Question

1. when the equation \\(\text{fe}_3\text{o}_4 + \text{al} \

ightarrow \text{al}_2\text{o}_3 + \text{fe}\\) is correctly balanced, what is the coefficient of \\(\text{fe}\\)?

a) 3
b) 4
c) 6
d) 9

Explanation:

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<reasoning>

Balance oxygen atoms

\[

$$\begin{aligned} &\text{Reactant: } \text{Fe}_3\text{O}_4 \quad (4 \text{ O atoms})\\ &\text{Product: } \text{Al}_2\text{O}_3 \quad (3 \text{ O atoms})\\ &\text{LCM of 4 and 3 is 12.}\\ &3\text{Fe}_3\text{O}_4 + \text{Al} ightarrow 4\text{Al}_2\text{O}_3 + \text{Fe} \end{aligned}$$

\]

Balance aluminum and iron atoms

\[

$$\begin{aligned} &\text{Reactant Fe: } 3 \times 3 = 9 \text{ atoms}\\ &\text{Product Al: } 4 \times 2 = 8 \text{ atoms}\\ &3\text{Fe}_3\text{O}_4 + 8\text{Al} ightarrow 4\text{Al}_2\text{O}_3 + 9\text{Fe} \end{aligned}$$

\]

Identify the coefficient of Fe

\[

$$\begin{aligned} &\text{Balanced Equation: } 3\text{Fe}_3\text{O}_4 + 8\text{Al} ightarrow 4\text{Al}_2\text{O}_3 + 9\text{Fe}\\ &\text{Coefficient of Fe} = 9 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 3</mcq-option>
<mcq-option>(B) 4</mcq-option>
<mcq-option>(C) 6</mcq-option>
<mcq-correct>(D) 9</mcq-correct>
</answer>

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Answer:

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<reasoning>

Balance oxygen atoms

\[

$$\begin{aligned} &\text{Reactant: } \text{Fe}_3\text{O}_4 \quad (4 \text{ O atoms})\\ &\text{Product: } \text{Al}_2\text{O}_3 \quad (3 \text{ O atoms})\\ &\text{LCM of 4 and 3 is 12.}\\ &3\text{Fe}_3\text{O}_4 + \text{Al} ightarrow 4\text{Al}_2\text{O}_3 + \text{Fe} \end{aligned}$$

\]

Balance aluminum and iron atoms

\[

$$\begin{aligned} &\text{Reactant Fe: } 3 \times 3 = 9 \text{ atoms}\\ &\text{Product Al: } 4 \times 2 = 8 \text{ atoms}\\ &3\text{Fe}_3\text{O}_4 + 8\text{Al} ightarrow 4\text{Al}_2\text{O}_3 + 9\text{Fe} \end{aligned}$$

\]

Identify the coefficient of Fe

\[

$$\begin{aligned} &\text{Balanced Equation: } 3\text{Fe}_3\text{O}_4 + 8\text{Al} ightarrow 4\text{Al}_2\text{O}_3 + 9\text{Fe}\\ &\text{Coefficient of Fe} = 9 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 3</mcq-option>
<mcq-option>(B) 4</mcq-option>
<mcq-option>(C) 6</mcq-option>
<mcq-correct>(D) 9</mcq-correct>
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