A mixture of N2 and O2 has a molecular mass of 29. Calculate the mole fraction of N2

To find the mole fraction of nitrogen (N2) in a mixture of nitrogen and oxygen (O2) with a given average molecular mass of 29 g/mol, we can use the concept of molecular weights and the definition of mole fraction. Let's break this down step by step.

Understanding Molecular Masses

The molecular mass of nitrogen (N2) is approximately 28 g/mol (since nitrogen has an atomic mass of about 14 g/mol, and there are two nitrogen atoms in a molecule). For oxygen (O2), the molecular mass is about 32 g/mol (with oxygen's atomic mass being around 16 g/mol). Now, we have:

• Molecular mass of N2 = 28 g/mol
• Molecular mass of O2 = 32 g/mol

Setting Up the Equation

The average molecular mass of the mixture can be expressed in terms of the mole fractions of N2 and O2. Let’s denote:

• X_N2 = mole fraction of N2
• X_O2 = mole fraction of O2

Since these are the only two components in the mixture, we know that:

X_N2 + X_O2 = 1

Average Molecular Mass Calculation

The average molecular mass of the mixture can be calculated using the formula:

Average Molecular Mass = (X_N2 * Molecular Mass of N2) + (X_O2 * Molecular Mass of O2)

Substituting the known values, we have:

29 g/mol = (X_N2 * 28 g/mol) + ((1 - X_N2) * 32 g/mol)

Solving for the Mole Fraction

Now, let’s simplify and solve for X_N2:

29 = 28X_N2 + 32 - 32X_N2

Combining like terms gives us:

29 = 32 - 4X_N2

Rearranging this equation leads to:

4X_N2 = 32 - 29

4X_N2 = 3

X_N2 = 3/4

X_N2 = 0.75

Final Result

Thus, the mole fraction of nitrogen (N2) in the mixture is 0.75. This means that 75% of the moles in the mixture are nitrogen molecules, while the remaining 25% are oxygen molecules. This calculation illustrates how the average molecular mass of a gas mixture can be used to derive the composition of the gases involved.