If He and `CH_(4)` are allowed to diffuse out of the container under similar conditions of temperature and pressure then the ratio of the rate of diffusion of He to `CH_(4)` is

Options

A. `2.0`
B. `1.0`
C. `0.5`
D. `4.0`

Answer

To solve the problem of finding the ratio of the rate of diffusion of helium (He) to methane (CH₄), we can use Graham's law of effusion, which states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass.

### Step-by-Step Solution:

1. **Identify the Molar Masses**:
- The molar mass of helium (He) is approximately 4 g/mol.
- The molar mass of methane (CH₄) is approximately 16 g/mol.

2. **Apply Graham's Law**:
- According to Graham's law, the ratio of the rates of diffusion of two gases is given by:
\[ \frac{R_1}{R_2} = \sqrt{\frac{M_2}{M_1}} \]
- Here, \(R_1\) is the rate of diffusion of helium, \(R_2\) is the rate of diffusion of methane, \(M_1\) is the molar mass of helium, and \(M_2\) is the molar mass of methane.

3. **Substitute the Molar Masses**:
- Substitute the values into the equation:
\[ \frac{R_{He}}{R_{CH_4}} = \sqrt{\frac{M_{CH_4}}{M_{He}}} = \sqrt{\frac{16}{4}} \]

4. **Calculate the Ratio**:
- Simplifying the fraction inside the square root:
\[ \frac{R_{He}}{R_{CH_4}} = \sqrt{4} = 2 \]

5. **Conclusion**:
- Therefore, the ratio of the rate of diffusion of helium to that of methane is:
\[ \frac{R_{He}}{R_{CH_4}} = 2 \]

### Final Answer:
The ratio of the rate of diffusion of He to CH₄ is 2:1.