Greenhouse Gases - Absolutely Small: How Quantum Theory Explains Our Everyday World - Michael D. Fayer 

Absolutely Small: How Quantum Theory Explains Our Everyday World - Michael D. Fayer (2010)

Chapter 17. Greenhouse Gases

IN THIS CHAPTER, we will look at what happens when we burn coal, oil, or natural gas in power plants to create energy. A major point is why coal produces so much more of the greenhouse gas, carbon dioxide, than does oil, which, in turn, produces more than natural gas per unit of energy. Furthermore, the reason that carbon dioxide is such an important greenhouse gas is caused by the fundamental quantum mechanical phenomena of black body radiation and quantized energy levels.

CARBON DIOXIDE FROM BURNING FOSSIL FUELS

Chapter 15 discussed turning wine (ethanol) into vinegar (acetic acid) by adding oxygen to ethanol. When this happens, we say that ethanol has been oxidized to acetic acid. Oxidation is a chemical process that can take many forms, but in the case of turning ethanol into acetic acid, it literally involves the addition of oxygen. The process is facilitated by biological enzymes. Hydrocarbons, such as methane or heating oil, can also be oxidized. However, hydrocarbons are very stable molecules. They will only oxidize at high temperatures. Burning fossil fuels is the process of oxidization. It takes heat to get the process going, but once the oxidation starts, the breaking of chemical bonds and the formation of new molecules liberates additional heat (thermal energy) that keeps the process going.

BURNING METHANE: NATURAL GAS

First, consider what happens when we burn methane (natural gas). A model of methane is shown in Figure 14.1. Methane (CH4) reacts with oxygen to give water (H2O) and carbon dioxide (CO2). The reaction can be written as follows.

CH4 + 2O2 → 2H2O + CO2

This chemical equation shows that one molecule of methane will react with two molecules of oxygen to give two molecules of water and one molecule of carbon dioxide. The arrow points from the reactants to the products. This reaction is said to be balanced because the number of carbon, hydrogen, and oxygen atoms is the same on both the left and right sides. In a chemical reaction, the combination of atoms that make up molecules changes, but the number of each type of atom never changes. Actually, another reaction product is heat. It takes energy to break the C—H bonds of methane. However, energy is released when the O—H and C—O bonds are formed to make the products. More usable energy (called free energy) is released in making the bonds to form water and carbon dioxide than is used to break the methane bonds. The net result is that burning methane releases energy that can be used to do things such as boil water to cook spaghetti or drive a steam turbine to make electricity.

WHAT IS A GREENHOUSE GAS?

Methane is a very good fuel, but it produces the greenhouse gas, CO2. What is a greenhouse gas? A real greenhouse, in which flowers or tomatoes are grown, is a building that lets in a lot of sunlight. Today, such buildings may be constructed with large expanses of plastic that are transparent to sunlight. So the sunlight pours in. When the sunlight lands on the materials inside the greenhouse, much of it is absorbed and converted to heat. You probably have experienced this effect if you have gotten into a car with black or dark color seats that have been illuminated by the sun through the windshield. The seats will be very hot. A black steering wheel may, in fact, even be too hot to touch. As discussed in connection with Figure 9.1, hot objects give off black body radiation, which is light with a wide range of colors. The hotter the object, the higher the frequency of light. The sun is very hot and gives off a great deal of visible light (see Figure 9.1). A black car seat heated by the sun is not very hot and gives off low-frequency (long wavelength) black body radiation. This long wavelength light is in the infrared portion of the electromagnetic spectrum. It is much lower in energy than visible light. In a greenhouse, the sunlight heats up the interior, but the energy that is emitted as infrared black body radiation cannot pass through plastic or glass. These materials are transparent for visible light, but not infrared light. Thus, the heat from the sun is trapped inside the greenhouse, which remains warm even if the outside temperature is much colder.

Carbon dioxide (water vapor and some other gases) makes the atmosphere act as a greenhouse for our entire planet. A great deal of energy falls on the Earth in the form of sunlight. The sunlight heats the Earth’s surface, and some of the heat energy is reradiated as infrared black body radiation. The atmosphere is predominantly composed of gaseous oxygen (O2) and nitrogen (N2). These gases are transparent in both the visible and infrared parts of the spectrum. If the atmosphere was composed only of oxygen and nitrogen, all of the black body radiation emitted by the warm surface of the Earth would fly right back out into space. The Earth would be much colder than it is and probably not suitable for human life. However, the atmosphere contains other gases. It is approximately 78% nitrogen, 21% oxygen, 0.9% argon, and 0.038% carbon dioxide. In addition, there are traces of other gases and a variable amount of water vapor in the air. The concentration of CO2 in the air is very small but very important. CO2 is transparent to visible light, but it absorbs infrared light. (The reasons that carbon dioxide absorbs important wavelengths of infrared light, making it such a serious greenhouse gas, are described below.) So CO2 lets the sunlight fall on the Earth’s surface, but it absorbs some of the infrared black body radiation, preventing it from escaping into space.

A good portion of the infrared black body radiation does escape into space. However, the balance is very delicate. Sunlight is heating the Earth. Black body infrared radiation emitted into space is cooling the Earth. Absorption of infrared by CO2 in the air reduces the cooling effect. With too little CO2 in the air, too much heat energy is radiated into space, and the Earth is too cold. But with too much CO2 in the air, not enough heat energy is radiated into space, and the Earth is too hot. The CO2 acts like the glass or plastic windows in a real greenhouse. It traps heat on the inside, in this case, the inside of the atmosphere.

Today the concentration of CO2 in the air is 0.038%, or 380 ppm (parts per million by volume). In 2000, it was 368 ppm. In 1990, it was 354 ppm. In 1980, it was 336 ppm. In 1970 it was 325 ppm. In 1960 it was 316 ppm. These numbers are from measurements made at Mauna Loa, Hawaii. From air trapped in ice, it was found that in 1832 the CO2 concentration in the air was 284 ppm. There is a clear trend in the CO2 concentration, and a great deal of scientific work has unmistakably demonstrated that the increase in atmospheric CO2 is produced by human activity. A major contributor to the increase in CO2 in the air is the burning of fossil fuels, although other activities, such as clear cutting of rain forests, are also contributors. What happens if the CO2 concentration in the atmosphere continues to rise? Venus is an extreme example. Its atmosphere is more than 90% CO2, and its temperature is approximately 900° F (480° C).

BURNING FOSSIL FUELS PRODUCES CARBON DIOXIDE

As we saw in the chemical equation for burning methane (reacting methane with oxygen), the chemical reaction produces CO2. Burning other fossil fuels also produces CO2. As discussed, heating oil is a mixture of long chain hydrocarbons, ranging from 14 to 20 carbons. We will use the 14-carbon molecule, tetradecane, as an example. Tetradecane is C14H30. The chemical equation for burning tetradecane is

C14H30 + 21.5O2 → 14CO2 + 15H2O.

Tetradecane has 30 H atoms, which make 15 water molecules, each with two H atoms. It also has 14 C atoms, which go into the 14 carbon dioxide molecules. To make the 14CO2 and 15H2O molecules requires 43 oxygen atoms, or 21.5 O2 molecules. That is the reason for the 21.5O2 on the left side of the chemical equation. Notice that in the chemical equation for burning methane, twice as many water molecules than carbon dioxide molecules are produced. In burning tetradecane, there are approximately the same number of water and carbon dioxide molecules produced. This will turn out to be important.

In addition to natural gas (methane) and oil (long chain hydrocarbons), the third common fossil fuel is coal. In its idealized form, coal is pure carbon. This is not actually true, but for right now we will accept this statement. Then, the chemical equation for burning coal is

C + O2 → CO2.

So, in contrast to burning hydrocarbons, burning coal does not produce any water, just CO2. In burning hydrocarbons, carbon-carbon and carbon-hydrogen bonds must be broken, which costs energy. Then, carbon-oxygen and oxygen-hydrogen bonds are formed to make carbon dioxide and water, which produces energy. Coal also has bonds that must be broken. These are carbon-carbon bonds. Initially, we will take coal to be graphite, which is pure carbon. We want to compare the amount of energy produced by burning each type of fossil fuel with how much of the greenhouse gas, CO2, is produced. Although graphite is not used as a fuel because it is difficult to ignite, its well-defined chemical structure makes it a useful example.

Energy Production and the Amount of Carbon Dioxide

First we will look at an idealized picture of energy production from burning fossil fuels. We ignore the fact that fuels are not pure and that a good deal of energy is lost in power plants. The actual energy production from real fuels will be discussed below. The three chemical equations for burning the fossil fuels are:

CH4 + 2O2 → 2H2O + CO2

C14H30 + 21.5O2 → 15H2O + 14CO2

C + O2 → CO2.

In the first and third equations for burning natural gas and coal, a single CO2 is produced in the reaction. For our model of heating oil (tetradecane), 14 CO2s are produced. We want to determine the amount of energy produced for one CO2. Using thermodynamics, it is possible to calculate the maximum usable energy (free energy) produced by each reaction. We assume that all of the reactions start at room temperature with methane (a gas), tetradecane (a liquid), and graphite (a solid). Of course, burning fuel will initially leave the products hot, but we will consider the situation after everything has cooled to room temperature. For natural gas, we just use the free energy produced by burning one molecule; for graphite, we use the energy produced by burning one carbon atom. For tetradecane, we divide the energy produced by burning one tetradecane by 14 to get the energy per one carbon dioxide molecule produced.

The results are:

methane (natural gas) 1.4 × 10-18 J free energy generated per CO2 produced

tetradecane (heating oil) 1.1 × 10-18 J free energy generated per CO2 produced

graphite (coal) 0.7 × 10-18 J free energy generated per CO2 produced

We see that getting the same amount of energy from coal generates twice as much carbon dioxide (greenhouse gas) as burning natural gas. Coal is also a factor of 1.6 worse in terms of greenhouse gas production for the same amount of energy produced than heating oil. Heating oil is a factor of 1.3 worse than natural gas.

Burning Real Fossil Fuels

The numbers given here are accurate except for coal. The different types of coal, that is, anthracite, bituminous, subbituminous, and lignite (brown coal), produce different amounts of energy per pound and also have different average carbon contents. Even for the same type of coal, the energy content and the carbon content vary. For example, bituminous coal is the most plentiful type in the United States. Its carbon content ranges from 45% to 86%, and its energy content varies by approximately ±20% around the average. The calculated value for coal given above using graphite as a model produces a result corresponding to the middle of the range of energy content of bituminous coal. Natural gas can have as much as 20% of the gaseous hydrocarbons ethane (C2H6), propane (C3H8), and butane (C4H10), in addition to methane (CH4). The mixture hardly changes the energy content or the energy per CO2produced compared to that calculated for pure methane. The same is true of oil, which is a mixture of long chain liquid hydrocarbons.

Real Numbers for Carbon Dioxide Production from Generating Electricity

The energy content of fossil fuels does not take into account power plant efficiencies, that is, the conversion of the fuel’s energy into electricity. The efficiencies of power plants, which vary depending on design and age, are similar regardless of the type of fossil fuel used. Typically, the efficiency is in the high 30s to 40% range. This means that only approximately 40% of the fuel’s energy is converted to electrical energy. In addition, the loss in power transmission lines is approximately 7%. Thus, if a plant efficiency value of 38% is combined with the transmission line loss the overall rate of conversion of fossil fuel energy to usable electricity in our homes is approximately 35%.

To understand what this means, let’s calculate how much CO2 is produced by a 100-watt lightbulb that burns 24 hours a day for a year. A watt is a J/s (one joule for one second). A year is 3.2 × 107 seconds. So, our 100-watt lightbulb will consume 3.2 × 109 J in a year. For natural gas, we said that one molecule of CO2 is produced for each 1.4 × 10-18 J of chemical energy produced. To get 3.2 × 109 J of energy, we will produce 3.2 × 109/1.4 × 10-18 = 2.3 × 1027 molecules of CO2. This amount is for perfect efficiency. With 35% overall efficiency, 6.4 × 1027 molecules of CO2 will be produced. 6.02 × 1023 molecules of CO2 weighs 44 g (grams). So, the weight in grams of the CO2 produced is 5 × 105 g or 1000 pounds. What we see is that running a 100-watt lightbulb for a year will put 1000 lb of CO2 into the atmosphere using natural gas. If we burn coal, it will be 2000 lb, or one ton. That is the weight of a small car. The first message is turn off the lights when you aren’t using them. That computer you leave on 24/7 uses 200 to 300 watts of electricity. So, if you get your electricity from a coal-fired power plant, your computer is responsible for putting 2 to 3 tons of CO2 into the atmosphere every year. The second message is that efficiency of the electrical devices we use and the choice of fossil fuel really matters. A compact fluorescent bulb that produces the same amount of light as a 100 W conventional bulb uses only 25 W. So a compact fluorescent running for a year from a natural gas power plant produces 250 lb of CO2, which should be compared to a conventional bulb run from a coal power plant that produces 2000 lb of CO2.

CARBON DIOXIDE IS A GREENHOUSE GAS BECAUSE OF QUANTUM MECHANICS

Why is carbon dioxide such a serious problem as a greenhouse gas? In other words, why does it trap heat in the atmosphere? And, why is water vapor (gas phase water molecules in the atmosphere) actually worse than CO2 as a greenhouse gas? The amount of water vapor is determined by evaporation and condensation of water. The Earth has huge pools of water, the oceans, from which water evaporates into the atmosphere. We also have rain, dew, and snow that remove water from the air. Humans have little effect on the amount of water in the air, although if the Earth continues to warm, the atmosphere will have more water vapor. The additional water vapor will amplify the influence of adding CO2, making greenhouse warming worse. H2O is a powerful greenhouse gas. However, we can influence the amount of CO2 in the air by the energy sources we use and the efficiency with which we use them. CO2 (and water) are serious greenhouse gases for reasons that come right out of quantum theory.

THE EARTH’S BLACK BODY SPECTRUM

In Chapters 4 and 9, we discussed black body radiation. Figure 9.1 shows the black body spectrum of the sun, whose surface temperature is almost 6000° C. The black body emission has a good deal of its intensity in the visible portion of the spectrum, with a substantial amount of light being emitted in the ultraviolet and the near infrared portions. The colors emitted by a hot object depend on the object’s temperature. Hotter objects emit shorter wavelengths. The Earth is, of course, much colder than the sun. Nonetheless, it is a black body emitter. Still, the wavelengths it emits are very long (very low energy photons). Sunlight with the spectrum given in Figure 9.1 falls on the Earth. Some of this light is reflected back into space by ice and other highly reflecting surface features. However, much of the light energy is converted into heat, which warms the Earth. Black body emission by the Earth radiates some of the energy that comes from the sun back into space.

The top portion of Figure 17.1 shows three calculated black body spectra of the Earth for three temperatures. The three curves are normalized, that is, their amplitudes adjusted to all have a maximum value of 1. 15° C (59° F) is the average surface temperature of the Earth; 27° C (81° F) is the surface temperature in the tropics; and -16° C (3° F) is the surface temperature in subarctic regions. While the curves vary somewhat, they are, by and large, very similar. The differences do not matter for discussing the influence of carbon dioxide.

Absorption of the Earth’s Black Body Radiation

The bottom two spectra in Figure 17.1 (note the frequency scale is different from the top spectrum) show the atmospheric transmission of infrared radiation through carbon dioxide and water in the long wavelength regions. A transmission of 1 means all of the light passes through the atmosphere. Zero transmission means that none of the light passes through the atmosphere. These spectra differ depending on which region of the Earth they are measured. The spectra shown are representative. In addition, a good deal of fine structure (peaks and troughs), particularly in the water spectrum, is not shown. The purpose of these curves is to display the essential features of the infrared absorption by carbon dioxide and water that are in the intense part of the Earth’s black body spectrum. These absorptions are indicated by the shaded regions. Water also has a strong absorption centered around 1750 cm-1, which is also shaded. The infrared absorption prevents a portion of the Earth’s black body emission from being radiated into space. Without the atmospheric absorption, the Earth would be much colder.

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FIGURE 17.1. Top: Calculated Earth black body spectra for three temperatures (solid curves). The shaded regions show the portions of the spectrum that are strongly absorbed by water and carbon dioxide in the atmosphere. Middle and bottom: spectra of the strong absorption by carbon dioxide and water in the range of 0 to 1000 cm-1. Note the scale difference with the top part of the figure.

The Reason Carbon Dioxide Is So Important

The reason carbon dioxide is so important can be seen by looking at the shaded regions of the black body spectrum and the absorption spectra. Water absorbs essentially everything at wavelengths longer than 500 cm-1. However, the bottom two spectra in Figure 17.1 show that carbon dioxide absorbs strongly in the region where water absorption is not very strong. The carbon dioxide absorption is very close to the peak of the Earth’s black body emission spectrum, as shown in the top part of Figure 17.1, regardless of which Earth surface temperature is used. Therefore, carbon dioxide strongly absorbs the Earth’s black body radiation in an important spectral range where other components of the atmosphere, particularly water, do not. The carbon dioxide spectrum (middle panel of Figure 17.1) shows that there is close to zero transmission in the middle of the spectrum, approximately 667 cm-1. However, as the concentration of CO2 increases, the region of very strong absorption becomes wider and portions of the spectrum, where a few percent are transmitted, will transmit virtually nothing from the Earth’s atmosphere into space. The net result is that CO2 absorbs strongly near the peak of the Earth’s black body spectrum where water doesn’t, and an increase in CO2 in the atmosphere will trap more black body radiation, thereby causing the planet to warm.

Why Carbon Dioxide Absorbs Where It Does

We see that carbon dioxide traps infrared light at the peak of the Earth’s black body emission and that an increase in CO2 concentration will have a deleterious effect on the Earth’s temperature. But why does CO2 absorb infrared light at wavelengths centered at 667 cm-1? In Chapters 8 through 11, we discussed the energy levels of a particle in a box, of the hydrogen atom, and of all of the other atoms. In Chapters 12 to 14, we discussed molecular orbitals and the associated energy levels. All of these discussions concerned the energy levels associated with electrons. Using the ideas of molecular orbitals, the nature of bonds that hold atoms together to form molecules was explicated. What we have not discussed is the motions of atoms that are bonded together to form molecules.

Figure 12.1 displays the potential energy curve for the hydrogen molecule, H2. The curve shows the energy at different separations of the hydrogen atom nuclei. The bond length is the separation where the energy is a minimum. However, the bond is not rigid. If we think about the bond using classical mechanics, the bond is a spring with two masses, the hydrogen atoms, attached at each end of the spring. A spring can be stretched and compressed. In a classical system, if you stretch the spring and let go, the masses will oscillate back and forth with the spring being alternately stretched and compressed. The masses of a classical oscillator will vibrate (oscillate) back and forth with a well-defined trajectory. Based on quantum theory, we should immediately suspect that a quantum vibration cannot have a well-defined trajectory. Such a trajectory would mean that we know the positions and moment of the particles (the atoms) precisely. Such knowledge for absolutely small systems, such as atoms bonded to form a molecule, violates the Heisenberg Uncertainty Principle.

Figure 17.2 shows a ball-and-stick model of carbon dioxide, CO2, as well as representations of its possible vibrational motions. CO2 is linear, with the two oxygens double bonded to the central carbon. CO2 has four different vibrational motions, called vibrational modes. The bonds can stretch and compress as well as bend. The bonds are represented by springs. We will describe the motions as if they are classical balls connected by springs to understand the nature of the modes.

The Vibrational Modes of Carbon Dioxide

In the symmetric stretch, the central carbon does not move. As shown by the solid arrows, the two oxygens move away from the carbon, thereby stretching the springs. The two oxygens then move back toward the central carbon, compressing the springs, as indicated by the dashed arrows. For a classical ball-and-spring system, this motion is repeated, so the positions oscillate back and forth. The frequency of the oscillation is determined by the masses and the strengths of the springs. In the asymmetric stretching mode, the two oxygens move to the right. The oxygen on the right compresses the spring, and the oxygen on the left stretches the spring. A vibration does not move the molecule to a new location. Because both oxygens are moving to the right, the carbon moves to the left in order to keep the molecule in the same location. Because the carbon moves to the left when the oxygens move to the right, the average position of all of the mass, called the center of mass, is unchanged. The motions are indicated by the solid arrows. The direction of each atom then reverses, as shown by the dashed arrows.

The symmetric and asymmetric stretches maintain all three atoms on a line. In the bending mode, the two oxygens move up and the carbon moves down. This keeps the center of mass in one place. Then the carbon moves up and the two oxygens move down. In addition to the bending mode shown in Figure 17.2, there is a second bending mode. The one shown has the motions of the atoms in the plane of the page. The second bending mode is identical except the atoms move into and out of the plane of the page.

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FIGURE 17.2. Top: Ball-and-stick model of carbon dioxide (CO2). Bottom: The three different vibration motions that the molecule can undergo. There are two bending modes: the one shown and the equivalent one with the atoms going in and out of the plane of the page.

Quantum Vibrations Have Discreet Energy Levels

In a classical vibrational oscillator made up of balls connected by springs, the energies the system can have are continuous. Consider the symmetric stretch. Three balls connected by two perfect springs are laying on a frictionless table with no air resistance. If you grab the outer two balls, stretch the springs the same amount, and let go, the balls will execute the symmetric stretching mode. Because the spring is perfect, the table is frictionless, and there is no air resistance (none of which is true in real life), the oscillation will continue forever. The period or frequency of the oscillation is independent of how far you stretch the springs. The period is determined by the springs’ strengths and the masses. If you stretch the springs only a little bit, the balls will move slowly. Their average kinetic energy is small. If you stretch the springs a lot, the balls will move fast, and the average kinetic energy is large. The energy of the oscillating ball and spring system is continuous. It only depends on how much you stretch the springs.

Molecules are not really balls and springs. They are quantum mechanical systems composed of atoms joined by chemical bonds. Rather than having a continuous range of energies, the quantum system has discreet vibrational energy levels. The quantization of the energy is equivalent to the particle in a box problem discussed in Chapter 8. Gerhard Herzberg (1904-1999) won the Nobel Prize in Chemistry in 1971 “for his contributions to the knowledge of electronic structure and geometry of molecules, particularly free radicals.” Herzberg’s work on determining the structure of molecules was based to a large extent on his explanations for the vibrational spectra of molecules.

The energy of a classical racquetball is continuous, but the energy of the quantum racquetball (particle in a box) has energy levels (see Figure 8.6). Figure 17.3 shows a potential curve for a vibrational mode of a molecule, like the one shown in Figure 12.1, but now the first several quantized vibrational energy levels are also shown. Again like the particle in a box, the lowest energy level, n = 0, does not have zero energy.

Energies of Quantized Vibrations

The simplest model for the vibrational energy levels gives the energies as

E = hν(n + 1/2),

where h is Planck’s constant, ν is the vibration frequency, and n is a quantum number that can take on values, 0, 1, 2, etc. For n = 0, the energy is 1/2hν. For n = 1, the energy is 3/2hν. So the difference in energy between the lowest energy level and the first excited vibration level is hν. In this model, all of the energy levels are equally spaced with a separation of hν. In real molecules, the energy levels get somewhat closer together as the quantum number increases. For our purposes, we only care about the spacing between the lowest energy level and first excited energy level.

CO2 Bending Mode Absorbs at the Peak of the Earth’s Black Body Spectrum

The bottom portion of Figure 17.3 shows the first two vibrational energy levels. Light will be absorbed at the energy of the separation of the levels, which is indicated by the dashed arrow. Since the difference in energy is ΔE = hν = c h/λ, measurement of the light frequency (ν) or the wavelength (λ) at which light is absorbed gives the oscillator frequency. As shown in the figure, ΔE = 667 cm-1 for the bending modes of carbon dioxide. The two bending modes have the same frequency because they only differ by the direction of the bend. (We can write the energy or frequency in wave numbers [cm-1] by dividing the energy, ΔE, by ch.) The frequency of light absorbed by the CO2 bends is almost exactly at the peak of the Earth’s black body spectrum. It is much easier (takes less energy) to bend a chemical bond than to stretch it. The carbon dioxide symmetric and asymmetric stretches are at much higher frequency. Neither contributes significantly to absorption of the Earth’s black body radiation.

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FIGURE 17.3. Top: A potential energy curve showing the energy as a function of the bond lengths with the vibrational quantum levels. Only the first few energy levels are shown. Bottom: The lowest vibrational energy level (n = 0) and the first excited level (n = 1) for the CO2bending modes (Figure 17.2.). This transition (arrow) will absorb the Earth’s black body radiation (see Figure 17.1).

CO2 GREENHOUSE EFFECT IS QUANTUM MECHANICAL

The important point is that at the most fundamental level, CO2’s contribution to the greenhouse effect and to global climate change is inherently quantum mechanical. First, the bonds that are broken and made in burning natural gas, oil, or coal are determined by the quantum mechanics that give us molecular orbitals, which control the bond strengths. The bond strengths determine the amount of energy that is released per CO2 produced. At an even more fundamental level, the shape of the black body spectrum emitted by the Earth is determined by quantum effects. Black body radiation was discussed in Chapters 4 and 9. Planck’s explanation of the shape of the black body spectrum and how it changes with the temperature of a hot object was the first application of quantum theory. The CO2 absorption centered at 667 cm-1 is a result of the quantized vibrational energy levels of molecules, a purely quantum effect. The CO2 bending modes have their quantized n = 0 to n = 1 vibrational transition at a key frequency in the Earth’s black body spectrum. While massive power plants, vast numbers of cars, trucks, and planes, burning of rain forests, etc. produce the greenhouse gas CO2, it is the quantum interaction between CO2 and the Earth’s infrared black body radiation that produces the greenhouse effect.