 ### Understanding Periodic Trends

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.

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.

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

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.

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.