The ratio between the number of molecules in equal masses of `CH_(4)` and `SO_(2)` is

Options

A. `1:1`
B. `4:1`
C. `1:4`
D. `2:1`

Answer

To find the ratio between the number of molecules in equal masses of methane (CH₄) and sulfur dioxide (SO₂), we can follow these steps:

### Step 1: Determine the molar masses of CH₄ and SO₂
- **Molar mass of CH₄**:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol (4 H atoms)
- Total = 12 + (4 × 1) = 16 g/mol

- **Molar mass of SO₂**:
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol (2 O atoms)
- Total = 32 + (2 × 16) = 64 g/mol

### Step 2: Define the mass of each substance
Let the mass of each substance (CH₄ and SO₂) be W grams.

### Step 3: Calculate the number of moles of each substance
- **Number of moles of CH₄**:
\[ \text{Number of moles of CH₄} = \frac{W}{\text{Molar mass of CH₄}} = \frac{W}{16} \]

- **Number of moles of SO₂**:
\[ \text{Number of moles of SO₂} = \frac{W}{\text{Molar mass of SO₂}} = \frac{W}{64} \]

### Step 4: Establish the ratio of the number of moles
The ratio of the number of moles of CH₄ to SO₂ is:
\[ \text{Ratio} = \frac{\text{Number of moles of CH₄}}{\text{Number of moles of SO₂}} = \frac{\frac{W}{16}}{\frac{W}{64}} \]

### Step 5: Simplify the ratio
- Cancel W from both the numerator and denominator:
\[ \text{Ratio} = \frac{1/16}{1/64} = \frac{64}{16} = 4 \]

### Step 6: Conclusion
The ratio between the number of molecules in equal masses of CH₄ and SO₂ is:
\[ \text{Ratio of molecules of CH₄ to SO₂} = 4:1 \]