Energy, Stability, and Probability

Before diving straight into the chemical properties of atoms and molecules, we are going to take a brief detour to discuss the concept of stability. In chemistry, stability has a very specific meaning. A system is said to be chemically stable when it is in its lowest energy state. A system that is chemically stable will stay in the same state until something from the outside changes the system.

One useful way to visualize stability is through the hills and valleys of an energy diagram. Imagine that you are a ball, and the green line above represents the energy profile of the different “states” you can have (or occupy). Six of these states are labeled. Where on this diagram could you stop at and remain in that state for any length of time? Clearly, states 1, 4, and 6 are out. If you were to come to a stop in state 1, you would immediately start “rolling” down toward state 2. If you were to come to a stop in either state 4 or 6, you would immediately start rolling down toward state 5. All three of those states are unstable in the sense that you cannot stay in them for more than a moment.

On the other hand, states 2, 3, and 5 are stable in the sense that you can stop in those states and stay in them for at least a little while. However, of those three states, only state 5 is considered chemically stable. Why? Because state 5 is the lowest energy state on our energy diagram, and moving from state 5 to any other state would take energy. In terms of chemical stability, states 2 and 3 are considered “metastable.” As a ball, you could theoretically stop in state 3 (it would be difficult but not impossible), but the tiniest disturbance would send you down toward either state 2 or state 5. State 2 is far more stable than state 3. Little disturbances would not be enough to knock you out of your valley, but a larger disturbance could. Going from state 2 to state 5 does take some initial energy to get you over the hill in state 3, but then it would be all downhill from there. Overall, going from state 2 to state 5 releases energy, while going from state 5 to state 2 takes energy. And over time, systems tend to move toward greater stability (lower energy states).

Stable forms of hydrogen

Hydrogen, by itself, typically exists in one of six states: hydrogen atoms (H), hydrogen anions (H-), hydrogen cations (H+), dihydrogen cations (H2+), trihydrogen cations (H3+), and diatomic hydrogen molecules (H2). [Dihydrogen and trihydrogen cations can be found in the interstellar medium, the matter between star systems.] Because ions are either positively or negatively charged, they are, at best, metastable. Ions quickly attract oppositely charged particles and take on new forms.

H- + H+ → H2
A hydrogen anion (H-) will attract positive hydrogen cations (H+) and form a hydrogen molecule (H2).
H+ + e- → H
H+ + H- → H2
A hydrogen cation (H+) will attract either negative free electrons (e-) or negative hydrogen anions (H-) and form a hydrogen atom (H) or a hydrogen molecule (H2).
H2+ + e- → H2
H2+ + H2 → H3+ + H
A dihydrogen cation (H2+) will attract negative free electrons (e-) and form a hydrogen molecule (H2). It can also run into a hydrogen molecule and form a trihydrogen cation (H3+) and a hydrogen atom (H).
H3+ + e- → H2 + H
H3+ + e- → H + H + H
A trihydrogen cation (H3+) will attract negative free electrons (e-) and decompose into either one hydrogen molecule (H2) and one hydrogen atom (H), or three hydrogen atoms. It will not be able to exist as a triatomic hydrogen molecule (H3) because that form of hydrogen is unstable and breaks down immediately.

Surprisingly, hydrogen atoms are also not very stable. When two hydrogen atoms meet, they will quickly form a hydrogen molecule [ H + H → H2 ]. The only places where you will typically find free hydrogen atoms are where the temperature is above 2000 K or in the interstellar medium. At temperatures above 2000 K, hydrogen has enough energy to jump easily from the low energy hydrogen molecule state to the higher energy hydrogen atom state (e.g., from state 5 to state 3). In the interstellar medium, the hydrogen atoms are so far apart that they do not meet all that often. However, when they do meet, they will form hydrogen molecules.

Diatomic hydrogen molecules are the chemically stable form of hydrogen. It takes quite a bit of energy to move hydrogen from its diatomic molecule state to another state. [Water (H2O) is more stable than H2, but you need oxygen to form water.]

Stable atoms

Even though atoms are the building blocks of matter, they are not particularly stable. Because they are not very stable, atoms tend to join (bond) with other atoms to form stable molecules. Of the 118 types of atoms in the periodic table, only six of them are chemically stable. [Ununquadium (atomic number 114) and ununoctium (atomic number 118) atoms may possibly be chemically stable, but those atoms have not been isolated long enough for us to properly study them.]

Helium atom (4He)
Neon atom (20Ne)
Argon atom (40Ar)
Krypton atom (84Kr)
Xenon atom (132Xn)

These six elements are collectively known as the noble gases and, except for helium, they all have eight electrons in their outermost shell. Helium cannot have eight electrons in its outermost shell because its outermost shell is the first electron shell, and that shell can only hold a maximum of two electrons.

Ionization energy and electron affinity

One way to analyze the stability of an atom is to measure how hard it is to add or remove an electron from it. Elements change chemical states by adding and removing electrons, and an atom that does not accept or lose electrons is very stable. An atom’s ionization energy is the amount of energy it takes to remove an electron from the atom. The higher the ionization energy, the harder it is to remove an electron. An atom’s electron affinity is the amount of energy it takes to remove an extra electron once one has been captured. The lower the electron affinity, the less likely an atom is to accept an additional electron (any additional electrons it may happen to capture are quickly and easily removed).

atom number of electrons 1st electron shell 2nd electron shell 3rd electron shell ionization energy
(1 × 10-18 J)
lithium 3 2 1 - 0.86
beryllium 4 2 2 - 1.49
boron 5 2 3 - 1.33
carbon 6 2 4 - 1.80
nitrogen 7 2 5 - 2.33
oxygen 8 2 6 - 2.18
fluorine 9 2 7 - 2.79
neon 10 2 8 - 3.46
sodium 11 2 8 1 0.82
magnesium 12 2 8 2 1.23

As the number of electrons in the outermost shell increases, it becomes increasingly harder to remove an electron from an atom. It takes 2-4 times as much energy to remove an electron from a neon atom compared to a lithium, beryllium, boron, or carbon atom. The ionization energy peaks with neon and its eight outermost electrons, and then drops down again with sodium and its one outermost electron.

atom number of electrons 1st electron shell 2nd electron shell 3rd electron shell electron affinity
(1 × 10-18 J)
oxygen 8 2 6 - 0.23
fluorine 9 2 7 - 0.54
neon 10 2 8 - ≈0.00
sodium 11 2 8 1 0.09

Although it is almost as hard to remove an electron from a fluorine atom as a neon atom, a fluorine atom will hold onto an additional electron while a neon atom will not. So a fluorine atom may not lose an electron easily, but it will accept an electron easily. Of all of the elements listed, neon is the only atom that neither accepts nor loses electrons easily. This is a chemical property shared by all six noble gas atoms, and it is why those atoms are chemically stable when others are not.

Ionization Energy and the Periodic Table
Stability, probability, and dynamic systems

Just because a state has the lowest energy and is chemically stable does not mean that all of the atoms will occupy that state. Like all dynamic systems, it is a matter of probability.

In this example, state 3 is chemically stable. However, if your system consists of many, many atoms, then you may easily find atoms in all five stable (or metastable) states. State 3 is simply the most probable state. Increasing the overall energy of the system increases the probability that atoms will occupy the higher-energy states. This is why, at low temperatures, it is very rare to find free hydrogen atoms [almost all of the hydrogen atoms will be chemically bound in the form of diatomic hydrogen molecules (H2)]. But at temperatures higher than 2000 K, you will find many free hydrogen atoms in addition to diatomic hydrogen molecules. The higher the temperature, the more free hydrogen atoms you will find.

While the probability of an individual state may be extremely low (e.g., states 2 and 4), it is worth remembering that we are dealing with massive numbers of atoms. One mole of atoms, which is not very many, is 6.022 × 1023 atoms. The probability of flipping a coin and getting sixty heads in a row may be incredibly small (≈0.0000000000000001%), but if you had 6.022 × 1023 people each flipping a coin, about 500,000 of them would get sixty heads in a row.