What the heck is a "ton of carbon in the air?"

January 28, 2010 4:54 PM

Help me visualize CO2 pollution. When we say we're spewing "tons of carbon" into the air, what does that look like? What does it mean when you measure a gas in tons? If I magically compressed a ton of carbon that's in the air to a density of, say, the graphite in pencil lead, what are the dimensions of that brick of carbon?
posted by Cool Papa Bell to grab bag (18 answers total)

A ton of graphite is a cube 76.3cm on a side.
posted by zsazsa at 5:04 PM on January 28, 2010

Graphite has a density of about 2.2 g/cm^3, so a (metric) ton of graphite would have a volume of about 450,000 cm^3. That's about half a cubic meter. Enough to fill up a good-sized household refrigerator.
posted by mr_roboto at 5:04 PM on January 28, 2010

The density of carbon dioxide varies based on its state, which varies based on temperature and pressure.

Dry ice at 1atm and -78.5C has a density of 1.562 g/mL, so a ton of that would be about half a cubic meter.

As a gas at 1atm and 20C, it has a density of 1.977g/L, so a ton of that would be substantially larger volume, 458 cubic meters.

Muck about with the temperature and pressure, and you can get varying densities, but those seem to be two good bounds there.
posted by valkyryn at 5:06 PM on January 28, 2010

Of course, carbon only makes up about 30% of carbon dioxide. (12/44 == 27%)
posted by Chocolate Pickle at 5:12 PM on January 28, 2010

At atmospheric pressure and room temperature, a ton of carbon dioxide takes up V=nRT/P=(1,000,000 g / 44 g/mol) * 8.2E-5 m^3 atm K^-1 mol^-1 * 293 K / 1 atm = 546 m^3, so the interior of about 1100 good-sized household refrigerators. Enough to fill a 2000 square-foot apartment (and suffocate all of the occupants).
posted by mr_roboto at 5:12 PM on January 28, 2010

CO2 is about 2kg/m^3 at standard temperature and pressure according to Wikipedia.
Thus 1 ton = 1000kg = 500m^3.
This is the volume of a room with 10ft ceilings (3m) with 166 sq m = 1800 sq ft of floor space, which is about three times the size of my modest apartment.

Note that this 1 ton of CO2 is composed of carbon and oxygen. C's atomic mass is 12 and O's is 16 so the carbon is about one quarter of the mass of CO2.

Graphite has a density of about 2g/cm^3 which is 2000 kg / m^3.
One ton of carbon dioxide is 250kg of carbon in the air. If this had the same density of graphite, it would have a volume of 250/2000 = 0.125 m^3.

This agrees with other estimates except the factor of four to account for the oxygen. "Carbon" and "carbon dioxide" are often conflated when talking about greenhouse gas emissions. The carbon that is present in the fossil fuels combines with oxygen during combustion to produce CO2.
posted by PercussivePaul at 5:13 PM on January 28, 2010

As a gas at 1atm and 20C, it has a density of 1.977g/L, so a ton of that would be substantially larger volume, 458 cubic meters.

However, CO2 is only 27% carbon by mass, so a ton of carbon would be about 1700 cubic meters.
posted by HumuloneRanger at 5:14 PM on January 28, 2010

However, CO2 is only 27% carbon by mass, so a ton of carbon would be about 1700 cubic meters

But carbon isn't a gas at 1 atm and 20 ºC.
posted by mr_roboto at 5:16 PM on January 28, 2010

A "ton of carbon" means enough CO₂ molecules so that the combined mass of all the carbon in those molecules is one tonne. A carbon atom has an atomic mass of 12 g/mol. So to get one tonne (1000kg), you need 83333 moles of carbon. A mole is 6.02 x 10²³ atoms, so you need approximately 5 x 10²⁸ atoms of carbon to make a tonne (and about 10% less to make a short ton (2000lbs)). In other words, a tonne of carbon is a whole lot of CO₂ molecules.

Graphite has a density of about 2.15 g/cm³, so one tonne of graphite would be about 0.465 m³ or a cube of about 77cm. One tonne of graphite is one tonne of carbon, so there you go. However, if you want to know the size of a cube made of condensed CO₂ which contains one tonne of carbon, you need to account for the oxygen. Oxygen has a atomic mass of 16 g/mol and you need two oxygens for every carbon, so your block must now be quite a bit larger as one tonne of carbon is equal to (44 g/mol / 12 g/mol) 3.67 tonnes of CO₂. 3.67 tonnes of CO₂, at the density of graphite, would make 1.71 m³ or a cube of about 120cm. Note that in order to compress the CO₂ to the density of graphite you'd have to get it very, very cold and/or squeeze the heck out of it.
posted by ssg at 5:23 PM on January 28, 2010

Reverse visualization exercise: take a piece of coal. Weigh it on a scale. Light it with a blowtorch, let burn completely. Weigh again. Notice there's quite a difference in weight? It's gone in the air as CO₂. Extrapolate the weight difference to a ton and you see how much is "a ton of carbon" in the air.

[NOT EXACT: COAL != PURE CARBON]
posted by _dario at 5:25 PM on January 28, 2010

Better way to think about things: Recognize that trees get their mass not from the soil, but from the air.

Trees are big.
posted by effugas at 5:27 PM on January 28, 2010 [4 favorites]

Effugas, a lot of a tree's mass derives from water, which the tree does get from the ground.
posted by Chocolate Pickle at 5:38 PM on January 28, 2010

Dang. I came in to say go outside and look at a tree, but effugas beat me to it. And while it's true that trees have a moisture content, much of a tree's mass is taken directly out of the atmosphere in the form of carbon. A tree can't derive it's mass from the ground in which it's rooted; it would be eating it's own foundation, and every tree would soon collapse into a pit of it's own making.
posted by dinger at 5:56 PM on January 28, 2010

"Trees are big"? Only because they grow for a hundred years. Grass gets its mass from the air too, I guess. Grass is small. So what?
posted by PercussivePaul at 6:35 PM on January 28, 2010 [1 favorite]

A quantity of gas only seems "weightless" because it's floating in a bath of air that's many many miles deep, mostly nitrogen and oxygen. But that doesn't mean the gas of interest is massless.
posted by intermod at 7:44 PM on January 28, 2010

Does it help to think of it in terms of black balloons? The average balloon holds 50g of gas.
posted by harriet vane at 2:54 AM on January 29, 2010

Here's another way to visualise atmospheric CO2. Imaging the worlds tallest building has just been built...it's a kilometer high, taller even than the current leader, the Burj Dubai at 828 meters.

1000 meters is a convenient yardstick because it's a million millimeters, and volumes of atmospheric gasses are commonly measured in parts per million. Imagine that the entire atmosphere has been compressed into a 1000 meter column, as high as that building. Now, further imagine that all the atmospheric gasses have been separated and stratified into layers, and that CO2 is the bottom layer. Now, get down on your hands and knees. Pre-industrial revolution, the concentration of CO2 in the atmosphere was approx. 280 ppm, slightly larger that a quarter meter on our kilometer building. Today, the concentration stands at 380ppm, an increase of 100mm on our column of air, or about the width of your hand. Imagine yourself putting marks on the side of our building at 280mm and 380mm above the sidewalk, then walk accross the street and take a look back at the building. That's a way to visualise the CO2 content of the atmosphere.

Data from the National Climatic Data Center.
posted by dinger at 3:16 AM on January 29, 2010

Thanks, all. The scientific measurements are great and exactly what I wanted. The black balloons, though, is an awesome visualization tool. Gotta love the Aussies.
posted by Cool Papa Bell at 8:13 AM on January 29, 2010