To determine the mole ratio of [tex]\( Fe \)[/tex] to [tex]\( Fe_2O_3 \)[/tex] from the given balanced chemical equation:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
we need to consider the stoichiometric coefficients of [tex]\( Fe \)[/tex] and [tex]\( Fe_2O_3 \)[/tex] in the equation. These coefficients indicate the number of moles of each substance involved in the reaction.
In this case, the balanced equation shows:
- 4 moles of [tex]\( Fe \)[/tex] react with
- 3 moles of [tex]\( O_2 \)[/tex] to produce
- 2 moles of [tex]\( Fe_2O_3 \)[/tex]
To find the mole ratio of [tex]\( Fe \)[/tex] to [tex]\( Fe_2O_3 \)[/tex], we compare their coefficients. The coefficient for [tex]\( Fe \)[/tex] is 4, and the coefficient for [tex]\( Fe_2O_3 \)[/tex] is 2. The mole ratio of [tex]\( Fe \)[/tex] to [tex]\( Fe_2O_3 \)[/tex] is thus:
[tex]\[ \frac{\text{moles of } Fe}{\text{moles of } Fe_2O_3} = \frac{4}{2} \][/tex]
Simplifying this fraction:
[tex]\[ \frac{4}{2} = 2.0 \][/tex]
Therefore, the correct fraction that represents the mole ratio to determine the mass of [tex]\( Fe \)[/tex] from a known mass of [tex]\( Fe_2O_3 \)[/tex] is:
[tex]\[ \frac{4}{2} \][/tex]
Thus, the fraction [tex]\(\frac{4}{2}\)[/tex] can be used for the mole ratio in this scenario.
