If isobutane and n-butane are present in a gas, then how much oxygen should be required for complete combustion of 5 kg of this gas

Options

A. 1.8 kg
B. 9 kg
C. 17.9 kg
D. 27 kg

Answer

To determine how much oxygen is required for the complete combustion of 5 kg of a gas mixture containing isobutane (C4H10) and n-butane (C4H10), we can follow these steps:

### Step 1: Write the balanced chemical equation for the combustion of butane.
The combustion of butane can be represented as:
\[ \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \]

### Step 2: Balance the equation.
For complete combustion, the balanced equation is:
\[ 2 \text{C}_4\text{H}_{10} + 13 \text{O}_2 \rightarrow 8 \text{CO}_2 + 10 \text{H}_2\text{O} \]
This means that 2 moles of C4H10 require 13 moles of O2.

### Step 3: Determine the amount of oxygen needed for 1 mole of C4H10.
From the balanced equation:
- 2 moles of C4H10 require 13 moles of O2.
- Therefore, 1 mole of C4H10 requires \( \frac{13}{2} = 6.5 \) moles of O2.

### Step 4: Calculate the molar mass of C4H10 and O2.
- The molar mass of C4H10 (butane) is calculated as:
\[ (4 \times 12) + (10 \times 1) = 48 + 10 = 58 \text{ g/mol} \]
- The molar mass of O2 is:
\[ 2 \times 16 = 32 \text{ g/mol} \]

### Step 5: Calculate the grams of oxygen required for the combustion of 58 g of C4H10.
From the equation, 58 g of C4H10 requires:
\[ \text{Oxygen required} = 6.5 \text{ moles of O2} \times 32 \text{ g/mol} = 208 \text{ g of O2} \]

### Step 6: Calculate the amount of oxygen required for 5 kg of the gas.
Since we need to find the amount of oxygen for 5 kg (or 5000 g) of C4H10:
- Using the unitary method:
\[ \text{Oxygen required for 1 g of C4H10} = \frac{208 \text{ g O2}}{58 \text{ g C4H10}} \]
- Therefore, for 5000 g of C4H10:
\[ \text{Oxygen required} = \frac{208}{58} \times 5000 \]

### Step 7: Perform the calculation.
Calculating the above expression:
\[ \text{Oxygen required} = \frac{208}{58} \times 5000 \approx 17,931 \text{ g O2} \]
Converting grams to kilograms:
\[ \text{Oxygen required} \approx 17.931 \text{ kg O2} \]

### Final Answer:
The amount of oxygen required for the complete combustion of 5 kg of the gas is approximately **17.9 kg**.

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