From Gen Chem to Organic Chem, Pt. 5 – Understanding Periodic Trends

by James

in Chemical Bonds, Functional Groups, General Chemistry, Organic Chemistry 1, Understanding Electron Flow, Where Electrons Are

Let’s revisit a few terms that you learned back in Gen chem:

  1. ionization energy – the amount of energy required to remove an electron from an atom
  2. electronegativity – a measure of the ability of an atom to attract electrons toward itself
  3. electron affinity – the energy change when an electron is added to the neutral species to form a negative ion.
  4. atomic radius – a measure of the typical distance of the atom from the nucleus to the boundary of the electron cloud
  5. ionic radius – a measure of the distance across an atom’s ion in a crystal lattice.

What do these five properties have in common? They follow periodic trends.

What else do they have in common? Well, these trends can all be understood on an intuitive level by grasping the Coulomb equation.

1-coulomb copy

As we talked about earlier, the Coulomb equation is the equation that describes the force between two point charges. In the case of chemistry, we can use it to describe the attractive force felt between the positively charged nucleus and the negatively charged valence electrons. The magnitude of the force is determined by two things:

  1. Zeff, the effective nuclear charge (the nuclear charge adjusted for shielding by the electrons between the valence electrons and the nucleus)
  2. The distance d from the valence electrons to the nucleus. Like gravity, the magnitude of the force falls off proportionally to the square of the distance.  The distance from the electrons to the nucleus is largely determined by the fact that electrons inhabit a discrete set of energy levels (orbitals)  in the atom. Like attendees at an open-air concert, the seats closest to the action are taken first, while the latecomers must settle for a spot further away.

The Coulomb equation is going to be at a maximum when Zeff is big and d is small, and at a minimum when Zeff is small and d is big. Let’s make a little graph.

2-periodic_trends

Let’s look at the maximum and minimum cases and how they impact the terms mentioned above.

Zeff large, d small:

  • The force between the valence electrons and the nucleus is at its maximum.
  • electronegativity will be at a maximum
  • Electron affinity will be at a maximum (assuming there is room for another electron in the orbital).
  • ionization energy will also be at a maximum because the force between the nucleus and the valence electron is at its strongest.
  • atomic radius and ionic radius will be at a minimum (since the Zeff is larger, the electrons will be held at a distance closer to the nucleus)

What element best fits this condition? Fluorine.

Zeff small, d large:

  • The force between the valence electrons and the nucleus is at its minimum.
  • Electronegativity will be at a minimum
  • Electron affinity will be at a minimum
  • Ionization energy will be at a minimum
  • Atomic radius and ionic radius will be at a maximum.

What element best fits this condition? Cesium.

There’s also the two intermediate cases of low Zeff/small d and high Zeff/large d. These cases are exemplified by Lithium and Iodine respectively.

Let’s make this diagram again.

3-periodictrends-2

Cesium and fluorine are truly the two solitudes.

The take home message: periodic trends are extremely important for understanding chemistry, and they can be grasped intuitively as a function of the attraction between the nucleus and the valence electrons.

Note: there’s another periodic trend (which I didn’t go into here) called polarizability that reflects how tightly the electrons are held by the atom. As you might expect, polarizability increases with size. It helps to explain why, for example, I(–) is a weaker conjugate base than F(–) [and hence more stable]. We’ll get to this some other time.

A final note: to get the most out of understanding periodic trends, it’s best to compare these properties either across a row or across a column – i.e. changing one variable at a time. Changing both variables at once – for instance, trying to rationalize the electronegativity of carbon versus phosphorus – can lead to variable outcomes.

Next Post – From Gen Chem to Organic Chem, Part 6 – Lewis Structures

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{ 4 comments… read them below or add one }

T.Rathinavelu

I think:
“We need two charges in the numerator to use coulumb’s force equation.But there is only one charge,Zeff, in your equation.In case you are talking of “per electronic force” 1. It must be clearly mentioned.2.There may be more than one valence electron.3. ‘per charge force” is “electric field”, not force.”
Please clarify.
T.Rathinavelu

Reply

Jake P

I am trying to get a better understanding on my homework and the first question says, “Group the electrons for each element based on ionization energies. How many electrons are in each group? You can change the scale of the vertical axis to better differentiate between groups.” I have two questions. The first one is can I use the coulomb equation to find out how many electrons are in each group? My second question is what is a “vertical axis” in your terms.

Reply

James

Thanks for the comment – sorry for late response.

I don’t think you need to use the coulomb equation.
Vertical axis is ionization energy, horizontal axis is atomic number

– not exactly sure what is being asked, but the diagram is probably something like this:
http://ths.talawanda.org/~bramblen/classroom/Pictures/first%20ion.%20graph.JPG

Use this diagram to see the patterns in ionization energies.

Reply

Apurv

James, can you help me out?
My question is more of gen Chem and inorg. I want to know the periodic trend if lattice and hydration enthalpies. That is like a question on solubility order of different compounds. I mean, why are carbonates less soluble down the group while hydroxides solubility increases (or is it the other way round?). I actually have problem only in this aspect of inorg.
You have helped me a lot in org. Org wasn’t such fun before I reached this blog. Thanks for helping out so many students like me!

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