The rate of diffusion of hydrogen gas is

Options

A. 1.4 times of He gas
B. Same as He gas
C. 5 times to He gas
D. 2 times to He gas

Explanation

To find the rate of diffusion of hydrogen gas using Graham's law of diffusion, we can follow these steps:

### 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, this can be expressed as:

\[ \text{Rate} \propto \frac{1}{\sqrt{M}} \]

where \(M\) is the molar mass of the gas.

### Step 2: Identify Molar Masses
For hydrogen gas (H₂), the molar mass is 2 g/mol. For helium (He), the molar mass is 4 g/mol.

### Step 3: Set Up the Ratio of Rates
We want to find the ratio of the rate of diffusion of hydrogen gas (R_H2) to that of helium (R_He):

\[ \frac{R_{H2}}{R_{He}} = \sqrt{\frac{M_{He}}{M_{H2}}} \]

### Step 4: Substitute the Molar Masses
Substituting the molar masses into the equation:

\[ \frac{R_{H2}}{R_{He}} = \sqrt{\frac{4 \, \text{g/mol}}{2 \, \text{g/mol}}} \]

### Step 5: Simplify the Expression
Now simplify the expression:

\[ \frac{R_{H2}}{R_{He}} = \sqrt{2} \]

### Step 6: Calculate the Rate of Diffusion
The numerical value of \(\sqrt{2}\) is approximately 1.414. This means that the rate of diffusion of hydrogen gas is approximately 1.414 times that of helium gas.

### Conclusion
Thus, the rate of diffusion of hydrogen gas compared to helium gas is 1.414.

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