The number of paramagnetic metal complex species among [textCo(textNH_3)_6]^3+$[\text{Co}(\text{NH}_3)_6]^{3+}$, [textCo(textC_2textO_4)_3]^3-$[\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}$, [textMnCl_6]^3-$[\text{MnCl}_6]^{3-}$, [textMn(textCN)_6]^3-$[\text{Mn}(\text{CN})_6]^{3-}$, [textCoF_6]^3-$[\text{CoF}_6]^{3-}$, [textFe(textCN)_6]^3-$[\text{Fe}(\text{CN})_6]^{3-}$ and [textFeF_6]^3-$[\text{FeF}_6]^{3-}$ with same number of unpaired electrons is dots$\dots$.

### Related Formula textParamagnetic species: Complexes with unpaired electron count (n) > 0$$\text{Paramagnetic species: Complexes with unpaired electron count } (n) > 0$$ ### Core Logic Let's perform electron tracking across every entry using CFT parameters: 1. [textCo(textNH_3)_6]^3+$[\text{Co}(\text{NH}_3)_6]^{3+}$: textCo^3+$\text{Co}^{3+}$ (3d^6$3d^6$), textNH_3$\text{NH}_3$ is SFL implies t2g^6 e_g^0$\implies t{2g}^6 e_g^0$, unpaired electrons = 0$= 0$ (Diamagnetic). 2. [textCo(textC_2textO_4)_3]^3-$[\text{Co}(\text{C}_2\text{O}_4)_3]^{3-}$: textCo^3+$\text{Co}^{3+}$ (3d^6$3d^6$), Oxalate acts as SFL here implies t_2g^6 e_g^0$\implies t_{2g}^6 e_g^0$, unpaired electrons = 0$= 0$ (Diamagnetic). 3. [textMnCl_6]^3-$[\text{MnCl}_6]^{3-}$: textMn^3+$\text{Mn}^{3+}$ (3d^4$3d^4$), textCl^-$\text{Cl}^-$ is WFL implies t_2g^3 e_g^1$\implies t_{2g}^3 e_g^1$, unpaired electrons = 4$= 4$. 4. [textMn(textCN)_6]^3-$[\text{Mn}(\text{CN})_6]^{3-}$: textMn^3+$\text{Mn}^{3+}$ (3d^4$3d^4$), textCN^-$\text{CN}^-$ is SFL implies t_2g^4 e_g^0$\implies t_{2g}^4 e_g^0$, unpaired electrons = 2$= 2$. 5. [textCoF_6]^3-$[\text{CoF}_6]^{3-}$: textCo^3+$\text{Co}^{3+}$ (3d^6$3d^6$), textF^-$\text{F}^-$ is WFL implies t_2g^4 e_g^2$\implies t_{2g}^4 e_g^2$, unpaired electrons = 4$= 4$. 6. [textFe(textCN)_6]^3-$[\text{Fe}(\text{CN})_6]^{3-}$: textFe^3+$\text{Fe}^{3+}$ (3d^5$3d^5$), textCN^-$\text{CN}^-$ is SFL implies t_2g^5 e_g^0$\implies t_{2g}^5 e_g^0$, unpaired electrons = 1$= 1$. 7. [textFeF_6]^3-$[\text{FeF}_6]^{3-}$: textFe^3+$\text{Fe}^{3+}$ (3d^5$3d^5$), textF^-$\text{F}^-$ is WFL implies t_2g^3 e_g^2$\implies t_{2g}^3 e_g^2$, unpaired electrons = 5$= 5$. ### Step 1: Finding Common Electronic Counts Reviewing unpaired counts among paramagnetic entities: - n=1$n=1$: 1 complex ([textFe(textCN)_6]^3-$[\text{Fe}(\text{CN})_6]^{3-}$) - n=2$n=2$: 1 complex ([textMn(textCN)_6]^3-$[\text{Mn}(\text{CN})_6]^{3-}$) - n=4$n=4$: 2 complexes ([textMnCl_6]^3-$[\text{MnCl}_6]^{3-}$ and [textCoF_6]^3-$[\text{CoF}_6]^{3-}$) - n=5$n=5$: 1 complex ([textFeF_6]^3-$[\text{FeF}_6]^{3-}$) The highest matching sub-group frequency has a count of 2. ### Pattern Recognition CFT Shortcut tracking: For 3d^4$3d^4$ weak field and 3d^6$3d^6$ weak field systems, the unpaired counts identically match (n=4$n=4$). Spotting that textMn^3+text/WFL$\text{Mn}^{3+}\text{/WFL}$ and textCo^3+text/WFL$\text{Co}^{3+}\text{/WFL}$ both leave 4 electrons unpaired immediately provides the pair answer. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Chemistry: Coordination Compounds