A gas mixture contains 50% He & 50% methane by volume. What is the % by mass of methane ?

To find the percentage by mass of methane in a gas mixture that consists of 50% helium (He) and 50% methane (CH₄) by volume, we need to consider the molar masses of both gases. This will allow us to convert the volume percentages into mass percentages.

Understanding Molar Masses

The first step is to determine the molar masses of helium and methane:

• Molar mass of Helium (He): Approximately 4 g/mol
• Molar mass of Methane (CH₄): Approximately 16 g/mol

Calculating Mass from Volume Percentages

Since the mixture is 50% He and 50% CH₄ by volume, we can assume a convenient total volume for our calculations. Let's say we have 100 liters of the gas mixture. This means:

• Volume of He = 50 liters
• Volume of CH₄ = 50 liters

Finding Masses of Each Component

Next, we convert these volumes into masses using the ideal gas law, which states that at standard temperature and pressure (STP), 1 mole of any gas occupies approximately 22.4 liters. Thus, we can calculate the number of moles for each gas:

• For He:
  • Number of moles = Volume / Molar volume = 50 L / 22.4 L/mol ≈ 2.24 moles
  • Mass of He = Moles × Molar mass = 2.24 moles × 4 g/mol ≈ 8.96 g
• For CH₄:
  • Number of moles = Volume / Molar volume = 50 L / 22.4 L/mol ≈ 2.24 moles
  • Mass of CH₄ = Moles × Molar mass = 2.24 moles × 16 g/mol ≈ 35.84 g

Calculating Total Mass and Percentage by Mass

Now that we have the masses, we can find the total mass of the gas mixture:

• Total mass = Mass of He + Mass of CH₄ = 8.96 g + 35.84 g = 44.80 g

To find the percentage by mass of methane in the mixture, we use the formula:

Percentage by mass of CH₄ = (Mass of CH₄ / Total mass) × 100

Substituting the values we calculated:

Percentage by mass of CH₄ = (35.84 g / 44.80 g) × 100 ≈ 80%

Final Result

Therefore, the percentage by mass of methane in the gas mixture is approximately 80%.