Electronic Configuration, Oxidation States, and Ionization Energy of First Transition Series

Electronic Configuration of the First Transition Series Elements

• Location in the Periodic Table:

  • Located in the 4th period, immediately following calcium ($_{20}\text{Ca}$).

  • Consists of ten elements with atomic numbers $Z = 21$ through $Z = 30$.

• Orbital Filling Rules (Hund's Rule and Aufbau Principle):

  • The five orbitals of the $(3d)$ sublevel are filled successively with single electrons first across the elements from scandium ($_{21}\text{Sc}$) to manganese ($_{25}\text{Mn}$), which attains the half-filled $3d^5$ configuration.

  • Electron pairing within the $(3d)$ orbitals commences at iron ($_{26}\text{Fe}$) and continues sequentially until the $(3d)$ sublevel is completely filled at zinc ($_{30}\text{Zn}$) with the $3d^{10}$ configuration.

• Ground-State Electronic Configurations ($Z = 21$ to $30$):

  • Scandium ($_{21}\text{Sc}$): $[\text{Ar}]\,4s^2\,3d^1$

  • Titanium ($_{22}\text{Ti}$): $[\text{Ar}]\,4s^2\,3d^2$

  • Vanadium ($_{23}\text{V}$): $[\text{Ar}]\,4s^2\,3d^3$

  • Chromium ($_{24}\text{Cr}$): $[\text{Ar}]\,4s^1\,3d^5$ (Anomalous configuration)

  • Manganese ($_{25}\text{Mn}$): $[\text{Ar}]\,4s^2\,3d^5$

  • Iron ($_{26}\text{Fe}$): $[\text{Ar}]\,4s^2\,3d^6$

  • Cobalt ($_{27}\text{Co}$): $[\text{Ar}]\,4s^2\,3d^7$

  • Nickel ($_{28}\text{Ni}$): $[\text{Ar}]\,4s^2\,3d^8$

  • Copper ($_{29}\text{Cu}$): $[\text{Ar}]\,4s^1\,3d^{10}$ (Anomalous configuration)

  • Zinc ($_{30}\text{Zn}$): $[\text{Ar}]\,4s^2\,3d^{10}$

• Number of Unpaired (Single) Electrons in Neutral Atoms:

  • Scandium ($\text{Sc}$): 1 unpaired electron

  • Titanium ($\text{Ti}$): 2 unpaired electrons

  • Vanadium ($\text{V}$): 3 unpaired electrons

  • Chromium ($\text{Cr}$): 6 unpaired electrons (1 electron in $4s$ + 5 electrons in $3d$)

  • Manganese ($\text{Mn}$): 5 unpaired electrons

  • Iron ($\text{Fe}$): 4 unpaired electrons

  • Cobalt ($\text{Co}$): 3 unpaired electrons

  • Nickel ($\text{Ni}$): 2 unpaired electrons

  • Copper ($\text{Cu}$): 1 unpaired electron (1 electron in $4s$)

  • Zinc ($\text{Zn}$): 0 unpaired electrons

• Anomalous Electronic Configurations (Chromium and Copper):

  • Chromium ($_{24}\text{Cr}$):

  • Expected Configuration: $[\text{Ar}]\,4s^2\,3d^4$

  • Actual Configuration: $[\text{Ar}]\,4s^1\,3d^5$

  • Reason: Transferring one electron from $4s$ to $3d$ creates a half-filled $3d^5$ sublevel and a half-filled $4s^1$ subshell, lowering the total energy of the atom and maximizing thermodynamic stability.

  • Copper ($_{29}\text{Cu}$):

  • Expected Configuration: $[\text{Ar}]\,4s^2\,3d^9$

  • Actual Configuration: $[\text{Ar}]\,4s^1\,3d^{10}$

  • Reason: Transferring one electron from $4s$ to $3d$ produces a completely filled $3d^{10}$ sublevel, which provides extra stability to the atom.

Formation and Configurations of Transition Metal Cations

• General Rule for Cation Formation:

  • When a transition element atom oxidizes to form an ion, electrons are lost first from the $4s$ subshell, which is located in the outermost principal energy level ($n = 4$) furthest from the nucleus.

  • Subsequent electrons are lost sequentially from the inner $(3d)$ subshell ($n = 3$).

• Procedure for Reverting Cations to Neutral Atoms:

  • To determine the neutral parent atom from a given cation configuration, add the total number of lost electrons (indicated by the charge) back into the subshells.

  • Always fill the $4s$ subshell first up to 2 electrons (or 1 electron in anomalous cases) before adding remaining electrons to the $3d$ subshell, taking stability exceptions ($d^5$ and $d^{10}$) into consideration.

• Detailed Cation Configuration Examples:

  • Titanium ($_{22}\text{Ti}$): $[\text{Ar}]\,4s^2\,3d^2$

  • $\text{Ti}^{2+}$: $[\text{Ar}]\,4s^0\,3d^2$

  • $\text{Ti}^{3+}$: $[\text{Ar}]\,4s^0\,3d^1$

  • $\text{Ti}^{4+}$: $[\text{Ar}]\,4s^0\,3d^0$

  • Cobalt ($_{27}\text{Co}$): $[\text{Ar}]\,4s^2\,3d^7$

  • $\text{Co}^{2+}$: $[\text{Ar}]\,4s^0\,3d^7$

  • $\text{Co}^{4+}$: $[\text{Ar}]\,4s^0\,3d^5$

  • Iron Cation Conversion ($_{26}\text{Fe}^{3+} \rightarrow {_{26}\text{Fe}}$):

  • Ion Configuration: $_{26}\text{Fe}^{3+}: [\text{Ar}]\,4s^0\,3d^5\n * Reversion Process: Add 3 electrons back (2 electrons to 4s$, 1 electron to$3d).\n * Neutral Element Configuration: $_{26}\text{Fe}: [\text{Ar}]\,4s^2\,3d^6

  • Manganese Cation Conversion ($_{25}\text{Mn}^{2+} \rightarrow {_{25}\text{Mn}}$):

  • Ion Configuration: $_{25}\text{Mn}^{2+}: [\text{Ar}]\,4s^0\,3d^5\n * Reversion Process: Add 2 electrons back (both go to 4s).\n * Neutral Element Configuration: $_{25}\text{Mn}: [\text{Ar}]\,4s^2\,3d^5

  • Chromium Cation Conversion ($_{24}\text{Cr}^{6+} \rightarrow {_{24}\text{Cr}}$):

  • Ion Configuration: $_{24}\text{Cr}^{6+}: [\text{Ar}]\,4s^0\,3d^0\n * Reversion Process: Add 6 electrons back.\n * Incorrect Naive Result: [\text{Ar}]\,4s^2\,3d^4$(unstable$3d^4 configuration).\n * Correct Neutral Configuration: [\text{Ar}]\,4s^1\,3d^5$(half-filled$3d^5 extra stability).\n * Copper Cation Conversion (_{29}\text{Cu}^{2+} \rightarrow {_{29}\text{Cu}}):\n * Ion Configuration: $_{29}\text{Cu}^{2+}: [\text{Ar}]\,4s^0\,3d^9

  • Reversion Process: Add 2 electrons back.

  • Incorrect Naive Result: $[\text{Ar}]\,4s^2\,3d^9$ (unstable $3d^9$ configuration).

  • Correct Neutral Configuration: $[\text{Ar}]\,4s^1\,3d^{10}$ (completely filled $3d^{10}$ extra stability).

Stability and Redox Behavior of Transition Metal Ions

• Relative Stability of $d$-Sublevel Electronic Configurations:

  • An atom or ion achieves maximum electronic stability when its $(d)$ sublevel adopts one of three specific configurations:

  • Completely empty ($d^0$)

  • Completely filled ($d^{10}$)

  • Half-filled ($d^5$)

  • General order of relative stability: $d^0 > d^{10} > d^5$

• Examples of Specific Stable Species:

  • Empty $d^0$ States: $\text{Sc}^{3+}, \text{Ti}^{4+}, \text{V}^{5+}, \text{Cr}^{6+}, \text{Mn}^{7+}$

  • Completely Filled $d^{10}$ States: $\text{Cu}, \text{Cu}^+, \text{Zn}, \text{Zn}^{2+}$

  • Half-Filled $d^5$ States: $\text{Cr}, \text{Mn}^{2+}, \text{Fe}^{3+}, \text{Co}^{4+}$

• Influence of Electronic Stability on Redox Reactions:

  • Oxidation of Iron(II) to Iron(III):

  • Reaction Process: ${_{26}\text{Fe}} ([\text{Ar}]\,4s^2\,3d^6) \xrightarrow{-2e^-} \text{Fe}^{2+} ([\text{Ar}]\,3d^6) \xrightarrow{-e^-} \text{Fe}^{3+} ([\text{Ar}]\,3d^5)$

  • Feasibility: Iron(II) is easily oxidized to Iron(III) because $\text{Fe}^{3+}$ contains a half-filled $3d^5$ sublevel, which possesses higher stability than the $3d^6$ configuration of $\text{Fe}^{2+}$. Redox reactions spontaneously proceed toward the formation of the more stable chemical species.

  • Oxidation of Manganese(II) to Manganese(III):

  • Reaction Process: ${_{25}\text{Mn}} ([\text{Ar}]\,4s^2\,3d^5) \xrightarrow{-2e^-} \text{Mn}^{2+} ([\text{Ar}]\,3d^5) \xrightarrow{-e^-} \text{Mn}^{3+} ([\text{Ar}]\,3d^4)$

  • Feasibility: Manganese(II) is resistant to oxidation and does not easily convert to Manganese(III). $\text{Mn}^{2+}$ is already in a highly stable half-filled $3d^5$ state; removing an electron to form $\text{Mn}^{3+}$ ($3d^4$) disrupts this stable arrangement.

• Summary of Favorable and Unfavorable Redox Transitions:

  • Easy Transitions (Proceed Spontaneously Toward $d^0, d^5, d^{10}$):

  • $\text{Fe}^{2+} \rightarrow \text{Fe}^{3+}$ (forms $3d^5$)

  • $\text{Mn}^{3+} \rightarrow \text{Mn}^{2+}$ (forms $3d^5$)

  • $\text{Ti}^{3+} \rightarrow \text{Ti}^{4+}$ (forms $3d^0$)

  • $\text{Co}^{3+} \rightarrow \text{Co}^{4+}$ (forms $3d^5$)

  • Difficult Transitions (Resisted, Moving Away from Stability):

  • $\text{Mn}^{2+} \rightarrow \text{Mn}^{3+}$ (disrupts $3d^5$)

  • $\text{Ti}^{4+} \rightarrow \text{Ti}^{3+}$ (disrupts $3d^0$)

  • $\text{Co}^{4+} \rightarrow \text{Co}^{3+}$ (disrupts $3d^5$)

  • $\text{Fe}^{3+} \rightarrow \text{Fe}^{2+}$ (disrupts $3d^5$)

• Key Limitation Caveat:

  • While empty ($d^0$), half-filled ($d^5$), or fully filled ($d^{10}$) sublevels provide substantial stability, subshell occupancy is not the sole factor governing total compound stability in solution or solid states. Other thermodynamic parameters such as hydration energy, lattice energy, and bond formation enthalpy play significant roles.

Oxidation States Across the First Transition Series

• Tabular Overview of Groups, Configurations, and Oxidation States:

  • Scandium ($_{21}\text{Sc}$): Group $\text{IIIB}$ | Config: $[\text{Ar}]\,4s^2\,3d^1$ | Oxidation State: $+3$ | Compounds: $\text{Sc}_2\text{O}_3$, $\text{ScCl}_3$

  • Titanium ($_{22}\text{Ti}$): Group $\text{IVB}$ | Config: $[\text{Ar}]\,4s^2\,3d^2$ | Oxidation States: $+2, +3, +4$ | Compounds: $\text{TiO}_2$

  • Vanadium ($_{23}\text{V}$): Group $\text{VB}$ | Config: $[\text{Ar}]\,4s^2\,3d^3$ | Oxidation States: $+2, +3, +4, +5$ | Compounds: $\text{V}_2\text{O}_5$, $\text{VO}$

  • Chromium ($_{24}\text{Cr}$): Group $\text{VIB}$ | Config: $[\text{Ar}]\,4s^1\,3d^5$ | Oxidation States: $+2, +3, +6$ | Compounds: $\text{Cr}_2\text{O}_3$, $\text{CrO}_3$

  • Manganese ($_{25}\text{Mn}$): Group $\text{VIIB}$ | Config: $[\text{Ar}]\,4s^2\,3d^5$ | Oxidation States: $+2, +3, +4, +6, +7$ | Compounds: $\text{MnO}_2$, $\text{KMnO}_4$

  • Iron ($_{26}\text{Fe}$): Group $\text{VIII}$ | Config: $[\text{Ar}]\,4s^2\,3d^6$ | Oxidation States: $+2, +3, +6$ | Compounds: $\text{FeCl}_2$, $\text{Fe}_2\text{O}_3$

  • Cobalt ($_{27}\text{Co}$): Group $\text{VIII}$ | Config: $[\text{Ar}]\,4s^2\,3d^7$ | Oxidation States: $+2, +3, +4$ | Compounds: $\text{CoCl}_2$, $\text{CoCl}_4^{2-}$

  • Nickel ($_{28}\text{Ni}$): Group $\text{VIII}$ | Config: $[\text{Ar}]\,4s^2\,3d^8$ | Oxidation States: $+2, +3, +4$ | Compounds: $\text{NiO}$, $\text{NiO}_2$

  • Copper ($_{29}\text{Cu}$): Group $\text{IB}$ | Config: $[\text{Ar}]\,4s^1\,3d^{10}$ | Oxidation States: $+1, +2$ | Compounds: $\text{Cu}_2\text{O}$, $\text{CuO}$, $\text{CuSO}_4$

  • Zinc ($_{30}\text{Zn}$): Group $\text{IIB}$ | Config: $[\text{Ar}]\,4s^2\,3d^{10}$ | Oxidation State: $+2$ | Compounds: $\text{ZnO}$

• Core Principles and Systemic Trends:

  • Uniqueness of Copper: Copper ($_{29}\text{Cu}$) is the only element in the first transition series that exhibits a $+1$ oxidation state.

  • Universal $+2$ State Exception: All elements from titanium to zinc exhibit a $+2$ oxidation state by losing the two electrons of the $4s$ subshell. Scandium ($_{21}\text{Sc}$) is the sole exception; it exhibits exclusively a single oxidation state of $+3$, which results in a completely empty $3d^0$ sublevel matching the argon core.

  • Maximum Oxidation State in Groups 3B through 7B: Elements from Group $\text{IIIB}$ (scandium) to Group $\text{VIIB}$ (manganese) attain their maximum oxidation state by losing all valence electrons in both the $4s$ and $3d$ subshells. In these groups, the maximum oxidation state equals the group number.

  • Post-Manganese Behavior (Iron to Zinc): From iron onwards, atoms do not lose all $4s$ and $3d$ electrons because increased effective nuclear charge holds the inner $d$-electrons more tightly. Consequently, their maximum oxidation states do not equal their group numbers or total valence electron count.

  • Trend in Maximum Oxidation States: Maximum oxidation state increases progressively from scandium ($+3$) to reach a peak at manganese ($+7$ in Group $\text{VIIB}$), after which it decreases step-wise down to zinc ($+2$ in Group $\text{IIB}$).

  • Group Number Rule and Exception: The highest oxidation state of any transition element does not exceed its group number, with the singular exception of Group $\text{IB}$ (Coinage metals: Copper, Silver, Gold), where Copper reaches $+2$ (and Gold reaches $+3$), exceeding their group number of 1.

  • Cause of Variable Oxidation States: Transition metals show variable oxidation states because the $ns$ and $(n-1)d$ sublevels are close in energy, permitting the continuous, sequential removal of valence electrons under chemical reaction conditions.

Ionization Energies of Transition Metals

• Definition:

  • Ionization potential (ionization energy) is the precise energy required to remove an electron completely from an isolated gaseous atom or ion in its ground state.

• Gradual Increase Across Successive Ionization Energies:

  • Unlike representative metals which show sudden massive jumps between shell removals, transition metals display a gradual, progressive increase in ionization energies across consecutive oxidation states.

  • Reason: Electrons are removed successively from $4s$ and $3d$ subshells that are close in energy. As each electron is removed, the net positive charge increases while nuclear charge stays constant, resulting in a higher effective nuclear charge ($Z_{\text{eff}}$). This increases electrostatic attraction on the remaining electrons, steadily increasing the energy needed for further ionization.

• Successive Ionization Potentials of Vanadium ($_{23}\text{V}$):

  • $1^{\text{st}}\text{ Ionization Energy } (\text{V} \rightarrow \text{V}^+): 648\,\text{kJ\,mol}^{-1}$

  • $2^{\text{nd}}\text{ Ionization Energy } (\text{V}^+ \rightarrow \text{V}^{2+}): 1364\,\text{kJ\,mol}^{-1}$

  • $3^{\text{rd}}\text{ Ionization Energy } (\text{V}^{2+} \rightarrow \text{V}^{3+}): 2858\,\text{kJ\,mol}^{-1}$

  • $4^{\text{th}}\text{ Ionization Energy } (\text{V}^{3+} \rightarrow \text{V}^{4+}): 4643\,\text{kJ\,mol}^{-1}$

  • $5^{\text{th}}\text{ Ionization Energy } (\text{V}^{4+} \rightarrow \text{V}^{5+}): 6523\,\text{kJ\,mol}^{-1}$

• Large Energy Jumps (Disrupting Noble Gas Cores):

  • A disproportionately large jump in ionization energy occurs when attempting to remove an electron from a completely filled inner principal energy shell (noble gas configuration).

  • Representative Metal Comparisons:

  • Sodium ($_{11}\text{Na}$):

    • $1^{\text{st}}\text{ IE} = 496\,\text{kJ\,mol}^{-1}$

    • $2^{\text{nd}}\text{ IE} = 4562\,\text{kJ\,mol}^{-1}$ (Huge jump; breaking neon core prevents formation of $\text{Na}^{2+}$).

  • Magnesium ($_{12}\text{Mg}$):

    • $1^{\text{st}}\text{ IE} = 738\,\text{kJ\,mol}^{-1}$

    • $2^{\text{nd}}\text{ IE} = 1451\,\text{kJ\,mol}^{-1}$

    • $3^{\text{rd}}\text{ IE} = 7733\,\text{kJ\,mol}^{-1}$ (Huge jump; breaking neon core prevents formation of $\text{Mg}^{3+}$).

  • Aluminium ($_{13}\text{Al}$):

    • $1^{\text{st}}\text{ IE} = 578\,\text{kJ\,mol}^{-1}$

    • $2^{\text{nd}}\text{ IE} = 1811\,\text{kJ\,mol}^{-1}$

    • $3^{\text{rd}}\text{ IE} = 2745\,\text{kJ\,mol}^{-1}$

    • $4^{\text{th}}\text{ IE} = 11540\,\text{kJ\,mol}^{-1}$ (Huge jump; breaking neon core prevents formation of $\text{Al}^{4+}$).

  • Transition Metal Energy Jump (Scandium):

  • Scandium ($_{21}\text{Sc}$) possesses ionization energies: $1^{\text{st}} = 633\,\text{kJ\,mol}^{-1}$, $2^{\text{nd}} = 1235\,\text{kJ\,mol}^{-1}$, $3^{\text{rd}} = 2388\,\text{kJ\,mol}^{-1}$.

  • $4^{\text{th}}\text{ IE} = 7090\,\text{kJ\,mol}^{-1}$ (Extremely large jump because removing the 4th electron requires breaking the filled $3p^6$ argon sublevel, making $\text{Sc}^{4+}$ impossible to obtain under normal chemical reaction conditions).

Definition and Classification Criteria of Transition Elements

• Rigorous Definition of a Transition Element:

  • A transition element is defined as any element that has partially filled / incomplete $(d)$ or $(f)$ sublevel orbitals (containing 1 to 9 electrons in $d$, or 1 to 13 electrons in $f$) either in its elemental atomic state or in any of its common oxidation states.

• Classification of Coinage Metals (Group 1B: $\text{Cu}, \text{Ag}, \text{Au}$):

  • Coinage metals ARE classified as true transition elements.

  • Although their neutral atomic states have completely filled $d^{10}$ sublevels:

  • Copper ($_{29}\text{Cu}$): $[\text{Ar}]\,4s^1\,3d^{10}$

  • Silver ($_{47}\text{Ag}$): $[\text{Kr}]\,5s^1\,4d^{10}$

  • Gold ($_{79}\text{Au}$): $[\text{Xe}]\,6s^1\,4f^{14}\,5d^{10}$

  • In their higher oxidation states ($+2$ and $+3$), their $d$-sublevels become incompletely filled:

  • $\text{Cu}^{2+}$: $[\text{Ar}]\,3d^9$

  • $\text{Ag}^{2+}$: $[\text{Kr}]\,4d^9$

  • $\text{Au}^{3+}$: $[\text{Xe}]\,4f^{14}\,5d^8$

  • Because $d$-orbitals are partially filled in these oxidized states, they satisfy the definition of transition elements.

• Classification of Group 2B Elements ($\text{Zn}, \text{Cd}, \text{Hg}$):

  • Group $\text{IIB}$ elements ARE NOT classified as typical transition elements (they are non-transition representative metals).

  • Reason: Their $d$-sublevels remain completely filled ($d^{10}$) both in their neutral ground atomic states and in their sole oxidation state ($+2$):

  • Zinc ($_{30}\text{Zn}$): Ground state $[\text{Ar}]\,4s^2\,3d^{10}$, $\text{Zn}^{2+}: [\text{Ar}]\,3d^{10}$

  • Cadmium ($_{48}\text{Cd}$): Ground state $[\text{Kr}]\,5s^2\,4d^{10}$, $\text{Cd}^{2+}: [\text{Kr}]\,4d^{10}$

  • Mercury ($_{80}\text{Hg}$): Ground state $[\text{Xe}]\,6s^2\,4f^{14}\,5d^{10}$, $\text{Hg}^{2+}: [\text{Xe}]\,4f^{14}\,5d^{10}$

  • Because $d$-orbitals are never partially filled in any accessible state, they fall outside the definition of transition elements.

Worked Practice Problems and Applications

• Problem 1:

  • Question: What is the electronic configuration of the transition element in the oxide used as a catalyst in the Contact Process?

  • Solution:

  • The catalyst used in the Contact Process for manufacturing sulfuric acid is vanadium pentoxide ($\text{V}_2\text{O}_5$).

  • The transition element present is vanadium ($_{23}\text{V}$).

  • Neutral vanadium configuration: $_{23}\text{V}: [\text{Ar}]\,4s^2\,3d^3$

  • In $\text{V}_2\text{O}_5$, vanadium has an oxidation state of $+5$ ($\text{V}^{5+}$).

  • Cation configuration: $\text{V}^{5+}: [\text{Ar}]\,4s^0\,3d^0$

• Problem 2:

  • Question: What is the electronic configuration of the transition element in the compound used in cosmetics to block ultraviolet rays?

  • Solution:

  • The UV-blocking compound used in sunscreens/cosmetics is titanium dioxide ($\text{TiO}_2$).

  • The transition element present is titanium ($_{22}\text{Ti}$).

  • Neutral titanium configuration: $_{22}\text{Ti}: [\text{Ar}]\,4s^2\,3d^2$

  • In $\text{TiO}_2$, titanium has an oxidation state of $+4$ ($\text{Ti}^{4+}$).

  • Cation configuration: $\text{Ti}^{4+}: [\text{Ar}]\,4s^0\,3d^0$

• Problem 3:

  • Question: What is the electronic configuration of the transition element in the compound used as a fungicide and in water purification treatment?

  • Solution:

  • The compound used as a fungicide and water purification agent is copper(II) sulfate ($\text{CuSO}_4$).

  • The transition element present is copper ($_{29}\text{Cu}$).

  • Neutral copper configuration: $_{29}\text{Cu}: [\text{Ar}]\,4s^1\,3d^{10}$

  • In $\text{CuSO}_4$, copper has an oxidation state of $+2$ ($\text{Cu}^{2+}$).

  • Cation configuration: $\text{Cu}^{2+}: [\text{Ar}]\,4s^0\,3d^9$

• Problem 4:

  • Question: Write the step-by-step electronic configuration change when a neutral Cobalt atom ($_{27}\text{Co}$) oxidizes to Cobalt(IV) ($\text{Co}^{4+}$).

  • Solution:

  • Step 1 (Neutral atom): $_{27}\text{Co}: [\text{Ar}]\,4s^2\,3d^7$

  • Step 2 (Lose 2 electrons from $4s$ to form $\text{Co}^{2+}$): $_{27}\text{Co}^{2+}: [\text{Ar}]\,4s^0\,3d^7$

  • Step 3 (Lose 2 additional electrons from $3d$ to form $\text{Co}^{4+}$): $_{27}\text{Co}^{4+}: [\text{Ar}]\,4s^0\,3d^5$

• Problem 5:

  • Question: Write the electronic configuration change when a Chromium(III) ion ($\text{Cr}^{3+}$) gains 3 electrons to convert back into its neutral atomic state ($\text{Cr}$).

  • Solution:

  • Chromium(III) ion configuration: $_{24}\text{Cr}^{3+}: [\text{Ar}]\,4s^0\,3d^3$

  • Electron gain process: Add 3 electrons.

  • Neutral atomic configuration: $_{24}\text{Cr}: [\text{Ar}]\,4s^1\,3d^5$ (re-establishing the stable half-filled $3d^5$ configuration).

• Problem 6:

  • Question: In which of the following species does the transition element ion NOT show its highest known oxidation state?

  • A) $\text{CrO}_4^{2-}$

  • B) $\text{MnO}_4^-$

  • C) $\text{VO}_4^{3-}$

  • D) $\text{NiO}_2$ (or $\text{Ni}^{2+}$ ion)

  • Solution:

  • In $\text{CrO}_4^{2-}$, Chromium is $+6$ (highest state for Cr).

  • In $\text{MnO}_4^-$, Manganese is $+7$ (highest state for Mn).

  • In $\text{VO}_4^{3-}$, Vanadium is $+5$ (highest state for V).

  • For Nickel, the highest known oxidation state is $+4$. In ions or compounds where Nickel is $+2$ or $+3$, it is not showing its maximum oxidation state.

• Problem 7:

  • Question: Two elements $X$ and $Y$ are from the first transition series. The trivalent ion of each contains 3 unpaired electrons. When these two elements are melted together, an alloy is formed. What is the main application of this alloy?

  • A) Railway lines

  • B) Heating coils and electric ovens

  • C) Car springs

  • D) Coating iron handles

  • Solution:

  • Trivalent ion with 3 unpaired electrons:

    • Chromium(III) ($\text{Cr}^{3+}$): $[\text{Ar}]\,3d^3$ $\rightarrow$ 3 unpaired electrons.

    • Nickel(III) ($\text{Ni}^{3+}$): $[\text{Ar}]\,3d^7$ $\rightarrow$ 3 unpaired electrons ($d^7$ has 2 paired orbitals and 3 unpaired orbitals).

  • Melting Chromium ($\text{Cr}$) and Nickel ($\text{Ni}$) together forms a Nickel-Chromium (Nichrome) alloy.

  • Application: Nichrome alloy resists corrosion and oxidation even when red-hot, making it ideal for heating coils and electric ovens. Correct Answer: B.

Comprehensive Chapter Summary Map

• Summary concept map illustrating electronic configuration, stability rules, oxidation state trends, ionization energies, and element definitions across the first transition series: