What is a possible mole-mole factor for the following equation? $$ 2 \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{C} \rightarrow 3 \mathrm{CO}_{2}+4 \mathrm{Fe} $$ View Available Hint(s) 2 moles Fe 3 moles $$ \mathrm{CO}_{2} $$ 2 moles $$ \mathrm{Fe}_{3} $$ moles C 3 moles $$ \mathrm{Fe}_{2} \mathrm{O}_{3} 2 $$ moles C 3 moles $$ \mathrm{CO}_{2} 2 $$ moles $$ \mathrm{Fe}_{2} \mathrm{O}_{3} $$

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Given the reaction

$$
2\, \mathrm{Fe}_{2}\mathrm{O}_{3} + 3\, \mathrm{C} \rightarrow 3\, \mathrm{CO}_{2} + 4\, \mathrm{Fe},
$$

we want to find a mole‐to‐mole conversion factor (mole-mole factor). One valid approach is to compare the coefficients of any two substances in the balanced equation.

Step 1. Identify the coefficients:
- For $$\mathrm{Fe}_{2}\mathrm{O}_{3}$$, the coefficient is 2.
- For $$\mathrm{CO}_{2}$$, the coefficient is 3.

Step 2. Write the mole-to-mole ratio:
$$
\frac{3\, \text{moles } \mathrm{CO}_{2}}{2\, \text{moles } \mathrm{Fe}_{2}\mathrm{O}_{3}}
$$

This tells us that for every 2 moles of $$\mathrm{Fe}_{2}\mathrm{O}_{3}$$ that react, 3 moles of $$\mathrm{CO}_{2}$$ are produced.

Step 3. Match with one of the provided options:
The option "3 moles $$\mathrm{CO}_{2}$$ 2 moles $$\mathrm{Fe}_{2}\mathrm{O}_{3}$$" represents the factor we obtained.

Thus, a possible mole-mole factor is:

$$
\boxed{ \frac{3\, \mathrm{CO}_{2}}{2\, \mathrm{Fe}_{2}\mathrm{O}_{3}} }
$$
A possible mole-mole factor is 3 moles of $$ \mathrm{CO}_{2} $$ for every 2 moles of $$ \mathrm{Fe}_{2}\mathrm{O}_{3} $$.

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