Correct Order of First and Second Ionisation Enthalpy for Chromium and Manganese

To determine the correct order of the first ($\Delta_i H_1$) and second ($\Delta_i H_2$) ionisation enthalpies for Chromium ($\text{Cr}$) and Manganese ($\text{Mn}$), we analyze their electronic configurations:

$\text{Cr } (Z = 24): [\text{Ar}] 3d^5 4s^1$ $\text{Mn } (Z = 25): [\text{Ar}] 3d^5 4s^2$

1. First Ionisation Enthalpy ($\Delta_i H_1$)

• For $\text{Mn}$, the first electron is removed from a fully filled $4s^2$ orbital. Additionally, $\text{Mn}$ has a higher effective nuclear charge ($Z = 25$) than $\text{Cr}$ ($Z = 24$).
• For $\text{Cr}$, removing one electron from $4s^1$ leads to a highly stable, half-filled $d$-orbital configuration ($\text{Cr}^+: 3d^5$).
• As a result, less energy is required to ionize $\text{Cr}$ compared to $\text{Mn}$: $\Delta_i H_1 (\text{Cr}) = 652 \text{ kJ mol}^{-1}$ $\Delta_i H_1 (\text{Mn}) = 717 \text{ kJ mol}^{-1}$

Thus, the order of first ionisation enthalpy is: $\Delta_i H_1 : \text{Mn} > \text{Cr} \quad \text{(Statement C is correct)}$

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2. Second Ionisation Enthalpy ($\Delta_i H_2$)

• Consider the electronic configurations of the monopositive cations: $\text{Cr}^+ : [\text{Ar}] 3d^5$ $\text{Mn}^+ : [\text{Ar}] 3d^5 4s^1$
• For $\text{Cr}^+$, removing the second electron requires breaking the extra-stable half-filled $3d^5$ configuration, which requires a very large amount of energy.
• For $\text{Mn}^+$, the second electron is removed from the $4s^1$ orbital, resulting in the formation of the stable $3d^5$ configuration in $\text{Mn}^{2+}$.
• Experimental values confirm this trend: $\Delta_i H_2 (\text{Cr}) = 1592 \text{ kJ mol}^{-1}$ $\Delta_i H_2 (\text{Mn}) = 1509 \text{ kJ mol}^{-1}$

Thus, the order of second ionisation enthalpy is: $\Delta_i H_2 : \text{Cr} > \text{Mn} \quad \text{(Statement B is correct)}$

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Conclusion

Statements B and C are correct, which corresponds to the option B and C only.