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I have to compare the stability of the following transition metal cations: $\ce{Co^3+, Fe^3+, Cr^3+, Sc^3+}$ in aqueous solution. (Source: Joint Entrance Exam (JEE) 2013 Mains India)

The first thing I looked at were the ions' electronic configurations:

$$ \begin{align} \ce{Co^3+}:&\ce{[Ar] 3d^6}&\\ \ce{Fe^3+}:&\ce{[Ar] 3d^5}\\ \ce{Cr^3+}:&\ce{[Ar] 3d^3}\\ \ce{Sc^3+}:&\ce{[Ar] 3d^0}\\ \end{align} $$

It suggests that $\ce{Fe^3+}$ should be the most stable, but the answer key given for increasing stability instead is $\ce{Co^3+ < Fe^3+ < Cr^3+ < Sc^3+}$. This seems to suggest that lower number of d-electrons leads to more stability, but I am not sure why that is true.

I also thought of the fact that more water of hydration would probably lead to higher stability, and that depends on charge/radius ratio. However, that would suggest $\ce{Sc^3+}$ to be the least stable, but that isn't the case here.

So, what factor is at play instead? And why are the stabilizing factors of half-filled d-subshell and greater water of hydration ignored?


Update: As pointed out in the comments below, to narrow down the cases, we may look at the enthalpies of formation, Gibbs free energy of formation, or the standard electrode potential - whichever one of these is the most applicable to ions in aqueous solution - to compare their relative stability.

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    $\begingroup$ "Stability" is an ambiguous term, which can encompass a variety of things. This question is very vague. $\endgroup$ May 15 '18 at 6:39
  • $\begingroup$ @TanYongBoon Can you give some examples of the "variety of things"? $\endgroup$ May 15 '18 at 6:42
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    $\begingroup$ Stability could be either thermodynamic stability or kinetic stability. Even defining the term in this manner would still have some ambiguity, the stability could also be seen as how easy it is for the species to undergo particular reactions. Those reactions would then also need to be specified. $\endgroup$ May 15 '18 at 6:46
  • $\begingroup$ @TanYongBoon Correct me if I'm wrong, but thermodynamic stability and kinetic stability were defined when a reaction actually occurs (example). In my question instead I'm just comparing the stability of these free ions in the aqueous solution. $\endgroup$ May 15 '18 at 6:52
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    $\begingroup$ Yes. These terms refer to the relative ease of the chemical species undergoing reaction. How else could you define stability if you do not use a reaction as a yardstick for comparison? $\endgroup$ May 15 '18 at 6:56
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It is written in NCERT Chemistry class 12 "In a medium like water, d3 is more stable than d5 (see CFSE).

CFSE stands for Crystal Field Stabilisation Energy. Basically in water there are h2o molecules which complexate the ions. Assuming octahedral geometry the d orbitals split into d3 (lower in energy compared to barycentre) and d2 (higher in energy compared to barycentre). If you only fill the d3 then you would actually have a more stable configuration as compared to d5 situation where the e.g. levels would also be occupied.

This is a more prominent factor than half filled orbital stability. In $\ce{Co^3+}$ there are no stabilizations involved and hence it is least stable.

$\ce{Sc^3+}$ has a noble gas configuration and this dominates all effects in terms of stabilizing the ion.

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