If the four tubes of a car are filled to the same pressure with `N_(2),O_(2) , H_(2)`, and helium separately , then which one will be filled first ?

Options

A. `N_(2)`
B. `O_(2)`
C. `H_(2)`
D. Ne

Answer

To determine which gas will fill the tubes first when they are all at the same pressure, we can use Graham's law of diffusion. This law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Therefore, gases with lower molar masses will diffuse faster than those with higher molar masses.

### Step-by-Step Solution:

1. **Identify the Gases and Their Molar Masses**:
- Helium (He): Molar mass = 4 g/mol
- Hydrogen (H₂): Molar mass = 2 g/mol
- Nitrogen (N₂): Molar mass = 28 g/mol (14 g/mol for each nitrogen atom)
- Oxygen (O₂): Molar mass = 32 g/mol (16 g/mol for each oxygen atom)

2. **List the Molar Masses in Order**:
- Hydrogen (2 g/mol)
- Helium (4 g/mol)
- Nitrogen (28 g/mol)
- Oxygen (32 g/mol)

3. **Apply Graham's Law**:
- According to Graham's law, the rate of diffusion (R) is inversely proportional to the square root of the molar mass (M):
\[ R \propto \frac{1}{\sqrt{M}} \]
- Therefore, the gas with the lowest molar mass will have the highest rate of diffusion.

4. **Determine the Order of Diffusion Rates**:
- Since hydrogen has the lowest molar mass, it will diffuse the fastest.
- The order of diffusion rates from highest to lowest is:
- Hydrogen (H₂) > Helium (He) > Nitrogen (N₂) > Oxygen (O₂)

5. **Conclusion**:
- Based on the diffusion rates, hydrogen (H₂) will fill the tube first, followed by helium, nitrogen, and finally oxygen.

### Final Answer:
Hydrogen (H₂) will be filled first.