Intermediate Physics for Medicine and Biology: November 2024

In last week’s blog post about A Toy Model for Climate Change, I wrote

“The main constituents of the atmosphere—oxygen and nitrogen—are transparent to both visible and thermal radiation, so they don’t contribute to e_A [the fraction of the earth’s infrared radiation that the atmosphere absorbs]. Thermal energy is primarily absorbed by greenhouse gases. Examples of such gases are water vapor, carbon dioxide, and methane.”

I never discussed why oxygen and nitrogen are not greenhouse gasses, although water vapor and carbon dioxide are. Today, I’ll address this question.

Below is a list of gasses in our atmosphere and their abundance.

Nitrogen	N₂	78%
Oxygen	O₂	21%
Argon	Ar	1%
Carbon dioxide	CO₂	0.03%
Water vapor	H₂O	0–4%
Neon	Ne	18 ppm
Helium	He	5 ppm
Methane	CH₄	2 ppm
Krypton	Kr	1 ppm
Sulfur dioxide	SO₂	1 ppm
Hydrogen	H₂	0.5 ppm
Nitrous Oxide	N₂O	0.5 ppm

In order to absorb infrared radiation, a molecule must have a dipole moment that can oscillate with the same frequency as the infrared electromagnetic wave. Let’s look at these molecules case by case.

Nitrogen

Nitrogen (N₂) is diatomic; it consists of two nitrogen atoms bound together. Because the two atoms are the same, they share the electron charge equally. If there is no charge separation, then there is no dipole moment to oscillate at the frequency of the infrared radiation. Therefore, diatomic nitrogen—by far the most abundant molecule in our atmosphere, with nearly four out of every five molecules being N₂—does not absorb infrared radiation. It’s not a greenhouse gas.

Oxygen

About one out of every five molecules in the atmosphere is oxygen (O₂), which is also diatomic with two identical atoms. Like nitrogen, oxygen can’t absorb infrared radiation.

Argon

Almost one out of every hundred molecules in the atmosphere is argon (Ar). Argon is a nonreactive noble gas, so it consists of individual atoms. A single atom cannot have a dipole moment, so argon can’t absorb infrared radiation. Neither can the other noble gasses: neon, helium, and krypton.

Carbon dioxide

The next most abundant gas is carbon dioxide (CO₂), which makes up less than one tenth of one percent of the atmosphere. The above table lists the abundance of carbon dioxide as 0.03%, which corresponds to 300 parts per million (ppm). I must have gotten the 300 ppm value from an old source. Its concentration is now over 400 ppm and is increasing every year. The main cause of global warming is the rapidly increasing carbon dioxide concentration.

The carbon dioxide molecule has a linear structure; it has a central carbon atom surrounded by two oxygen atoms, one on each side, so the molecule forms a straight line. Perhaps instead of writing it as CO₂ we should write OCO. The electrons of this molecule are more attracted to the oxygen atoms than the carbon atom, so the carbon carries a partially positive charge and the two oxygen atoms each are partially negative. But because of its linear structure, at equilibrium there is no net dipole moment. You can think of it as consisting of two dipoles with equal strength but oriented in opposite directions, so they cancel out.

Carbon dioxide has three types of “vibrational modes” (see the video at the end of this post). One is a symmetric stretch, where the two oxygen atoms move together outward or inward from the central carbon atom. This makes the OCO molecule first get longer and then shorter, but it still consists of two equal but opposite dipoles that add to zero. Thus, this mode does not produce a dipole, so it cannot absorb infrared radiation.

Carbon dioxide can also undergo an asymmetric vibration, in which one of the oxygen atoms is moving inward or outward, and the other is moving outward or inward. In this case, the molecule maintains the same length, but the position of the oxygen atoms oscillate back and forth, with one being closer to the carbon atom and then the other. Now the two dipoles don’t cancel, so there’s a net dipole moment. (Think of the dipole moment as the charge times the distance; Even if the partial charge on each atom does not change, the different distances of each oxygen atom from the central carbon atom will alter the net dipole moment.) So, this mode of vibration will absorb infrared radiation. Carbon dioxide is a greenhouse gas.

Just for completeness, CO₂ also has bending modes, where the two oxygen atoms move back and forth in a plane parallel to the line of the molecule (see the video). Again, these modes induce a dipole that can oscillate in synchrony with infrared radiation and are therefore greenhouse active. Carbon dioxide is the primary contributor to climate change.

The earth is lucky that carbon dioxide has such a low concentration in its atmosphere. I wonder what would happen if most of our atmosphere consisted of CO₂ instead of oxygen and nitrogen. Oh, wait… we don’t have to wonder. The atmosphere of Venus is 96% CO₂, and Venus has an average surface temperature of 464°C (well above the boiling point of water). Wow!

Water vapor

Water vapor (H₂O) is a special case. Its abundance in the atmosphere is not constant. It can vary from nearly zero to about 4%, depending on the humidity. A molecule of water is also different than carbon dioxide because it is not a linear molecule. Figure 6.18 in Intermediate Physics for Medicine and Biology shows the structure of a water molecule, with its oxygen atom having a partial negative charge and its hydrogen atoms being partially positive. Even when at rest, a molecule of water has a dipole moment. The water molecule has several vibrational modes, all of which cause this dipole moment to change, and it’s therefore an absorber of infrared radiation.

Fig. 6.18 from Intermediate Physics for Medicine and Biology, showing the structure of a water molecule.

In the last post, I mentioned that feedback loops affect the climate. Water vapor provides an example. As the atmosphere heats up, it can hold more water vapor (see Homework Problems 65 and 66 in Chapter 3 of IPMB). More water vapor means more infrared absorption. More infrared absorption means more heating of the atmosphere, which means the atmosphere can hold more water vapor, which means more infrared absorption and heating, and so on. A positive feedback loop is sometimes called a vicious cycle.

Some of the water in the atmosphere is in the form of clouds. Clouds play a complex role in climate change. They can block the sunlight and therefore contribute to cooling. But it’s complicated.

Methane

Methane (CH₄) is a very active infrared absorber. The methane molecule consists of a central carbon atom with partial negative charge, surrounded by a tetrahedron of four hydrogen atoms each with a partial positive change. Like carbon dioxide, when in equilibrium methane has no net dipole moment. However, methane has many complicated rotational and vibrational modes, in part because it consists of so many atoms. Many of those modes result in a changing dipole moment, similar to what we saw for carbon dioxide. So, methane can absorb infrared radiation and is an important greenhouse gas. Molecule for molecule, methane is a much stronger greenhouse gas than carbon dioxide. The only reason it doesn’t contribute more to global warming is that its concentration is so low.

Sulfur dioxide

A molecule of sulfur dioxide (SO₂) is a lot like a molecule of water, with a bent shape. In this case, the central sulfur atom carries a partial positive charge and the two oxygen atoms are partially negative. Water is a stable molecule but sulfur dioxide is chemically reactive. If it is present in a high concentration it’s hazardous to your health. In that case, its contribution as a greenhouse gas will be the least of your problems. It’s often emitted when burning fossil fuels (especially coal), and is considered an air pollutant.

Sulfur dioxide can interact with water vapor to form tiny droplets called aerosols. These aerosols can remain in the air for years and reflect incoming sunlight (somewhat like clouds do). In this way, sulfur dioxide can have a cooling effect in addition to its greenhouse gas warming effect. On the whole, the aerosol cooling dominates, so sulfur dioxide cools the earth. It’s often released during volcanic eruptions, which can lead to cooler summers and colder winters for a few years.

Hydrogen

There is a tiny bit of hydrogen gas (H₂) in the atmosphere, but like oxygen and nitrogen it’s diatomic so it doesn’t absorb infrared radiation.

Nitrous oxide

Finally, nitrous oxide (laughing gas, N₂O) is similar in structure to sulfur dioxide and water. Like sulfur dioxide, it’s a form of air pollution and can be a greenhouse gas too (although its concentration is so small that it doesn’t make much contribution to global warming). Our atmosphere consists mostly of nitrogen and oxygen. We are fortunate that the most common form these elements take in the atmosphere are diatomic N₂ and O₂. Imagine what would happen if chemistry was slightly different, so that a large fraction of our atmosphere was N₂O instead of N₂ and O₂. Yikes!