The ratio of rates of diffusion of `SO_(2)`, `O_(2)` and `CH_(4)` is

Options

A. `1 : sqrt(2):2`
B. `1 : 2 : 4`
C. `2: sqrt(2):1`
D. `1:2:sqrt(2)`

Answer

To find the ratio of rates of diffusion of SO₂, O₂, and CH₄, we can use Graham's law of effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass (molecular weight).

### Step-by-step solution:

1. **Identify the gases and their molecular weights:**
- SO₂ (Sulfur Dioxide): Molecular weight = 64 g/mol
- O₂ (Oxygen): Molecular weight = 32 g/mol
- CH₄ (Methane): Molecular weight = 16 g/mol

2. **Write the formula for the rate of diffusion:**
According to Graham's law:
\[ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Molecular weight}}} \]

3. **Set up the ratio of rates of diffusion:**
The ratio of the rates of diffusion of SO₂, O₂, and CH₄ can be expressed as:
\[ \frac{\text{Rate of SO₂}}{\text{Rate of O₂}} : \frac{\text{Rate of O₂}}{\text{Rate of CH₄}} = \frac{1/\sqrt{64}}{1/\sqrt{32}} : \frac{1/\sqrt{32}}{1/\sqrt{16}} \]

4. **Calculate the individual rates:**
- For SO₂:
\[ \frac{1}{\sqrt{64}} = \frac{1}{8} \]
- For O₂:
\[ \frac{1}{\sqrt{32}} = \frac{1}{\sqrt{16 \cdot 2}} = \frac{1}{4\sqrt{2}} \]
- For CH₄:
\[ \frac{1}{\sqrt{16}} = \frac{1}{4} \]

5. **Combine the ratios:**
Now we can express the ratio:
\[ \text{Rate of diffusion of SO₂} : \text{Rate of diffusion of O₂} : \text{Rate of diffusion of CH₄} = \frac{1}{8} : \frac{1}{4\sqrt{2}} : \frac{1}{4} \]

6. **Simplify the ratio:**
To simplify, we can multiply each term by 8 (the least common multiple):
\[ 1 : 2\sqrt{2} : 2 \]

7. **Express the final ratio:**
The final ratio of the rates of diffusion of SO₂, O₂, and CH₄ is:
\[ 1 : 2\sqrt{2} : 2 \]

### Final Answer:
The ratio of rates of diffusion of SO₂, O₂, and CH₄ is \( 1 : 2\sqrt{2} : 2 \).