The rate of diffusion of hydrogen is about:

Options

A. one-half that of helium
B. 1.4 times that of helium
C. twice that of helium
D. four times that of helium.

Answer

To solve the question regarding the rate of diffusion of hydrogen compared to helium, we will use Graham's Law of Effusion. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand Graham's Law of Effusion
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
In this case, we are comparing hydrogen (H₂) and helium (He).
- Molar mass of hydrogen (H₂) = 2 g/mol (since it is diatomic)
- Molar mass of helium (He) = 4 g/mol (it is monatomic)

### Step 3: Apply Graham's Law
Using the molar masses in Graham's Law:

\[ \frac{\text{Rate of diffusion of H₂}}{\text{Rate of diffusion of He}} = \sqrt{\frac{4}{2}} = \sqrt{2} \]

### Step 4: Calculate the Rate of Diffusion of Hydrogen
From the equation, we can express the rate of diffusion of hydrogen in terms of the rate of diffusion of helium:

\[ \text{Rate of diffusion of H₂} = \sqrt{2} \times \text{Rate of diffusion of He} \]

### Step 5: Numerical Calculation
The value of \(\sqrt{2}\) is approximately 1.414. Therefore, we can write:

\[ \text{Rate of diffusion of H₂} \approx 1.414 \times \text{Rate of diffusion of He} \]

### Step 6: Conclusion
This means that the rate of diffusion of hydrogen is about 1.414 times that of helium. When looking at the options provided, the closest option is "about four times that of helium," which is not correct. The correct interpretation is that it is approximately 1.4 times that of helium.

### Final Answer
The rate of diffusion of hydrogen is approximately 1.414 times that of helium.

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