HW 3.83

[Hannah Guo 3D]

3.81 Arrange the cations Rb+, Be2+, and Sr2+ in order of increasing polarizing power. Give an explanation of your arrangement.
3.83 Arrange the anions Cl-, Br-, N3-, and O2- in order of increasing polarizability and give reasons for your decisions.

According to HW 3.81, smaller, more highly charged cations have greater polarizing power (Be2+ > Sr2+ > Be2+).
So I put O2- > N3- > Cl- > Br- for 3.83, but the correct answer is O2- < N3- < Cl- < Br-. The solution manual explains that the polarizability increases as the ion gets larger and less electronegative. This explanation is a little contradicting with 3.81. Please explain why so.

Thank you very much!

[Christy Lee 2H]

Polarizing power and polarizability are opposites. Polarizing power refers to the cation's ability to pull electrons toward it, so when the atom is smaller, there are less electrons, so the anion will be closer to the nucleus and feel a stronger pull. Polarizability is how easily an atom's electron cloud can be pulled/distorted, so when the atom is bigger, the electron cloud is farther from the nucleus and can be distorted more easily.

[404995677]

So does that mean cations have higher polarization power, and anions have higher polarizability?

[Liam Maxwell 2E]

yes that is correct. I was a little confused with this problem as well. Originally I put Br->Cl->N3->O2 because I thought this described the trend of largest anion radius to smallest. Why are does oxygen go before nitrogen?

[Madeleine Farrington 1B]

I am confused for 3.83 why the polarizability of N^3- is greater than O^2-. I know that polarizability increases as an ion gets larger and less electronegative, but if both of these anions are in the same row of the table and have a full valence with the added electrons, aren't they the same size?

[Bianca Nguyen 1B]

Answering Madeleine’s question:

N3- and O2- are isoelectronic or have the same amount of electrons, which is 10. So to figure out which one is bigger, we have to look at the amount of protons. N3- has 7 protons while O2- has 8 protons, therefore O2- is going to have a smaller ionic radius because there is going to be a stronger pull on the electrons from the nucleus. Since O2- is smaller than N3-, it will thus have a lower polarizability than N3-. Hope that helps!

[Anna De Schutter - 1A]

Another way to look at it is that N is less electronegative than O which is another reason why N3- has a higher polarizability than O2- because the polarizability of an anion increases as its electronegativity decreases.

What I don't really understand is why do smaller cations have a higher polarizing power? I understand why more highly charged cations have a higher polarizing power but not why smaller ones do. Could someone explain this to me? Thank you!!

Anna De Schutter - section 1A

[Anisa Subbiah 14B 1L]

Smaller cations will have greater effective nuclear charge and their nucleus will have greater polarizing power, because they are smaller
For example comparing Na+ and K+, K+ has more protons but Na+ will have greater polarizing power because it is smaller.