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Q4.6:
Name the oxometal anions of the first series of the transition metals in which the metal exhibits the oxidation state equal to its group number.

Solution :

Step 1: Identifying the Transition Metal Series

The first series of transition metals corresponds to the $3d$ series, spanning from Scandium ($Z=21$) to Zinc ($Z=30$). The objective is to identify oxometal anions where the oxidation state ($O.S.$) of the metal is numerically equivalent to its Group number in the Periodic Table.

Step 2: Analytical Matrix of Group Numbers and Oxidation States

To determine the oxometal anions, we must evaluate the maximum oxidation state of elements in Groups 3 through 7, as higher groups (8–12) do not typically form stable oxoanions where the oxidation state equals the group number.

Group Element Max Oxidation State (Group Number) Oxometal Anion Calculation of O.S. ($x$)
6 Chromium ($Cr$) +6 Chromate ($CrO_4^{2-}$) $x + 4(-2) = -2 \Rightarrow x = +6$
6 Chromium ($Cr$) +6 Dichromate ($Cr_2O_7^{2-}$) $2x + 7(-2) = -2 \Rightarrow 2x = 12 \Rightarrow x = +6$
7 Manganese ($Mn$) +7 Permanganate ($MnO_4^-$) $x + 4(-2) = -1 \Rightarrow x = +7$

Step 3: Justification of Findings

  • For Chromium ($Cr$): Chromium belongs to Group 6. In $CrO_4^{2-}$ and $Cr_2O_7^{2-}$, the oxidation state of $Cr$ is $+6$. [Per the rules of oxidation number determination, the sum of oxidation states in an ion must equal the net charge of the ion].
  • For Manganese ($Mn$): Manganese belongs to Group 7. In $MnO_4^-$, the oxidation state of $Mn$ is calculated as: $x + 4(-2) = -1$, yielding $x = +7$. This matches the Group 7 designation. [Based on the electronic configuration $3d^5 4s^2$, $Mn$ can utilize all seven valence electrons for bonding].

Step 4: Geometric Representation of Primary Anions

Chromate (CrO₄²⁻) Cr O Permanganate (MnO₄⁻) Mn O

Step 5: Synthesis of Conclusion

The transition metals of the first series that form oxoanions where the oxidation state equals the group number are Chromium ($Group\ 6$) and Manganese ($Group\ 7$). The specific species are the Chromate ion ($CrO_4^{2-}$), the Dichromate ion ($Cr_2O_7^{2-}$), and the Permanganate ion ($MnO_4^-$).

Final Solution: The oxometal anions are the Chromate ion ($CrO_4^{2-}$), the Dichromate ion ($Cr_2O_7^{2-}$), and the Permanganate ion ($MnO_4^-$).


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