Mole Fraction of Nitrogen in Air

Mole fraction is the ratio of the number of moles of a specific component in a mixture to the total number of moles in the mixture. In the case of air, the mixture consists of several gases, including nitrogen, oxygen, argon, carbon dioxide, neon, helium, and others. The mole fraction of nitrogen in air can be determined using the following steps:

Step 1: Determine the Total Number of Moles of Gases in Air

The first step is to determine the total number of moles of gases in air. This can be done using the ideal gas law, which states that the pressure, volume, and temperature of a gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

Assuming that air is at standard temperature and pressure (STP), which is defined as 0°C and 1 atm, respectively, the total number of moles of gases in air can be calculated as follows:

n = PV/RT
n = (1 atm) (22.4 L/mol)/(0.0821 L atm/mol K) (273 K)
n = 1.00 mol

Therefore, the total number of moles of gases in air is 1.00 mol.

Step 2: Determine the Number of Moles of Nitrogen in Air

The next step is to determine the number of moles of nitrogen in air. According to the composition of air, nitrogen makes up 78.08% of the total volume of gases. Therefore, the volume of nitrogen in air can be calculated as follows:

V(N2) = (78.08/100) (22.4 L/mol)
V(N2) = 17.5 L/mol

Using the ideal gas law, the number of moles of nitrogen can be calculated as follows:

n(N2) = PV/RT
n(N2) = (1 atm) (17.5 L/mol)/(0.0821 L atm/mol K) (273 K)
n(N2) = 0.62 mol

Therefore, the number of moles of nitrogen in air is 0.62 mol.

Step 3: Calculate the Mole Fraction of Nitrogen in Air

Finally, the mole fraction of nitrogen in air can be calculated as follows:

X(N2) = n(N2)/n(total)
X(N2) = 0.62 mol/1.00 mol
X(N2) = 0.62

Therefore, the mole fraction of nitrogen in air is 0.62 or 62%. This means that for every 100 moles of gases in air, 62 moles are nitrogen.