The Periodic Table: It's Kinky!

This past week my general chemistry class has covered electronic configurations, the development of the periodic table, and how certain atomic properties trend across the periodic table.

The periodic table has an organizational beauty. Unless you stare at the nitty-gritty.

The periodic table is powerful. In broad hand-waving sweeps. But the details are devilish.

If you look closely enough, the elements in the periodic table (excepting the hydrogen atom with its single electron) are idiosyncratic. Each is unique. Probed closely enough, the elements seem an unruly bunch, artificially constrained by a man-made construct. But there’s no doubt that the organizing principles in our modern periodic table are powerful and useful. That’s what I try to tell students.

The most useful broad division is to divide the elements into metals, non-metals and noble gases as I’ve illustrated below. Hydrogen (H) is considered a non-metal in this regard. The ‘metalloids’ can be treated as non-metals for the arguments made below. Note that we are considering the behavior of the elemental substances as they are found in nature at ambient temperatures and pressures.

Using these divisions, and ignoring subtleties for the moment, we can now broadly describe four broad groups of compounds. The noble gases do not form chemical bonds and remain stable as atoms. All other elements are unstable as atoms, so they combine with other atoms to become more stable. There are three possible combinations. Metals + Metals, Non-Metals + Non-Metals, Metals + Non-Metals. 

This gives rise broadly to three ‘types’ of compounds: metallic, covalent, ionic, respectively. Each of these types broadly have the same properties as shown below. 

That’s a very powerful organizing principle. With the periodic table’s help, I can start to predict the properties of different combinations of elements to form new and interesting compounds. At least broadly.

Why are the metals on the left and towards the bottom? Why are the non-metals on the right and towards the top? And why are the noble gases in the rightmost column? This is actually a tricky question. The defining property of a metal is probably its ability to conduct electricity as a pure element under ambient conditions. Why do metals conduct electricity? In chemistry class parlance, they have mobile charged particles, in this case electrons that can ‘freely’ move across the entire substance – from one atom to the next, and the next, and so on. But we are talking about the bulk property of a substance with gazillions of atoms ‘connected’ or chemically bonded in some way. The periodic table, on the other hand, is organized based on atomic properties. A single metal atom does NOT conduct electricity.

Stage left. Enter Ionization Energy.

The Ionization Energy (I.E.) is the energy required to remove an electron completely away from the influence of the atom’s nucleus, thus turning the atom into an ion. The first I.E. is the energy required to remove the electron that’s easiest to pull off. Remarkably the periodic table is arranged in such a way that the (first) I.E. increases going up a column and across a row. Thus, you could say that I.E. increases along a diagonal from the bottom left (lowest I.E.) to top right (highest I.E.). (Students in my class learn how to explain this trend.)

At this point, you could hand-wave an analogy. Metals should have low I.E.; they give up electrons more easily, requiring less energy, and that’s why you have mobile electrons and electrical conductivity. Notice how I slid from an atomic property to a bulk property. I explicitly tell the students I’m doing this in class. Now, it turns out that because we’ve covered the photoelectric effect in class two weeks prior, and I’ve hammered the point home that the work function of a metal (the energy required to eject an electron from an irradiated metal surface) is closely related to, but not exactly the same as I.E. because one is a bulk property and the other is an atomic property. My students have also compared these two numbers for the same element and see that the work function is smaller in magnitude compared to the atomic I.E.

Based on the I.E. trend, you should expect to see the diagonal separating metals and non-metals. Wow, that’s nice! Perhaps, not just coincidental. Furthermore, I.E. values give us ‘hard’ numbers allowing us to make quantitative predictions. They turn out to be very useful in a variety of contexts, including predicting what sorts of ionic compounds will form and what their most likely chemical formulae will be. Powerful stuff!

The companion to I.E. is the Electron Affinity (E.A.). It is the energy change when an electron (from far, far away) is added to a nucleus to form an ion. On the far right, the noble gases have zero or energetically unfavorable E.A., and that’s often used as an argument as to why they’re noble – it costs gobs of energy to give up an electron, there is no advantage in receiving an electron, so they’re already stable as they are. No close companions needed. The E.A. trends across the rest of the periodic table, however, are not so clean. 

You might expect that, excluding the noble gases, the bottom left should have the least energetically favorable E.A. and the top right the most energetically favorable E.A., since the definition of E.A. is kinda sorta* opposite to I.E. And you kinda sorta see that, except it’s not so clear. If you look at the actual values (picture below from the current G-Chem textbook we’re using), it looks like there’s all sorts of idiosyncracy going on at first glance. 

Plotting out these numbers (for the main group elements) below makes things a little clearer. Note that my axis has a minus sign in the name (–EA₁). You can see that the halogens (F, Cl, Br, I, At) do have the most favorable E.A., and that favorability increases across a row in the periodic table, but there is no clear trend down a column. There are also a bunch of zeroes contributing to the jaggedness of the graph. That’s because these unfavorable E.A. values can’t be easily measured. I would say there are kinks all over the place. There is some trend across a row but it’s kinky. Our current textbook doesn’t even try to graphically represent it (although some textbooks do).

But textbooks do display visual representations for I.E. because the trend is much cleaner. Here’s the one from our current textbook (in 3D-bar format). What a beautiful looking chart!

Except that if you look closely, you can see the kinks. I’ve plotted the appropriate graph below for the main group elements. The trends are still apparent. I.E. increases up a row and across a column in the periodic table.

It also becomes clearer that the kinks also follow a trend. Kinky-ness is trendy? I use the word ‘kink’ in class because the line actually looks like it has kinks. (I didn’t learn that the word has other shades of meaning until a number of years after I had been using the word and it became a habit.) The current textbook avoids such words and refers to the kinks as ‘anomalies’.

In a standard college-level G-Chem class, we delve into why the kinks are there. The standard argument for Kink #1 makes use of pictures such as the one shown below for why you see the I.E. of B is lower than Be, but then we’re back on track with C following the general trend. Kink #2 relies on Hund’s rule to explain why the I.E. of O is lower than N, but then we’re back on track with F following the general trend. My students have already been drilled about all orbital energies being pulled down as nuclear charge increases, so none of this is particularly complicated at this point in class. Orbitals are used in both these arguments (although I don’t think this one case justifies the teaching of orbitals in G-Chem).

The way I think about E.A. is that it’s kinda, sorta like the zeroth I.E. (with the opposite sign). I tell my students that if this analogy helps them, then great. If not, they can still memorize the standard definition. When you think about it this way, you can see why the magnitudes are smaller relative to the first I.E., and that the kinks kinda, sorta appear in the same places, but shifted by one. For a less jagged E.A. graph, you can potentially estimate what the unfavorable E.A. values are from quantum calculations. CCCBDB at NIST has these values. With the appropriate scales, the E.A. trend across a row (taking into account the minus sign) now looks somewhat like an I.E. trend across a row.

We could save ourselves the trouble in general chemistry and skip the kinks. After all, unless the student is a chemistry major, or someone who takes inorganic chemistry just for kicks (or kinks), these anomalies don’t come up when describing common examples of structure and reactivity. But on the other hand, it was seeing some of this strangeness in introductory chemistry and learning that there were deeper explanations for such anomalies, that lured me into chemistry. I was taking organic chemistry and a sophomore-level inorganic chemistry class when I realized that chemistry was by far the most interesting subject I was studying. And yes, learning about orbitals helped push me to major in chemistry. I saw the beauty and symmetry of molecules and their orbitals, and at the same time witnessing their power in predicting chemical stability and reactivity. I’ve also come to appreciate the beautiful, idiosyncratic, unique, unruly, elements, displayed in a powerful and useful artifact, discreetly holding its secrets, and waiting to be stumbled upon in joyful discovery!

*Hopefully you’ve seen why ‘kinda sorta’ (kind of, sort of) broad, hand-waving arguments are made all over the place in introductory chemistry classes after reading this post.

P.S. Except for the two pictures I explicitly mentioned as coming from the textbook, I made all the rest in PowerPoint.