How many grams of [tex]CO[/tex] would be required to generate [tex]635 \, g \, CO_2[/tex]?

[tex]\[
\begin{array}{l}
Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2 \\
\text{Molar mass of CO: } 28.01 \, g/mol \\
\text{Molar mass of CO}_2\text{: } 44.01 \, g/mol \\
\end{array}
\][/tex]



Answer :

To find out how many grams of CO would be required to generate 635 grams of CO[tex]\(_2\)[/tex], we will follow a series of stoichiometric calculations based on the given chemical equation:

[tex]\[ \text{Fe}_2\text{O}_3 + 3 \text{CO} \rightarrow 2 \text{Fe} + 3 \text{CO}_2 \][/tex]

The molar masses provided are:
- [tex]\( \text{CO}_2 \)[/tex]: 44.01 g/mol
- [tex]\( \text{CO} \)[/tex]: 28.01 g/mol

### Step-by-Step Solution

1. Calculate the number of moles of [tex]\( \text{CO}_2 \)[/tex] produced:

First, we need to convert the mass of [tex]\( \text{CO}_2 \)[/tex] into moles. We use the molar mass of [tex]\( \text{CO}_2 \)[/tex]:

[tex]\[ \text{Number of moles of } \text{CO}_2 = \frac{\text{mass of } \text{CO}_2}{\text{molar mass of } \text{CO}_2} \][/tex]

[tex]\[ \text{Number of moles of } \text{CO}_2 = \frac{635 \text{ g}}{44.01 \text{ g/mol}} \approx 14.43 \text{ moles} \][/tex]

2. Use stoichiometry to find the number of moles of [tex]\( \text{CO} \)[/tex] required:

According to the balanced chemical equation, 3 moles of [tex]\( \text{CO} \)[/tex] produce 3 moles of [tex]\( \text{CO}_2 \)[/tex]. This means that the mole ratio of [tex]\( \text{CO} \)[/tex] to [tex]\( \text{CO}_2 \)[/tex] is 1:1.

Therefore, the number of moles of [tex]\( \text{CO} \)[/tex] required to produce 14.43 moles of [tex]\( \text{CO}_2 \)[/tex] is also 14.43 moles.

3. Calculate the mass of [tex]\( \text{CO} \)[/tex] required:

To find the mass, convert the moles of [tex]\( \text{CO} \)[/tex] back into grams using the molar mass of [tex]\( \text{CO} \)[/tex]:

[tex]\[ \text{Mass of } \text{CO} = \text{number of moles of } \text{CO} \times \text{molar mass of } \text{CO} \][/tex]

[tex]\[ \text{Mass of } \text{CO} = 14.43 \text{ moles} \times 28.01 \text{ g/mol} \approx 404.14 \text{ g} \][/tex]

### Conclusion

Therefore, 404.14 grams of CO would be required to generate 635 grams of [tex]\( \text{CO}_2 \)[/tex].