Converting from a mass of carbon to a mass of carbon dioxide

A very short post about a very small point of arithmetic.

C + O₂ → CO₂

Carbon dioxide emissions are sometimes quoted as a mass of carbon, and sometimes as a mass of carbon dioxide. This often causes a bit of confusion. In fact several of the comments on this blog have voiced concern that I may have overlooked this point myself.

This question comes up so often in discussions (and indeed on this blog) that I’ve decided to devote an entire post to this one very short calculation.

CO₂ emissions quoted as a mass of carbon refer to the mass of carbon atoms present in the fuel being burnt. Emissions quoted as a mass of carbon dioxide refer to the mass of the molecular CO₂ after combustion.

How do the two differ?

The atomic mass of carbon is 12, the atomic mass of oxygen is 16, so the molecular mass of a CO₂ molecule is the mass of one carbon atom plus two oxygen atoms, that is, 12 + (2×16) = 44.

In other words, every 12 grams of elemental carbon will burn to form 44 grams of carbon dioxide. To convert from an emissions figure given as a mass of carbon to the equivalent mass of carbon dioxide, the mass as carbon must be multiplied by 44/12 = 3.67. For example, an emissions figure quoted as 100 g of carbon converts to 367 g of carbon dioxide. The two numbers refer to the same amount of emissions, just expressed in different ways.

Well, erm, that’s it for this post. That’s the only point I’m making here – multiply by 44/12 to convert from emissions expressed as a mass of carbon to the equivalent mass of carbon dioxide.

To end with a remark about this blog, several of the posts here are sets of data collated from many diverse sources, and the original data I’ve brought in are expressed in many different units. The data have to be presented in some standardised set of units to allow for easy comparison, and I’ve been performing the unit conversions needed to do that. Barring some “fat fingers” mistakes on a spreadsheet, I’m pretty confident the conversions are correct.

Update, Sept. 23, 2008: Oh dear, having said that, a transcription error has now been pointed out to me, in this comment. Oops, fixed now.