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Name: Thorin
Status: student
Grade: 6-8
Location: Canada
Date: June 2008

Question:
Hi, one of the energy projects here in Alberta releases 40 million tons of CO2 a year. I have a hard time picturing this. How big is one ton of CO2 gas, at the altitude of my home town, about 3000 feet above sea level?



Replies:
Hi Thorin,

Well my assumption was that your altitude my make your pressure about 0.95 atmospheres. I assumed standard temperature of 25 deg C. At this point I just used ideal gas law and used the fact that the molecular weight of CO2 is 44.01 grams / mole. I then came to the conclusion that 40,000,000 tons of mass of carbon dioxide would work out to be about 5.07 cubic miles of volume. To put it another way... This amount of CO2 emission would fill a cube that measures 1.72 miles x 1.72 miles x 1.72 miles.

We better start planting some trees, huh?

Thanks for the very good question.

Darin Wagner


Thorin,

A gas will occupy the size of its container. But as a general rule, the quick answer that you might be looking for is that 1 mole of gas occupies 22.3 liters of volume at STP (standard temperature and pressure, 0 degrees C and just about 1 atm of pressure). So think of this as just over 11, 2-liter bottles of soda per mole of CO2. I will not trouble you with the math, especially if you do not know what a mole is, but one ton of CO2 would occupy 230,372 2-liter bottles. So if you have 40 million tons, then you have 9.2 Trillion 2-litter bottles of CO2 per year. This would be about 1 bottle for each dollar of national debt the U.S. has! (2008)

Matt Voss


Thorin,

We could roughly estimate the volume of 1 ton of gas by using the ideal gas equation: PV = nRT (where P is the pressure in atmospheres, V is the volume in liters, n is the number of moles = mass in grams/molar mass of the gas, R is the gas constant = 0.08206 L.atm/K.mol, T is the temperature in Kelvin).

So, rewriting, we have V = nRT/P

then convert 1 ton to grams, molar mass of CO2 is 12+16*2, T we will assume is 27 deg-C (be sure to convert to Kelvin), and assume a uniform pressure at 3000 ft to be roughly 680 torr (be sure to convert to atm).

Hope that helps,

Greg (Roberto Gregorius)


Thorin:

How about this?

If that much gas were made into dry ice it would produce a cube slightly larger than 925 feet (about 280 meters) on a side! That is about 3 football fields long by 3 football fields wide by a 90 story building high!

Or put another way, that would make a column of dry ice about 9 inches on a side reaching to the moon.

Robert Avakian


Hi Thorin,

The 'ideal gas law' which describes the volume of gases. The ideal gas law as an equation is PV=nRT where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. This law shows how pressure, temperature, and the amount of gas determine its volume. 'Moles' is a unit that refers to the number of molecules. Using algebra, we can rearrange this equation as V = nRT/P, which is a form that you can use to calculate the volume of the CO2.

So now we just have to plug in values for n, R, T, and P. At 3000 feet in altitude, the pressure is approximately 0.9 atmospheres. I'm going to assume a hot summer day, about 80F (27C), which is 300K (a nice round number). To find the number of moles of CO2, we need to convert the mass of CO2 to a number of CO2 molecules. 40 million tons is about 3.6x10^13 grams. Since the molecular weight of CO2 is 44 grams per mole, we have about n = 3.6e13 / 44 = 8.2e11 moles of CO2. The ideal gas constant depends on the units you use -- we're using degrees Kelvin, atmospheres, and moles, and let's express volume in liters (you could choose whatever unit you want) -- for these units, R = 0.082 (approximately).

So we now have: V = 8.2e11 * 0.082 * 300 / 0.9 = 2e13.

So the volume of 40 million tons of pure CO2 at 0.9 atmospheres is 2x10^13 liters, or 2x10^10 cubic meters. You can do whatever conversions you want -- that's a square 90 miles wide by 90 miles long and a meter deep.

Of course, the CO2 will not stay 'separate' from the other gases -- it mixes with the air and moves around the planet. Plants and animals absorb or add to it, etc. etc.

Hope this helps,

Burr Zimmerman


Here is how it goes without the correction for altitude.

1ton CO2 = 2000 lb CO2
2.2 lb = 1 kg
So, 1 ton CO2 = 909 kg = 909,000 gm CO2
1 mol CO2 = 44 gm CO2
So, 909,000 gm CO2 = 20659 mol CO2

At S.T.P. (standard Temperature = 273 K, standard Pressure = 1 atm) 1 mol CO2 = 22.4 liters

So, 20,695 mol CO2 = 463,568 liters at S.T.P.

You can now use the ideal gas law (P x V = R x T) to adjust this volume at 273 kelvins and 1 atm to any temperature or pressure you desire. (Here R = 0.08205 liter-atm / Kelvin) is the gas constant in the consistent set of units. Or you can use ratios of T and 1/P to adjust the volume to any desired temperature (expressed in kelvins) and pressure (expressed in atmospheres).

Vince Calder



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