A mixture contains 10.0 g each of the three gases nitrogen, oxygen, and argon. What is the mole fraction of nitrogen in the mixture?
mols N2 = grams/molar mass = ?
mols O2 = grams/molar mass = ?
mols Ar = grams/molar mass = ?
Total mols = mols N2 + mols O2 + mols Ar.
XN2 = mols N2/total mols.
To find the mole fraction of nitrogen in the mixture, we need to calculate the total moles of the three gases and then calculate the mole fraction of nitrogen.
Step 1: Calculate the moles of each gas.
Given that the mass of each gas is 10.0 g and their molecular masses are:
Nitrogen (N2) -> 28.02 g/mol
Oxygen (O2) -> 32.00 g/mol
Argon (Ar) -> 39.95 g/mol
Moles of nitrogen:
moles_N2 = mass_N2 / molar_mass_N2
moles_N2 = 10.0 g / 28.02 g/mol
Moles of oxygen:
moles_O2 = mass_O2 / molar_mass_O2
moles_O2 = 10.0 g / 32.00 g/mol
Moles of argon:
moles_Ar = mass_Ar / molar_mass_Ar
moles_Ar = 10.0 g / 39.95 g/mol
Step 2: Calculate the total moles.
total_moles = moles_N2 + moles_O2 + moles_Ar
Step 3: Calculate the mole fraction of nitrogen.
mole_fraction_N2 = moles_N2 / total_moles
Now, let's calculate the moles and mole fraction step by step.
Moles of nitrogen:
moles_N2 = 10.0 g / 28.02 g/mol
moles_N2 ≈ 0.35 mol
Moles of oxygen:
moles_O2 = 10.0 g / 32.00 g/mol
moles_O2 ≈ 0.31 mol
Moles of argon:
moles_Ar = 10.0 g / 39.95 g/mol
moles_Ar ≈ 0.25 mol
Total moles:
total_moles = moles_N2 + moles_O2 + moles_Ar
total_moles ≈ 0.35 mol + 0.31 mol + 0.25 mol
total_moles ≈ 0.91 mol
Mole fraction of nitrogen:
mole_fraction_N2 = moles_N2 / total_moles
mole_fraction_N2 ≈ 0.35 mol / 0.91 mol
mole_fraction_N2 ≈ 0.3846 or 38.46% (rounded to two decimal places)
Therefore, the mole fraction of nitrogen in the mixture is approximately 0.3846 or 38.46%.
To determine the mole fraction of nitrogen in the mixture, we first need to calculate the total number of moles of the three gases in the mixture.
To calculate the number of moles, we need to use the molar mass of each gas. The molar mass of nitrogen (N2) is approximately 28.02 g/mol, oxygen (O2) is 32.00 g/mol, and argon (Ar) is 39.95 g/mol.
Given that the mixture contains 10.0 g of each gas, we can calculate the number of moles for each gas using the formula:
Number of moles = Mass (g) / Molar mass (g/mol)
For nitrogen:
Number of moles of nitrogen = 10.0 g / 28.02 g/mol = 0.356 mol
Similarly, for oxygen and argon:
Number of moles of oxygen = 10.0 g / 32.00 g/mol = 0.312 mol
Number of moles of argon = 10.0 g / 39.95 g/mol = 0.251 mol
Now, to calculate the mole fraction of nitrogen, we use the formula:
Mole fraction of a component = Number of moles of the component / Total number of moles of the mixture
Total number of moles of the mixture = Number of moles of nitrogen + Number of moles of oxygen + Number of moles of argon
Total number of moles of the mixture = 0.356 mol + 0.312 mol + 0.251 mol = 0.919 mol
Finally, the mole fraction of nitrogen (X nitrogen) in the mixture can be calculated as:
X nitrogen = Number of moles of nitrogen / Total number of moles of the mixture
X nitrogen = 0.356 mol / 0.919 mol = 0.387 (rounded to three decimal places)
Therefore, the mole fraction of nitrogen in the mixture is 0.387.