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 balanced chemical equation for the combustion of propane (C₃H₈).

The complete combustion of propane can be represented as:
\[ C_3H_8 + O_2 \rightarrow CO_2 + H_2O \]

### Step 2: Balance the equation for propane.

1. **Carbon atoms**: There are 3 carbon atoms in propane, so we need 3 CO₂.
2. **Hydrogen atoms**: There are 8 hydrogen atoms in propane, so we need 4 H₂O.
3. **Oxygen atoms**: Now, we count the oxygen atoms needed:
- From 3 CO₂, we get 3 × 2 = 6 O atoms.
- From 4 H₂O, we get 4 × 1 = 4 O atoms.
- Total O atoms needed = 6 + 4 = 10 O atoms.
- Since O₂ has 2 O atoms, we need \( \frac{10}{2} = 5 \) moles of O₂.

Thus, the balanced equation for propane is:
\[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \]

### Step 3: Write the balanced chemical equation for the combustion of butane (C₄H₁₀).

The complete combustion of butane can be represented as:
\[ C_4H_{10} + O_2 \rightarrow CO_2 + H_2O \]

### Step 4: Balance the equation for butane.

1. **Carbon atoms**: There are 4 carbon atoms in butane, so we need 4 CO₂.
2. **Hydrogen atoms**: There are 10 hydrogen atoms in butane, so we need 5 H₂O.
3. **Oxygen atoms**: Now, we count the oxygen atoms needed:
- From 4 CO₂, we get 4 × 2 = 8 O atoms.
- From 5 H₂O, we get 5 × 1 = 5 O atoms.
- Total O atoms needed = 8 + 5 = 13 O atoms.
- Since O₂ has 2 O atoms, we need \( \frac{13}{2} = 6.5 \) moles of O₂.

Thus, the balanced equation for butane is:
\[ C_4H_{10} + \frac{13}{2}O_2 \rightarrow 4CO_2 + 5H_2O \]

### Step 5: Calculate the total moles of O₂ required.

Now, we sum the moles of O₂ required for both propane and butane:
- For propane: 5 moles of O₂
- For butane: \( \frac{13}{2} = 6.5 \) moles of O₂

Total moles of O₂ required:
\[ 5 + 6.5 = 11.5 \]

### 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 **11.5 moles**.

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