If both gases (`O_2` and `He` ) have same temperature so rate of diffusion of `O_2` will be

Options

A. Four times of He
B. Two times of He
C. 0.35 times of He
D. eighth times of He

Answer

To solve the problem of comparing the rate of diffusion of oxygen gas (O₂) and helium gas (He) at the same temperature, we can use Graham's Law of Diffusion. Here’s the step-by-step solution:

### Step 1: Understand Graham's Law of Diffusion
Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be expressed as:
\[ \frac{\text{Rate of diffusion of gas 1}}{\text{Rate of diffusion of gas 2}} = \sqrt{\frac{\text{Molar mass of gas 2}}{\text{Molar mass of gas 1}}} \]

### Step 2: Identify the Gases and Their Molar Masses
For this problem, we have:
- Gas 1: O₂ (Oxygen)
- Gas 2: He (Helium)

The molar masses are:
- Molar mass of O₂ = 32 g/mol
- Molar mass of He = 4 g/mol

### Step 3: Apply Graham's Law
Using Graham's Law, we can set up the equation:
\[ \frac{\text{Rate of diffusion of O₂}}{\text{Rate of diffusion of He}} = \sqrt{\frac{\text{Molar mass of He}}{\text{Molar mass of O₂}}} \]
Substituting the molar masses:
\[ \frac{\text{Rate of diffusion of O₂}}{\text{Rate of diffusion of He}} = \sqrt{\frac{4}{32}} \]

### Step 4: Simplify the Equation
Now, simplify the fraction inside the square root:
\[ \frac{4}{32} = \frac{1}{8} \]
Thus, we have:
\[ \frac{\text{Rate of diffusion of O₂}}{\text{Rate of diffusion of He}} = \sqrt{\frac{1}{8}} = \frac{1}{\sqrt{8}} = \frac{1}{2\sqrt{2}} \approx 0.3536 \]

### Step 5: Conclusion
This means:
\[ \text{Rate of diffusion of O₂} \approx 0.35 \times \text{Rate of diffusion of He} \]
Therefore, the rate of diffusion of O₂ is approximately 0.35 times that of He.

### Final Answer
The correct option is 0.35 times that of Helium.

---