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How to fill two Ford Explorers with a single gallon of gasoline

Shiny balloonsTo satisfy our readers’ seemingly insatiable desire for high school chemistry problems, we today turn our attention to the question of exactly how much space is taken up by the carbon dioxide emissions created from one gallon of gasoline.

To solve this riddle, we turn to our old friend, the Ideal Gas Law, which is not, as it might sound, a piece of renewable energy legislation, but instead an equation relating the volume of gas to pressure and temperature:

PV = nRT

P stands for pressure. Because we’re writing this post from our comfortable sea-level office, rather than, say, from the top of Kiliminjaro, we will use a pressure of 1 atmosphere.

V stands for volume. That’s the number we’re trying to figure out, so for now it remains unknown.

Moles are not rodentsn stands for the number of moles of gas. The humanities majors among you will be disappointed to learn that chemistry moles have nothing at all to do with blind, burrowing insectivores, and everything to do with the number of molecules in a lump of matter. In our case, 19.564 pounds of carbon dioxide contains 201.7 moles.

R is the so-called molar gas constant. Roll that one around in your mouth for a while. Its value is 0.082058, of course.

T stands for temperature. Our reader wants to know the volume at 70° F, which we must first convert to 294.3° Kelvin.

Punching a few keys on our wristwatch calculators yields a solution:

Volume = (201.7 x 0.082058 x 294.3)/1 = 4,870 liters

Huh? Not a very useful number. So let’s break it down a different way. That’s the same as 172 cubic feet of emissions, which is what you’d get if you had a cube that was 5 and a half feet on each side. In other words, a gallon of gasoline yields a cube of carbon dioxide roughly as long, tall, and wide as an adult person.

Or how about this way: 172 cubic feet is roughly twice the cargo capacity of a Ford Explorer. You could pack two Ford Explorers full with the carbon dioxide emissions from a single gallon of gas.

Or 12 Honda Accords. Or 32 Mazda Miatas. Now you know.

P.S. I feel reasonably good about my math, because my number roughly matches the number at the International Carbon Bank And Exchange. So how ’bout it? Show me up.

Update: You showed me. Conversion to Kelvin fixed.

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