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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  1. Anonymous - April 6, 2006

    Harvard Green Campus Initiative used party balloons.

    The university’s emissions are equal to more than two million ballons PER person.


  2. Anonymous - April 10, 2006

    Theres a math error… 70 degrees F is not 277.6K
    70 degrees Fahrenheit = 294.261111 kelvin
    (From google calculator)

  3. Adam - April 11, 2006

    Sigh. Fixed. Thanks.
    Weird thing is, I used Google calculator the first time around. I blame this tricky keyboard.

  4. Anonymous - October 31, 2007

    This is an interesting parlor game, calculating the volume of CO2 produced at atmospheric pressure. However, it does not address the underlying issues. Is this a LOT of CO2, or a little? Numbers by themselves mean little or nothing.
    Without knowing the capcacity of the biosphere to absorb CO2 (through photsynthesis) it is hard to understand whether this is a relavant amount of gas. It amounts to little more than “Gee, whiz, that’s a lot of gas!”. Or at least is SEEMS like a lot.
    As Tony Blair noted before he left office, even if the UK were to cease all carbon emissions, that “savings” would be negated within a year or two by the increase in carbon emissions from China.
    Coal burning power plants are a much larger source of CO emissions than cars.
    So, while it is all well and good to examine the CO2 emissions from our own sources here in the USA, if we ignore much larger sources and problems, we are doing little to change the situation.
    How many cubic feet (or lbs) of CO2 are produced by burning a ton of coal? And how many tons of coal are burned every year in the USA? That would be intersting numbers to crunch.

  5. Pangolin - March 25, 2008

    I’m imagining a clown act where two clowns with a funnel try to stuff a five foot sq. cube back into a gas tank with a funnel. Then some unfortunate hijinks with dry ice.
    It’s much easier to demonstrate that you have to bury about 6 lbs of charcoal (5.3 lb carbon) per gallon of gas burned to break even just on the gas. Counting drilling, shipping, refining and transport you probably have to bury about 10 lbs of charcoal (hardwood charcoal too, no brickets) to break even on a single gallon of gas.
    But 10 lbs of charcoal cost more than a gallon of gas you say? Yup, that’s the whole point. The environmental cost of burning that gallon of gas is more expensive than the benefit.