Which coefficients would balance this chemical equation? Fe2O3 ---> Fe + O2
Understand the Problem
The question is asking which coefficients would properly balance the provided chemical equation involving iron (Fe) and oxygen (O2) based on the decomposition of iron(III) oxide (Fe2O3). The user needs to determine the correct stoichiometric coefficients for each compound involved in the reaction.
Answer
The balanced coefficients are \(2, 4, 3\).
Answer for screen readers
The coefficients that balance the equation are (2, 4, 3).
Steps to Solve
- Identify the Reaction Components
The chemical equation is:
$$ __\text{Fe}_2\text{O}_3 \rightarrow __\text{Fe} + __\text{O}_2 $$
Where ( \text{Fe}_2\text{O}_3 ) is iron(III) oxide, and it decomposes into iron (Fe) and oxygen (O2).
- Count the Atoms of Each Element
Count the number of atoms for each element in the reactants and products.
-
On the left (reactants):
- Iron (Fe): 2
- Oxygen (O): 3
-
On the right (products):
- Iron (Fe): 1 (from Fe)
- Oxygen (O): 2
- Balance the Iron Atoms
To balance the iron atoms, place a coefficient of 2 in front of Fe on the product side:
$$ \text{Fe}_2\text{O}_3 \rightarrow 2\text{Fe} + __\text{O}_2 $$
Now we have:
- Iron (Fe): Left: 2 | Right: 2
- Balance the Oxygen Atoms
Now balance the oxygen atoms. We have 3 oxygen atoms in (\text{Fe}_2\text{O}_3) and only 2 in (O_2). To balance 3 oxygen atoms, place a coefficient of ( \frac{3}{2} ) in front of (O_2):
$$ \text{Fe}_2\text{O}_3 \rightarrow 2\text{Fe} + \frac{3}{2}\text{O}_2 $$
- Convert to Whole Numbers
To eliminate the fraction, multiply all coefficients by 2:
$$ 2\text{Fe}_2\text{O}_3 \rightarrow 4\text{Fe} + 3\text{O}_2 $$
Now we have whole numbers for the coefficients:
- Fe2O3: 2
- Fe: 4
- O2: 3
The coefficients that balance the equation are (2, 4, 3).
More Information
The balanced chemical equation for the decomposition of iron(III) oxide shows that two molecules of (\text{Fe}_2\text{O}_3) decompose to produce four iron atoms and three oxygen molecules.
Tips
- Incorrect Counting: Miscounting the atoms on either side can lead to errors in balancing.
- Using Fractions: Sometimes, people forget to multiply coefficients to get whole numbers.
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