Final answer:
To find the percentage of the total number of atoms that corresponds to each of the components in the mixture, calculate the moles of each gas and then the total number of atoms for each gas. Finally, determine the percentage for each gas.
Step-by-step explanation:
To find the percentage of the total number of atoms that corresponds to each of the components in the mixture, we need to calculate the moles of each gas. Then, we can calculate the total number of atoms for each gas and determine the percentage.
First, let's calculate the number of moles for each gas. The moles of argon = mass of argon / molar mass of argon = 1.27 g / 39.948 g/mol = 0.0318 mol. The moles of neon = mass of neon / molar mass of neon = 2.40 g / 20.180 g/mol = 0.119 mol. The moles of helium = mass of helium / molar mass of helium = 3.00 g / 4.0026 g/mol = 0.749 mol.
Next, let's calculate the total number of atoms for each gas. The total number of atoms of argon = moles of argon * Avogadro's number = 0.0318 mol * 6.02 × 10^23 atoms/mol = 1.91 × 10^22 atoms. The total number of atoms of neon = moles of neon * Avogadro's number = 0.119 mol * 6.02 × 10^23 atoms/mol = 7.17 × 10^22 atoms. The total number of atoms of helium = moles of helium * Avogadro's number = 0.749 mol * 6.02 × 10^23 atoms/mol = 4.51 × 10^23 atoms.
Finally, let's calculate the percentage of the total number of atoms for each gas. Percentage of argon atoms = (total number of argon atoms / total number of atoms in the mixture) * 100 = (1.91 × 10^22 atoms / (1.91 × 10^22 atoms + 7.17 × 10^22 atoms + 4.51 × 10^23 atoms)) * 100. Percentage of neon atoms = (total number of neon atoms / total number of atoms in the mixture) * 100. Percentage of helium atoms = (total number of helium atoms / total number of atoms in the mixture) * 100.