How many moles of oxygen are needed to react with 23.8 moles of aluminum?
Understand the Problem
The question is asking how many moles of oxygen are required to fully react with a given quantity of aluminum (23.8 moles). This involves using stoichiometry from a balanced chemical equation, likely for the reaction of aluminum and oxygen.
Answer
$17.85$ moles of oxygen are needed to react with $23.8$ moles of aluminum.
Answer for screen readers
The number of moles of oxygen needed to react with 23.8 moles of aluminum is $17.85$ moles.
Steps to Solve
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Identify the balanced chemical equation
The reaction between aluminum and oxygen can be represented by the balanced equation:
$$ 4 \text{Al} + 3 \text{O}_2 \rightarrow 2 \text{Al}_2\text{O}_3 $$
This shows that 4 moles of aluminum react with 3 moles of oxygen. -
Determine the mole ratio
From the balanced equation, the mole ratio of aluminum to oxygen is:
$$ \frac{4 \text{ moles Al}}{3 \text{ moles O}_2} $$ -
Calculate the moles of oxygen needed
Using the mole ratio, calculate the required moles of oxygen for 23.8 moles of aluminum:
$$ \text{moles of O}_2 = \frac{3 \text{ moles O}_2}{4 \text{ moles Al}} \times 23.8 \text{ moles Al} $$ -
Perform the calculation
Calculate the moles of oxygen:
$$ \text{moles of O}_2 = \frac{3}{4} \times 23.8 = 17.85 \text{ moles O}_2 $$
The number of moles of oxygen needed to react with 23.8 moles of aluminum is $17.85$ moles.
More Information
This calculation is based on stoichiometry, where balanced equations allow us to determine how much of a reactant is needed to react with a given amount of another substance. In this specific case, aluminum oxide ($\text{Al}_2\text{O}_3$) is produced when aluminum and oxygen react.
Tips
- Incorrect mole ratio: Sometimes students confuse the mole ratio from the balanced equation. Always verify the correct ratio.
- Omitting units: Forgetting to account for moles can lead to wrong calculations. Keep track of your units throughout.
- Not using the balanced equation: Using initial unbalanced equations can lead to errors in calculations. Always start from a balanced equation.
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