Hello, Joseph,
The mole ratio is obtained from the coefficients of a balanced equation. This one looks balanced, so I trust that it takes 2 moles of Fe2CO3 to produce 3 moles CO2. Just use the coefficients to determine the molar ratio of the compounds. We can use that ratio to answer the next part of the question.
2 Fe2O3 + 3 C → 4 Fe + 3 CO2
___2_moles Fe2O3 : _3__moles CO2
This is simply a conversion factor. We can arrange the terms such that "moles CO2" is either on the top (for a 3/2 ratio) or on the bottom (2/3 ratio).
If you started this reaction with 7.7 moles of Fe2O3, how many moles of CO2 would be produced?
We can use the above conversion factor, with moles CO2 on top.
(7.7 moles Fe2O3)*(3 moles CO2/2 moles Fe2CO3) = 23.1 moles CO2
Bob
Bob