# How to calculate weight of CO₂ in one kg of fuel

I'm trying to do homework and I have the answers to the problems but I can't read the explanation because it's illegible and I can't find how it's done in my notes.

Here's the simplest example:

$$\ce{ C + O_2 \to CO_2}$$

It looks like the answer is 44/12 but I don't understand where the 12 comes from at all. How is a question like this approached? (Didn't know what to search in google to get an explanation).

• Do you know what the concept of "molar mass" is? And "relative atomic mass" (aka "atomic weight")? – EnergyNumbers Feb 10 '13 at 16:27

You have 1 mol $\ce{C}$ reacting with 1 mol $\ce{O_2}$ to give 1 mol of $\ce{CO_2}$

What you need now is something to relate weight and mol. This is called molar mass, notated with the letter M, and has the unit g/mol. You'd just look that up on the internet, but it's calculated from the weight of the atoms in each molecule. If a molecule weighs 32.2 units, then it'd have a molar mass of 32.2 g/mol.

The calculations are pretty straight forward. How many moles of fuel per kilo? $1000g / M(\ce{C})$, where M, as noted, indicates molar mass.

You know that 1 mol carbon turned into 1 mol carbondioxide. So the number you just calculated is thus also the moles of carbondioxide. You need to find out how many grams those x mol carbondioxide corresponds to: $n(\ce{CO_2}) * M(\ce{CO_2}) = m(\ce{CO_2})$.

If you're not confident in this, pay attention to the units. n = mol; M = g/mol; m = g. Thus multiplying M by n yields a figure in grams. Is that clear?