How much volume of oxygen at STP in litres is required to burn 4g of methane gas completely?

Options

A. 11.2
B. 5.6
C. 2.8
D. 8

Answer

To determine the volume of oxygen required to burn 4g of methane gas completely at STP (Standard Temperature and Pressure), we can follow these steps:

### Step 1: Write the Balanced Chemical Equation
The combustion of methane (CH₄) can be represented by the following balanced equation:
\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} \]

### Step 2: Calculate the Molar Mass of Methane
The molar mass of methane (CH₄) is calculated as follows:
- Carbon (C) has an atomic mass of 12 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol.
- Therefore, the molar mass of CH₄ = 12 + (4 × 1) = 16 g/mol.

### Step 3: Calculate the Moles of Methane
Now, we can calculate the number of moles of methane in 4g:
\[ \text{Moles of CH}_4 = \frac{\text{mass}}{\text{molar mass}} = \frac{4 \text{ g}}{16 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 4: Use Stoichiometry to Find Moles of Oxygen Required
From the balanced equation, we see that 1 mole of CH₄ reacts with 2 moles of O₂. Therefore, for 0.25 moles of CH₄, the moles of O₂ required can be calculated as:
\[ \text{Moles of O}_2 = 0.25 \text{ moles CH}_4 \times \frac{2 \text{ moles O}_2}{1 \text{ mole CH}_4} = 0.5 \text{ moles O}_2 \]

### Step 5: Calculate the Volume of Oxygen at STP
At STP, 1 mole of any gas occupies 22.4 liters. Thus, the volume of 0.5 moles of O₂ is:
\[ \text{Volume of O}_2 = 0.5 \text{ moles} \times 22.4 \text{ L/mole} = 11.2 \text{ L} \]

### Conclusion
The volume of oxygen required to burn 4g of methane completely at STP is **11.2 liters**.

---