For complete combustion of 1 mole of each propane and butane. Find sum of minimum number of moles of `O_2` required

Answer

To find the sum of the minimum number of moles of O₂ required for the complete combustion of 1 mole of propane (C₃H₈) and 1 mole of butane (C₄H₁₀), we will follow these steps:

### Step 1: Write the combustion reaction for propane (C₃H₈)
The balanced equation for the combustion of propane is:
\[ C_3H_8 + O_2 \rightarrow CO_2 + H_2O \]

### Step 2: Balance the combustion reaction for propane
1. **Count the number of carbon (C) atoms**: There are 3 carbon atoms in propane, so we will produce 3 CO₂:
\[ C_3H_8 + O_2 \rightarrow 3CO_2 + H_2O \]

2. **Count the number of hydrogen (H) atoms**: There are 8 hydrogen atoms in propane, so we will produce 4 H₂O:
\[ C_3H_8 + O_2 \rightarrow 3CO_2 + 4H_2O \]

3. **Count the total number of oxygen (O) atoms needed on the product side**:
- From 3 CO₂, we need \(3 \times 2 = 6\) O atoms.
- From 4 H₂O, we need \(4 \times 1 = 4\) O atoms.
- Total O atoms needed = \(6 + 4 = 10\) O atoms.

4. **Determine the moles of O₂ required**: Since O₂ has 2 O atoms per molecule, we need:
\[ \frac{10}{2} = 5 \text{ moles of } O_2 \]

### Step 3: Write the combustion reaction for butane (C₄H₁₀)
The balanced equation for the combustion of butane is:
\[ C_4H_{10} + O_2 \rightarrow CO_2 + H_2O \]

### Step 4: Balance the combustion reaction for butane
1. **Count the number of carbon (C) atoms**: There are 4 carbon atoms in butane, so we will produce 4 CO₂:
\[ C_4H_{10} + O_2 \rightarrow 4CO_2 + H_2O \]

2. **Count the number of hydrogen (H) atoms**: There are 10 hydrogen atoms in butane, so we will produce 5 H₂O:
\[ C_4H_{10} + O_2 \rightarrow 4CO_2 + 5H_2O \]

3. **Count the total number of oxygen (O) atoms needed on the product side**:
- From 4 CO₂, we need \(4 \times 2 = 8\) O atoms.
- From 5 H₂O, we need \(5 \times 1 = 5\) O atoms.
- Total O atoms needed = \(8 + 5 = 13\) O atoms.

4. **Determine the moles of O₂ required**: Since O₂ has 2 O atoms per molecule, we need:
\[ \frac{13}{2} = 6.5 \text{ moles of } O_2 \]

### Step 5: Calculate the total moles of O₂ required
Now, we will sum the moles of O₂ required for both propane and butane:
\[ 5 + 6.5 = 11.5 \text{ moles of } O_2 \]

### Final Answer
The sum of the minimum number of moles of O₂ required for the complete combustion of 1 mole of propane and 1 mole of butane is:
\[ \boxed{11.5} \]