a gaseous mixture contains O2 , N2 and He in equal fraction of moles . Find the mass of He if 28g of N is present and 32g of O is present.

To find the mass of helium (He) in the gaseous mixture containing equal fractions of oxygen (O2), nitrogen (N2), and helium, we first need to establish the number of moles of each gas present in the mixture. Given that we have 28 grams of nitrogen and 32 grams of oxygen, we can use their molar masses to calculate the moles of each gas and then determine the moles of helium based on the equal fraction condition.

Step-by-Step Calculation

1. Calculate Moles of Nitrogen (N2)

The molar mass of nitrogen (N2) is approximately 28 g/mol. To find the number of moles of nitrogen, we can use the formula:

Number of moles = Mass (g) / Molar mass (g/mol)

Substituting the values:

Number of moles of N2 = 28 g / 28 g/mol = 1 mole

2. Calculate Moles of Oxygen (O2)

The molar mass of oxygen (O2) is about 32 g/mol. Using the same formula:

Number of moles of O2 = 32 g / 32 g/mol = 1 mole

3. Determine Moles of Helium (He)

Since the mixture contains equal fractions of moles of O2, N2, and He, we can conclude that the moles of helium are also 1 mole. Thus:

Number of moles of He = 1 mole

4. Calculate Mass of Helium (He)

The molar mass of helium (He) is approximately 4 g/mol. Now, we can find the mass of helium using the number of moles we just calculated:

Mass of He = Number of moles × Molar mass

Substituting the values:

Mass of He = 1 mole × 4 g/mol = 4 grams

Final Result

Therefore, the mass of helium in the gaseous mixture is 4 grams.

Summary

• Moles of N2: 1 mole (28 g)
• Moles of O2: 1 mole (32 g)
• Moles of He: 1 mole
• Mass of He: 4 grams

This approach illustrates how to use molar masses and the concept of equal fractions in a mixture to find the mass of an unknown component. If you have any further questions or need clarification on any part of the process, feel free to ask!