NO}_{2}\right)_{2}\right] \mathrm{I}$

1. The central transition metal ion is Cr. 2. Since there is one iodide ion (I) with a charge of -1, the complex must have a +1 charge. The charge on the Cr ion is +1. 3. Chromium (Cr) has an atomic number of 24. Its electron configuration is \(1s^22s^22p^63s^23p^64s^13d^5\). 4. Adjust the electron configuration for a +1 charge on the Cr ion: remove 1 electron from the 4s orbital. The electron configuration for Cr^+ is \(1s^22s^22p^63s^23p^63d^5\).

Key concepts

Iron (Fe) Electron Configuration

Iron, a common transition metal, is located in the middle of the periodic table with an atomic number of 26. This means it has 26 electrons in its neutral state. The electron configuration of neutral iron is written as: \[ 1s^22s^22p^63s^23p^64s^23d^6 \] However, in its ionized state, such as in the compound \( K_{3}[\text{Fe}(\text{CN})_{6}] \), iron is often found in a +3 oxidation state. For iron to achieve this oxidation state (Fe\(^{3+}\)), it must lose three electrons. Typically, electrons are removed first from the 4s orbital and then from the 3d orbital. Thus, the electron configuration for Fe\(^{3+}\) is:\[ 1s^22s^22p^63s^23p^63d^5 \] Here, the 4s orbitals lose two electrons, followed by one electron loss from the 3d orbital, resulting in a stable half-filled 3d subshell (5 electrons). This configuration illustrates the typical loss of 4s electrons before 3d, a notable characteristic of transition metals.

Silver (Ag) Electron Configuration

Silver is another important transition metal with an atomic number of 47. This means, in its neutral state, silver has 47 electrons. The electron configuration of a neutral silver atom is:\[ 1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10} \] In the compound \( [\text{Ag}(\text{NH}_{3})_{2}] \text{Cl} \), silver is found in a +1 oxidation state. When silver forms Ag\(^{+}\), it loses an electron from the 5s orbital, leading to the electron configuration:\[ 1s^22s^22p^63s^23p^64s^23d^{10}4p^64d^{10} \] This configuration notably shows that, even after losing one electron, the 4d subshell remains completely filled with 10 electrons. This provides a stable electron arrangement that contributes to many of silver's chemical properties. Silver's propensity to maintain a filled d subshell illustrates its unique electron behavior among transition metals.

Nickel (Ni) Electron Configuration

Nickel is positioned to play a crucial role in transition metal chemistry due to its placement in the middle of the periodic table with an atomic number of 28. Its neutral electron configuration is:\[ 1s^22s^22p^63s^23p^64s^23d^8 \] In various compounds, such as \( [\text{Ni}(\text{H}_{2} \text{O})_{6}] \text{Br}_{2} \), nickel often adopts a +2 oxidation state. For Ni\(^{2+}\), nickel loses two electrons primarily from the 4s orbital and one from the 3d orbital, resulting in the configuration:\[ 1s^22s^22p^63s^23p^63d^8 \] The remaining electrons in the 3d orbital account for nickel's magnetic properties and ability to form complex compounds. The transition metals' general tendency is to lose 4s electrons first, which makes this electronic rearrangement occur smoothly.

Chromium (Cr) Electron Configuration

Chromium is noted for its unique electron distribution and varied oxidation states. This element, with an atomic number of 24, has an electron configuration in its ground state of:\[ 1s^22s^22p^63s^23p^64s^13d^5 \] Chromium prefers a half-filled 3d subshell and a single electron in the 4s subshell due to the stability associated with half-filled electron shells. In compounds like \( [\text{Cr}(\text{H}_{2} \text{O})_{4}(\text{NO}_{2})_{2}] \text{I} \), chromium most commonly appears as Cr\(^{3+}\). Upon ionizing, chromium loses its 4s electron and two 3d electrons, leaving the 3d shell half-filled, which leads to the electron configuration:\[ 1s^22s^22p^63s^23p^63d^5 \] This electron configuration illustrates chromium’s flexibility in forming different ions. By achieving a half-filled 3d orbitals, chromium stabilizes itself, demonstrating its unique electronic structure compared to other transition metals. This half-filled subshell provides stability, making chromium an interesting study in transition state behavior.