One Pound of Coal = 625 L of CO2

Climate Change

Official sources usually describe greenhouse gas emissions by the weight of the gas produced, typically in kilograms of CO2.  This is strange because we normally use kilograms to refer to the amount of a solid substance (weight), and we use volume to refer to the amount of a liquid or gas (e.g. Liters). 

When CO2 is in solid form it is known as “dry ice” and it sublimates into a gas at any temperature above -78.51 C.  In fact liquid CO2 can only be formed at high pressures greater than 5 atmospheres.  Since CO2 is normally a gas called carbon dioxide, don’t you sometimes wonder how much of the gas is actually produced and how much space it takes up? 

Chemistry

There is no easy conversion of weight to volume because different liquids and gases have different molecular densities.  The only easy exception is that proves this rule is that 1 liter of water weighs 1 kilogram at sea level (the original definition for these units).

The combustion of all carbon containing fuels, such as methane (natural gas), petroleum distillates (gasoline, diesel, kerosene, propane), but also of coal and wood, will yield carbon dioxide and, in most cases, water. As an example the chemical reaction between methane and oxygen is given below.

CH4 + 2 O2 → CO2 + 2 H2O

Since coal is 60 – 80% pure carbon (depending on the “hardness” of the coal in question), burning coal is pretty much the same as burning carbon.  Burning carbon in the presence of oxygen (O2) has two possible combustion reactions: C + O2 -> CO2 (i.e. carbon dioxide) and C + 0.5*O2 -> CO (i.e. carbon monoxide). 

If too much carbon is present (relative to the amount of oxygen) when the combustion occurs, then CO will be produced.  When sufficient oxygen is present CO2 will be produced instead of CO, unless the combustion occurs at very high temperatures such as above 800 C.  Since the self ignition temperature of coal is 400 to 425 C (depending on moisture content and environmental conditions), the burning of coal is well below this threshold and CO2 is the main byproduct of the combustion.

Calculation

To calculate how much CO2 is produced in the chemical reaction from burning coal, we need to calibrate the chemical formula using moles.  Carbon has a molecular mass of 12.011 grams per mole and CO2 has a molecular mass of 44.009 grams per mole. 

1 pound of coal contains 453.59 g/lb x 70% =  317.5 g carbon, or 317.5 / 12 g/mol = 26.4 mols of carbon.  Since the number of atoms in a chemical reaction remain unchanged, this means that buring 1 pound of coal must produce 26.4 mols of CO2.  This amount of CO2 will weigh 26.4 x 44 = 1163 grams = 1.16 Kg.

We can apply the law for ideal gases, V=nRT/P, to convert from mols to liters if we know the temperature and the pressure of the gas:

  • n is the number of mols
  • R is the universal gas constant = 8.3145 (L x Pa) / (mol x K)
  • T is the absolute temperatures measured on the Kelvin scale.  It is possible to mix Kelvin and Celsius in this equation as long as we adjust for zero (0 C = 273.15 K) because 1 degree Celsius has the same gradation in heat as one degree Kelvin
  • P is the pressure measured in kiloPa

Suppose the coal is burned at 415 Celsius at sea level (101.325 kPa is the average sea level barometric pressure),

V = (26.43 Mols) * (8.3145 L*kPa/Mols/K) * (415 Celsius+273.15 Kelvin) / 101.325kPa = 1492 Litres 

Of course, the resulting CO2 gas won’t stay that hot and it will contract in volume as it cools.  By using the same calculation with 15 degrees C (the average temperature of the earth, across all seasons and geographic areas) instead of 415 C,

V = (26.43 Mols) * (8.3145 L*kPa/Mols/K) * (15 Celsius+273.15 Kelvin) / 101.325kPa = 624.98 Litres 

So  1 pound of coal cools into 625 Litres of CO2 once the gas has cooled down to ambient air temperature.  The density of this gas is 26.43 mols x 44 g/mol / 625 L =  1.86 g/L.

Impact

Burning 1 long ton of coal (2240 pounds) produces 635,013 L of CO2 gas that weighs 1.18 metric tons.  This volume of gas is roughly 5x the volume of the 40′ x 20′ in-ground swiming pool in my backyard.  This is a pretty big pool that can easily be seen from space by the Google satellite in the centre of the photo below.

Paul\'s Pool

So for every ton of coal burned, we end up with 5 swimming pools worth of CO2 hanging around in the atmosphere. 

We could plant a lot of trees to absorb that, but a typical mature tree typically weighs about 3 tons, just over 2 tons of that comes from carbon dioxide.  Each ton of coal would need 1 tree planted and 50 years to grow to offset the carbon dioxide.  But, as Ronald Reagan pointed out trees cause pollution because they also release carbon dioxide.

If this is taken into account then an average tree will absorb about 25 grams more CO2 per day than it releases. Since a typical person generates about 2 to 2.2 pounds of CO2 per day, so for the entire Earth’s population, humans alone generate about 6 to 7 million tons of CO2 per day just by breathing.  Just to keep up with human CO2 output from breathing we would need about 100 billion trees – without offsetting the burning any coal!

The other major natural carbon sink is the ocean which currently absorbs approx 6 Billion Tons of CO2 per year.  Although this is a very large number, studies estimate that it is already only 27% of our collective CO2 emissions worldwide.

Guess we’ll just have to find ways to burn less coal!

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