Answer :
To solve this problem, we need to follow a few key steps: balancing the chemical equation and using stoichiometry to find the moles of oxygen required. Let's go through these steps:
1. Balance the chemical equation:
The unbalanced equation for the combustion of propane ([tex]\(C_3H_8\)[/tex]) is given as:
[tex]\[
C_3H_8 + O_2 \rightarrow H_2O + CO_2
\][/tex]
First, let's balance the carbon atoms. Propane has 3 carbon atoms, so we need 3 carbon dioxide molecules ([tex]\(CO_2\)[/tex]) on the right side:
[tex]\[
C_3H_8 + O_2 \rightarrow H_2O + 3CO_2
\][/tex]
Next, balance the hydrogen atoms. Propane has 8 hydrogen atoms, so we need 4 water molecules ([tex]\(H_2O\)[/tex]) to have 8 hydrogen atoms on the right side:
[tex]\[
C_3H_8 + O_2 \rightarrow 4H_2O + 3CO_2
\][/tex]
Finally, balance the oxygen atoms. On the right side, we have [tex]\(3 \times 2 = 6\)[/tex] oxygen atoms from [tex]\(CO_2\)[/tex] and [tex]\(4 \times 1 = 4\)[/tex] oxygen atoms from [tex]\(H_2O\)[/tex], giving a total of 10 oxygen atoms needed:
[tex]\[
C_3H_8 + 5O_2 \rightarrow 4H_2O + 3CO_2
\][/tex]
The balanced equation is:
[tex]\[
C_3H_8 + 5O_2 \rightarrow 4H_2O + 3CO_2
\][/tex]
2. Determine the moles of oxygen required:
According to the balanced equation, 5 moles of [tex]\(O_2\)[/tex] are required to completely burn 1 mole of [tex]\(C_3H_8\)[/tex].
3. Calculate the moles of oxygen needed for 5.00 moles of propane:
If we have 5.00 moles of propane, the moles of oxygen required can be calculated by multiplying the moles of propane by the ratio of moles of oxygen to moles of propane from the balanced equation:
[tex]\[
\text{Moles of } O_2 = 5.00 \, \text{moles of } C_3H_8 \times 5 \, \frac{\text{moles of } O_2}{\text{mole of } C_3H_8} = 25.00 \, \text{moles of } O_2
\][/tex]
Therefore, 25.0 moles of oxygen are required to completely burn 5.00 moles of propane.
1. Balance the chemical equation:
The unbalanced equation for the combustion of propane ([tex]\(C_3H_8\)[/tex]) is given as:
[tex]\[
C_3H_8 + O_2 \rightarrow H_2O + CO_2
\][/tex]
First, let's balance the carbon atoms. Propane has 3 carbon atoms, so we need 3 carbon dioxide molecules ([tex]\(CO_2\)[/tex]) on the right side:
[tex]\[
C_3H_8 + O_2 \rightarrow H_2O + 3CO_2
\][/tex]
Next, balance the hydrogen atoms. Propane has 8 hydrogen atoms, so we need 4 water molecules ([tex]\(H_2O\)[/tex]) to have 8 hydrogen atoms on the right side:
[tex]\[
C_3H_8 + O_2 \rightarrow 4H_2O + 3CO_2
\][/tex]
Finally, balance the oxygen atoms. On the right side, we have [tex]\(3 \times 2 = 6\)[/tex] oxygen atoms from [tex]\(CO_2\)[/tex] and [tex]\(4 \times 1 = 4\)[/tex] oxygen atoms from [tex]\(H_2O\)[/tex], giving a total of 10 oxygen atoms needed:
[tex]\[
C_3H_8 + 5O_2 \rightarrow 4H_2O + 3CO_2
\][/tex]
The balanced equation is:
[tex]\[
C_3H_8 + 5O_2 \rightarrow 4H_2O + 3CO_2
\][/tex]
2. Determine the moles of oxygen required:
According to the balanced equation, 5 moles of [tex]\(O_2\)[/tex] are required to completely burn 1 mole of [tex]\(C_3H_8\)[/tex].
3. Calculate the moles of oxygen needed for 5.00 moles of propane:
If we have 5.00 moles of propane, the moles of oxygen required can be calculated by multiplying the moles of propane by the ratio of moles of oxygen to moles of propane from the balanced equation:
[tex]\[
\text{Moles of } O_2 = 5.00 \, \text{moles of } C_3H_8 \times 5 \, \frac{\text{moles of } O_2}{\text{mole of } C_3H_8} = 25.00 \, \text{moles of } O_2
\][/tex]
Therefore, 25.0 moles of oxygen are required to completely burn 5.00 moles of propane.
