Combustion comparison

How much $CO_2$ (in grams) is produced for each 1 Calorie (=1 kilocalorie) of energy? You'll calculate that below.

Gasoline (av. octane) - $C_8H_{18}$ - combustion: 10.8 Calories / gram

$$2\,C_8H_{18} + 25\,O_2 \to 16\,CO_2+18\,H_2O$$ Atomic weight of...

2 octanes = 16*12g ($C$) + 36*1g ($H_{18}$) = 228g
16 carbon dioxide = 16*12g ($C$) + 16*2*16g ($O_2$) = 704g

So, 704g of $CO_2$ are produced for every 228g of gasoline : 704g $CO_2$ / 228g gasoline.

We want grams of $CO_2$ / calorie: $$\frac{704\text{g }CO_2}{228\text{g } gasoline}*\frac{1\text{g } gasoline}{10.8 \text{Cal}}= \frac{704*1}{228*10.8}=0.29 \text{g of }CO_2 / \text{ 1 Calorie}.$$

Natural gas (methane) - $CH_4$ - combustion: 13.3 calories / gram

$$CH_4 + 2\,O_2\to CO_2+2\,H_2O$$ Atomic weight of...

methane = ? = $CH_4$: molecular weight = 12g + 4*(1g) = 16g
carbon dioxide = ? 12g + 2*(16g) = 44g

So, 44g of $CO_2$ are produced for every 16g of methane :

We want grams of $CO_2$ / calorie:

$$\frac{44\text{g }CO_2}{16\text{g }CH_4}*\frac{1\text{g } CH_4}{13.3 \text{cal}}= \frac{44*1}{16*13.3}=0.21 \text{g of }CO_2 / \text{ 1 calorie}.$$

Coal - $~C$ - combustion: 6.5 Calories / gram

$$C + O_2 \to CO_2$$ Atomic weight of...

Coal = 12g
1 Carbon dioxide = 44g

We want grams of $CO_2$ / calorie:

$$\frac{44\text{g }CO_2}{12\text{g }C}*\frac{1\text{g } C}{6.5 \text{cal}}= \frac{44*1}{12*6.5}=0.56 \text{g of }CO_2 / \text{ 1 calorie}.$$

So now we can compare $CO_2$ emissions for the same heat (in calories) for different fuels:

Fuel $CO_2$ emissions (g/cal)

hydrogen 0.0

natural gas (methane) 0.21

gasoline (~octane) 0.29

coal (~ pure carbon) 0.56

Fuel	$CO_2$ emissions (g/cal)
hydrogen	0.0
natural gas (methane)	0.21
gasoline (~octane)	0.29
coal (~ pure carbon)	0.56

Cost comparison

This page http://tinyurl.com/costofE (from a government agency) contains a table which compares the costs of coal, oil, and natural gas in US$ per million BTU. Make sure you can do the calculation of cost/energy from the numbers they provide and get the same answer.

Apparently...$$ \frac{\$56.35}{1 \text{ barrel}}\times\frac{1 \text{ barrel}}{6 \text{ million BTU}} = \$9.39 / \text{ million BTU}$$

The number of BTUs for each fuel type doesn't change, but the costs they cite may be out of date. Scour the Internet to find recent costs of oil, coal, and natural gas. For each price, cite the website you used, find out and write a sentence or two about the organization behind the website, and write a sentence or two on why you think it's trustworthy.

Then recalculate the table using the current costs you found for each fuel, to get a figure in $ / Million BTUs based on the costs you uncovered. You may need to do further conversions, e.g. on WolframAlpha. Show each calculation with units.