CASE STUDY: Altering the Atmosphere by Burning Fossil Fuels

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Source:

Warning! This model requires a comfort level with converting units. A chemistry background is helpful as well!

Goal:

Background Reading:

When fossil fuels are burned, the carbon in these fuels combines with the oxygen in the atmosphere to form carbon dioxide, and the hydrogen in the atmosphere combines with oxygen to form water. We also see some water produced when coal is burned, as coal is 10-15% (by weight) water. When coal is burned, the water in it is vaporized and released to the atmosphere.

The mathematics of the burning of a fossil fuel are shown below. Fossil fuels contain carbon (C) and hydrogen (H) in some proportion. Petroleum, for example, has the general formula C₁H_1.5. This means for every one carbon there are 1.5 hydrogens. Coal has the formula C₁H_0.8, and natural gas (also known as methane) has the formula CH₄. We can show the "stoichiometric" (mathematical) reaction for the combustion of a fossil fuel as below:

This shows the ratios or amounts of products that come out of this reaction. Perhaps an example is helpful:

One of the common fossil fuels burned, especially in automobiles, is a mixture of various types of octanes. The prefix "oct-" is Latin for the number "8". Octane has 8 carbons, and 1.5 x 8, or 12, hydrogens (note for those of you who have taken chemistry -- you should recall that pure octane actually has 18 hydrogens. The octane being used here is actually a combination of octanes and other hydrocarbons). We can now assign values to x and y:

Now we can write the reaction:

If we do the math, we have:

This reaction says that if we combine one octane with 11 oxygens (from the atmosphere) we will produce 8 carbon dioxides and 6 waters.

This model is a model of ratios. What we wish to measure is the number of moles of CO₂ going to the atmosphere, and the number of moles of H₂O going to the atmosphere. A mole is a chemical short-hand term for "gram molecular weight". It is equivalent to the idea of a dozen. What's a dozen? A dozen is 12 somethings. It doesn't matter what the somethings are, if you have 12 of them, you have a dozen. A mole is somewhat the same idea:

For example, water has a molecular weight of 18 grams - hydrogen weighs one (and you have two of them) and oxygen weighs 16 grams, for a total of 18 grams. If I have 32 grams of water, how many moles of water do I have?

Carbon weighs 12 grams and oxygen weighs (again) 16 grams, so one mole of carbon dioxide is 44 grams. Methane (CH4) has a gram molecular weight of 16 grams, so 16 grams of methane equals one mole of methane.

Why is this important? In this model, we need to know how many moles of CO₂ and H₂O are going into the atmosphere, so we will need to convert.

Before we can do that, however, there are other conversions that need to be made. We start with some data from the year 1989.

In 1989, the energy content released by the burning of petroleum was 1.35 x 10²⁰ J, where "J" stands for Joules, a unit of heat energy. In order to run this model, we need to know how many grams of petroleum was burned in order to produce this amount of energy. To do this, we need another conversion factor. Petroleum has a "heat content" value of 4.3 x 10¹⁰ Joules per ton. This means for every ton of petroleum burned, 4.3 x 10¹⁰ Joules of energy are produced. To convert the energy content into tons of petroleum burned, simply divide the energy content by the heat content:

We now need to convert tons to grams, then convert grams to moles. One ton is equal to 1.0 x 10⁶ grams, therefore:

We're not out of the woods yet, however. It seems that petroleum does not burn completely (which causes lots of other pollution problems not discussed in this case study!). Only 98% of petroleum burns to completion, so to get the true amount of grams burned, we need to multiply the grams of petroleum by this value:

One more calculation to do. We must now convert grams to moles, as described above. For petroleum, we typically use the formula CH_1.5. This formula has a gram molecular weight of 13.5 (12 for C and 1.5 for a hydrogen and a half). We can now easily convert grams to moles:

Calculating moles of the natural gas is a different story, since it is a gas, not a liquid or solid as is the case with petroleum and coal.

For natural gas, you should use these conversion factors (it is left as a problem for you to figure out multiplications/divisions!)

Energy content in 1989: 6.00 x 10¹⁹ Joules
Heat content of natural gas: 3.9 x 10³ Joules/cubic meter of gas
Conversion of cubic meters to moles: 44.6 moles = 1 cubic meter of any gas

For this model, you should use the table below:

For each of the two quantities we wish to measure -- amount of CO₂ in the atmosphere and amount of H₂O in the atmosphere -- we have three sources of stuff:

1. CO₂ or H₂O from petroleum
2. CO₂ or H₂O from natural gas
3. CO₂ or H₂O from coal

In addition, we have to take into account that there is some moisture in coal that also contributes to water in the atmosphere, becoming the fourth source of water. 13% of coal is water, so you will also need to include this algorithm as a source of water:

The 75% comes from the fact that 75% of coal is burnable stuff, and 13% is water.

Finally, you will need to be careful about the stoichiometric values used. You should use these formulas for this model:

• Petroleum: CH_1.5
• Natural gas: C_1.12H₄ (the 1.12 takes into account that methane is actually a mixture of several different types of methane!)
• Coal: CH_0.8

As an example of how to use this information: how much CO₂ is produced from the burning of natural gas? You should use the formula presented at the top of the page:

Substituting in the values for natural gas, you would have:

gives:

Look at the numbers after the C's on both sides. You have 1.12 C's in the natural gas, and 1 C in the carbon dioxide. There is a ratio of 1.12 to 1. So, for every ONE mole of natural gas burned, 1.12 moles of CO₂ are produced.

NOTE: you should WRITE DOWN all three reactions, so that you know these stoichiometric values. One more example:

O₂ used via burning of coal

Experimenting with the model:

1. Add sliders to the model to control the values of the converters representing annual consumption of coal, natural gas, and petroleum. Scale the sliders to permit a reduction of each fossil fuel by one-half and an increase by a factor of two (in other words, you want a range from 0.5 times the annual amount of each fuel up to a maximum of 2 times the annual amount of each fuel.
2. A realistic view of fuel tradeoffs must account for the differing energy content of various fuels. Modify your model so that as you adjust petroleum consumption, coal consumption automatically changes to maintain a constant consumption of energy. This will require a connector from the petroleum converter to the coal converter and a change to the coal converter so that its value is computed from the petroleum consumption.

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