What volume of oxygen gas `(O_(2))` measured at `0^(@)C` and 1 atm is needed to burn completely `1 L` of propane gas `(C_(3)H_(8))` measured under the same condition?

Options

A. (a)`6 L`
B. (b)`5 L`
C. (c )`10 L`
D. (d)`7 L`

Explanation

To solve the problem of how much volume of oxygen gas (O₂) is needed to completely burn 1 L of propane gas (C₃H₈) at 0°C and 1 atm, we can follow these steps:

### Step 1: Write the Balanced Chemical Equation
The combustion of propane (C₃H₈) can be represented by the following balanced chemical equation:

\[ C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \]

This equation shows that 1 mole of propane reacts with 5 moles of oxygen.

### Step 2: Determine the Molar Volume of a Gas
At standard temperature and pressure (0°C and 1 atm), 1 mole of any ideal gas occupies a volume of 22.4 L.

### Step 3: Calculate the Moles of Propane
Since we have 1 L of propane gas, we can calculate the number of moles of propane using the molar volume:

\[ \text{Moles of } C_3H_8 = \frac{\text{Volume of } C_3H_8}{\text{Molar Volume}} = \frac{1 \text{ L}}{22.4 \text{ L/mol}} \approx 0.04464 \text{ moles} \]

### Step 4: Calculate the Moles of Oxygen Required
From the balanced equation, we know that 1 mole of propane requires 5 moles of oxygen. Therefore, the moles of oxygen required can be calculated as follows:

\[ \text{Moles of } O_2 = 5 \times \text{Moles of } C_3H_8 = 5 \times 0.04464 \text{ moles} \approx 0.2232 \text{ moles} \]

### Step 5: Calculate the Volume of Oxygen Required
Now, we can find the volume of oxygen gas required at the same conditions (0°C and 1 atm):

\[ \text{Volume of } O_2 = \text{Moles of } O_2 \times \text{Molar Volume} = 0.2232 \text{ moles} \times 22.4 \text{ L/mol} \approx 5.00 \text{ L} \]

### Final Answer
The volume of oxygen gas needed to burn completely 1 L of propane gas at 0°C and 1 atm is approximately **5.00 L**.

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