- Given the unbalanced equation: C3H8 + O2 CO2 + H2O a. How many moles of oxygen gas are required to make 4.00 moles of carbon dioxide? b. How many moles of C3H8 must be used to produce 2.00 grams of water?
The Correct Answer and Explanation is :
To address the questions based on the unbalanced chemical equation:
[ \text{C}_3\text{H}_8 + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} ]
a. How many moles of oxygen gas are required to make 4.00 moles of carbon dioxide?
First, balance the chemical equation:
[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} ]
From the balanced equation, the stoichiometric ratio between oxygen gas (O₂) and carbon dioxide (CO₂) is 5:3.
This means that for every 3 moles of CO₂ produced, 5 moles of O₂ are consumed.
To find the moles of O₂ required for 4.00 moles of CO₂:
[
\text{Moles of O}_2 = \left( \frac{5 \, \text{moles O}_2}{3 \, \text{moles CO}_2} \right) \times 4.00 \, \text{moles CO}_2 = 6.67 \, \text{moles O}_2
]
Therefore, 6.67 moles of oxygen gas are required to produce 4.00 moles of carbon dioxide.
b. How many moles of C₃H₈ must be used to produce 2.00 grams of water?
The molar mass of water (H₂O) is approximately 18.02 g/mol.
To find the moles of H₂O produced from 2.00 grams:
[
\text{Moles of H}_2\text{O} = \frac{2.00 \, \text{g}}{18.02 \, \text{g/mol}} \approx 0.111 \, \text{moles H}_2\text{O}
]
From the balanced equation, the stoichiometric ratio between propane (C₃H₈) and water (H₂O) is 1:4.
This means that for every 1 mole of C₃H₈, 4 moles of H₂O are produced.
To find the moles of C₃H₈ required to produce 0.111 moles of H₂O:
[
\text{Moles of C}_3\text{H}_8 = \left( \frac{1 \, \text{mole C}_3\text{H}_8}{4 \, \text{moles H}_2\text{O}} \right) \times 0.111 \, \text{moles H}_2\text{O = 0.0278 moles C}_3\text{H}_8}
]
Therefore, approximately 0.0278 moles of C₃H₈ are required to produce 2.00 grams of water.
Explanation:
Stoichiometry involves using the relationships between reactants and products in a balanced chemical equation to calculate the quantities of substances involved in a reaction.
In part (a), the balanced equation indicates that 5 moles of O₂ are required to produce 3 moles of CO₂.
By setting up a proportion, we can determine that 6.67 moles of O₂ are needed to produce 4.00 moles of CO₂.
In part (b), the balanced equation shows that 1 mole of C₃H₈ produces 4 moles of H₂O.
By calculating the moles of H₂O from its mass and using the stoichiometric ratio, we find that 0.0278 moles of C₃H₈ are required to produce 2.00 grams of water.
These calculations demonstrate how stoichiometric relationships allow chemists to predict the amounts of reactants needed to produce desired amounts of products in chemical reactions.