Answer :
To solve this problem, we need to balance the chemical equation for the complete combustion of propane (C₃H₈) and then determine how many moles of oxygen (O₂) are required to burn 5.00 moles of propane.
Step 1: Balance the chemical equation
The unbalanced equation is:
[tex]\[ C_3H_8 + O_2 \rightarrow H_2O + CO_2 \][/tex]
To balance it, we need to make sure there are equal numbers of each type of atom on both sides of the equation.
- Carbon (C): There are 3 carbon atoms in C₃H₈, so we need 3 CO₂ molecules to balance the carbon atoms. This gives us:
[tex]\[ C_3H_8 + O_2 \rightarrow H_2O + 3CO_2 \][/tex]
- Hydrogen (H): There are 8 hydrogen atoms in C₃H₈, so we need 4 H₂O molecules to get 8 hydrogen atoms on the right side. This gives us:
[tex]\[ C_3H_8 + O_2 \rightarrow 4H_2O + 3CO_2 \][/tex]
- Oxygen (O): Now, count the number of oxygen atoms needed on the right side. We have 3 CO₂ (which gives 6 oxygen atoms) and 4 H₂O (which gives 4 oxygen atoms), totaling 10 oxygen atoms. Therefore, we need 5 O₂ molecules to provide these 10 oxygen atoms. The balanced equation is:
[tex]\[ C_3H_8 + 5O_2 \rightarrow 4H_2O + 3CO_2 \][/tex]
Step 2: Calculate the moles of oxygen required
According to the balanced equation, 1 mole of propane (C₃H₈) reacts with 5 moles of oxygen (O₂). Thus, 5.00 moles of propane would react with:
[tex]\[ 5.00 \, \text{moles of C}_3\text{H}_8 \times \frac{5 \, \text{moles of O}_2}{1 \, \text{mole of C}_3\text{H}_8} = 25.0 \, \text{moles of O}_2 \][/tex]
Therefore, 25.0 moles of oxygen are required to completely burn 5.00 moles of propane.
Step 1: Balance the chemical equation
The unbalanced equation is:
[tex]\[ C_3H_8 + O_2 \rightarrow H_2O + CO_2 \][/tex]
To balance it, we need to make sure there are equal numbers of each type of atom on both sides of the equation.
- Carbon (C): There are 3 carbon atoms in C₃H₈, so we need 3 CO₂ molecules to balance the carbon atoms. This gives us:
[tex]\[ C_3H_8 + O_2 \rightarrow H_2O + 3CO_2 \][/tex]
- Hydrogen (H): There are 8 hydrogen atoms in C₃H₈, so we need 4 H₂O molecules to get 8 hydrogen atoms on the right side. This gives us:
[tex]\[ C_3H_8 + O_2 \rightarrow 4H_2O + 3CO_2 \][/tex]
- Oxygen (O): Now, count the number of oxygen atoms needed on the right side. We have 3 CO₂ (which gives 6 oxygen atoms) and 4 H₂O (which gives 4 oxygen atoms), totaling 10 oxygen atoms. Therefore, we need 5 O₂ molecules to provide these 10 oxygen atoms. The balanced equation is:
[tex]\[ C_3H_8 + 5O_2 \rightarrow 4H_2O + 3CO_2 \][/tex]
Step 2: Calculate the moles of oxygen required
According to the balanced equation, 1 mole of propane (C₃H₈) reacts with 5 moles of oxygen (O₂). Thus, 5.00 moles of propane would react with:
[tex]\[ 5.00 \, \text{moles of C}_3\text{H}_8 \times \frac{5 \, \text{moles of O}_2}{1 \, \text{mole of C}_3\text{H}_8} = 25.0 \, \text{moles of O}_2 \][/tex]
Therefore, 25.0 moles of oxygen are required to completely burn 5.00 moles of propane.
