Which element has a greater second electron affinity, sulfur or oxygen?

Question

I found a question asking the above which states that sulfur has a lesser second electron affinity than oxygen. But since the inter-electronic repulsion in sulfur is lesser, shouldn't it be willing to take up another electron more easily than an oxygen ion with a -1 charge?

Answer 1

The most important fact here is that the electron added to $\ce{S-}$ goes into an $n=3$ orbital ($3p$), whereas the one added to $\ce{O-}$ goes into an $n=2$ orbital ($2p$).

The larger $n=3$ orbitals are further from the nucleus and hence experience a weaker attraction to the nucleus and are much higher in energy. This dependence with quantum number scales approximately $E\sim - n^{-2}$ so is very important [1].

The dependance of orbital energy also scales quadratically with effective nuclear charge, however effective nuclear charges falls significantly compared to the true nuclear charge due to shielding and repulsion from other electrons. A common first order approximation for the effective nuclear charge is given by Slater's rules [2]

Combining these two approximations we can calculate very approximate orbital energies.

$$ \begin{align}E_{2p}(\ce{O^2+}) & {} = - R_\infty h c \frac{Z_{eff}^2}{n^2} \\ & {} = - R_\infty h c \frac{(8-4.15)^2}{2^2} \\ & {} = - 3.7 \text{ Ry} \\ E_{3p}(\ce{S^2+}) & {} = - R_\infty h c \frac{Z_{eff}^2}{n^2} \\ & {} = - R_\infty h c \frac{(16-11.25)^2}{3^2} \\ & {} = - 2.5 \text{ Ry} \end{align} $$

Where 1 Ry is the electronic energy of a hydrogen atom.

As you can see, to first order, the energy of the new electron is much lower when added to $\ce{O-}$ than when added to $\ce{S-}$, leading to a more favourable electron affinity for $\ce{O-}$ than $\ce{S-}$, driven by the fact that the orbital occupied has a lower principal quantum number $n$

[1] - See the energy of a hydrogenic ion - Wikipedia.

[2] - Slater's rules - Wikipedia

Answer 2

Sulfur has 3 shells while oxygen has 2.This increase in shell reduces the nuclear charge and lessens the second I.P.Further Explanation:

Due to the extra shell, the electron in the outermost shell is held , but not as strongly as an oxygen atom has held its electron. So the second Ionization Enthalpy of sulfur will be less than that of Oxygen,because more energy is required to extract the electron from oxygen atom.