# What does 5,000,000 tonnes of CO2 look like?

Reading a news article Probe after Gorgon releases millions of tonnes of greenhouse gas, I am confused. CO2 is a gas, right? Gases are not very dense, right? So what does 5MT of the stuff look like? How big a tank do we need to hold it?

• Please deselect the answer you have chosen. It is very wrong. May 11 '18 at 5:38
• Ummm... How so? May 11 '18 at 5:42
• In general, it's polite to wait at least a few hours (or days) before accepting an answer, in case a much better one comes along :-) May 11 '18 at 6:40
• I think there may well be several best answers here. :)) May 11 '18 at 6:54
• @David Hammen: Read the comments to that answer. It is not (very) wrong GIVEN THE ORIGINAL INPUT. If you know how to write answers that automatically adjust themselves when the question is changed, please feel free to tell us lesser minds how you do it :-) May 12 '18 at 19:22

The question is hard to give a definitive answer to, as it depends on the pressure at which the gas is kept in the tank. But to try to give an intuitive sense of how much gas this is, let's work out two things: Firstly, how big the box would be at atmospheric pressure; and secondly, how many standard gas bottles it would take.

## At atmospheric pressure

The mass of one mole of CO2 is 44 grams. So 5 MT of CO2 is $\frac{5\times 10^{12}}{44} = 114\times 10^9$ moles of gas.

The ideal gas law tells us that

$PV = nRT$

where $P$ is pressure, $V$ is volume, $n$ is the number of moles of the gas, $R$ is a constant, and $T$ is the temperature in Kelvin. If we assume a pressure of 100,000 Pa (roughly atmospheric pressure) and a temperature of 300 K (roughly room temperature), then

$V = \frac{nRT}{P} = \frac{114 \times 10^9 \times 8.314 \times 300}{10^5} = 2.8\times 10^9$ m3.

That volume works out to a cube with sides of 1.4 km.

## In gas bottles

A standard large CO2 bottle of the type that is familiar in the UK looks like the one on the right of this picture:

and according to BOC contains 34 kg of gas, at a pressure of up to 50 bar. So that's 29.4 cylinders per tonne or, to contain 5 million tonnes of CO2, 147 million of these cylinders.

"Look like" is not quite right, since gaseous CO2 is transparent to visible light. To get a sense of the volume, we can do some simple math, which unless I've made a mistake somewhere gives an area 21 km/13 miles on a side, stretching from sea level to space.

Showing my work:

x = 5 Gt = 5000000000 * 2000 lbs/ton = 10000000000000 lbs

Sea level pressure = 14.7 lbs/in^2, so 680272108843 in^2

144 in^2 per ft^2, so an area of 4724111866 ft^2, or a square 68732 ft on a side

Convert to miles = 13 miles on a side Convert to km = 20.9 km

• OK, my bad. One day I'll get used to all those prefixes... Post will be edited to reflect Million rather than 1000 Million. However, I think it is fair to say we're looking at a Very Big 100Km-high (Karman Line) Box. May 11 '18 at 5:25
• This should not be the correct answer. It is very wrong. Major problem: 5 million is 5000000, not 5000000000. Another problem: A pound mass and a pound force are different units. It happens to be a wash in this case, but equating the two (pounds mass and pounds force) is a sign of sloppiness. Rather minor problem: The article talked about tonnes (1000 kg) rather than tons (2000 lb). May 11 '18 at 5:42
• @David Hammen - Apart from my complete ineptitude with Mega-Giga-, jamesqf's arithmetic looks OK to me. My own check using his logic but my corrected number shows a 222.14m square, which sanity-checks with removing excess zeroes. So the Very Big Box meta-answer is still good enough for me. May 11 '18 at 6:05
• About "proper" units. In Oz we have been saddled with the Pascal as the unit of pressure, While this is technically correct, it is in fact rather useless for the laity. We note that in most of Europe (and France is the Home of SI) pressure is routinely expressed as Kg/cm^2. This avoids the possiblity of introducing headaches like momentum and acceleration. May 11 '18 at 6:15
• Using this approach (but in SI units, and with 5Mt rather than 5Gt), I reckon it's a block of the atmosphere resting on a square of sides around 700m. Done in a very quick 'n dirty fashion, though, so might well be wrong. Also, kinda wrong in principle, since the mass of that volume of CO2 would be significantly more than the mass of that volume of air. May 11 '18 at 6:37