Equal masses of H₂, O₂ and methane have been taken in a container of volume V at temperature 27°C in identical conditions. What would be the ratio of the volumes of gases H₂:O₂:methane?

• A) 8:16:1
• B) 16:8:1
• C) 16:1:2
• D) 8:1:2

To determine the ratio of the volumes of hydrogen (H₂), oxygen (O₂), and methane (CH₄) when equal masses of each gas are placed in a container under identical conditions, we can utilize the ideal gas law and the concept of molar volume. Since all gases are at the same temperature and pressure, we can focus on their molar masses to find the volume ratios.

Understanding Molar Masses

The molar mass of each gas is crucial for this calculation:

• Hydrogen (H₂): Approximately 2 g/mol
• Oxygen (O₂): Approximately 32 g/mol
• Methane (CH₄): Approximately 16 g/mol

Calculating Moles from Equal Masses

Let’s assume we have 32 grams of each gas for simplicity. We can calculate the number of moles for each gas:

• For H₂:

  Number of moles = mass / molar mass = 32 g / 2 g/mol = 16 moles

• For O₂:

  Number of moles = mass / molar mass = 32 g / 32 g/mol = 1 mole

• For CH₄:

  Number of moles = mass / molar mass = 32 g / 16 g/mol = 2 moles

Volume Ratios Based on Moles

According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules. Therefore, the volume of each gas is directly proportional to the number of moles. Thus, the volume ratios can be expressed as:

• Volume of H₂ : 16 moles
• Volume of O₂ : 1 mole
• Volume of CH₄ : 2 moles

Finding the Final Ratio

To express the volumes in a ratio, we can simplify the moles:

• H₂ : O₂ : CH₄ = 16 : 1 : 2

Conclusion

The ratio of the volumes of hydrogen, oxygen, and methane in the container is therefore 16:1:2. This corresponds to option C) 16:1:2. Understanding these relationships helps clarify how gas behavior is influenced by their molecular weights and the conditions they are under.