What mass of oxygen is required to burn (1) 480 g of methane, (ii) `500 cm^(3)` of methane?
Equation: `CH_(4) + 2O_(2) to CO_(2) + 2H_(2)O`
Relative atomic mass: `C = 12, H = 1, O = 16`

Explanation

To solve the problem, we will break it down into two parts as per the question:

### Part 1: Finding the mass of oxygen required to burn 480 g of methane.

1. **Write the balanced chemical equation**:
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]

2. **Determine the molar mass of methane (CH₄)**:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Molar mass of CH₄ = 12 + 4 = 16 g/mol

3. **Use the mole-to-mole ratio from the balanced equation**:
- According to the equation, 1 mole of CH₄ reacts with 2 moles of O₂.
- Therefore, 16 g of CH₄ reacts with 64 g of O₂ (since 1 mole of O₂ = 32 g, and 2 moles = 64 g).

4. **Calculate the mass of oxygen required for 480 g of methane**:
- First, find the number of moles of CH₄ in 480 g:
\[ \text{Moles of CH₄} = \frac{480 \text{ g}}{16 \text{ g/mol}} = 30 \text{ moles} \]
- Now, use the mole ratio to find the moles of O₂ required:
\[ \text{Moles of O₂} = 30 \text{ moles CH₄} \times 2 = 60 \text{ moles O₂} \]
- Convert moles of O₂ to grams:
\[ \text{Mass of O₂} = 60 \text{ moles} \times 32 \text{ g/mol} = 1920 \text{ g} \]

### Answer for Part 1:
The mass of oxygen required to burn 480 g of methane is **1920 g**.

---

### Part 2: Finding the mass of oxygen required to burn 500 cm³ of methane.

1. **Use the balanced chemical equation again**:
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \]

2. **Use the volume-to-volume ratio**:
- According to the equation, 1 volume of CH₄ reacts with 2 volumes of O₂.
- Therefore, 500 cm³ of CH₄ will react with:
\[ 500 \text{ cm³ CH₄} \times 2 = 1000 \text{ cm³ O₂} \]

3. **Convert the volume of O₂ to moles**:
- At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 L (or 22400 cm³).
- Therefore, the number of moles of O₂ in 1000 cm³ is:
\[ \text{Moles of O₂} = \frac{1000 \text{ cm³}}{22400 \text{ cm³/mol}} \approx 0.04464 \text{ moles} \]

4. **Convert moles of O₂ to grams**:
- The molar mass of O₂ is 32 g/mol:
\[ \text{Mass of O₂} = 0.04464 \text{ moles} \times 32 \text{ g/mol} \approx 1.426 \text{ g} \]

### Answer for Part 2:
The mass of oxygen required to burn 500 cm³ of methane is approximately **1.43 g**.

---