Final answer:
To find the number of individual atoms in 62.1 g of dinitrogen heptoxide, one must first determine the number of moles of the compound, then calculate the number of molecules, and finally multiply by the number of atoms per molecule.
Step-by-step explanation:
To determine how many individual atoms are in 62.1 grams of dinitrogen heptoxide (N₂O₇), we first need to calculate the molar mass of the compound and then use that to find the number of moles in 62.1 grams. The molar mass of dinitrogen heptoxide is the sum of the masses of two nitrogen atoms (2 x 14.0 g/mol) and seven oxygen atoms (7 x 16.0 g/mol), which equals 14.0 x 2 + 16.0 x 7 = 164.0 g/mol. To find the number of moles of N₂O₇ in 62.1 grams, we divide the mass of the sample by the molar mass, 62.1 g / 164.0 g/mol.
The number of moles can then be multiplied by Avogadro's number (6.022 x 10²³ molecules/mol) to find the number of molecules of N₂O₇. Finally, each molecule of N₂O₇ contains 9 atoms (2 nitrogen and 7 oxygen), so we multiply the number of molecules by 9 to find the total number of individual atoms.
The calculation steps are:
- Calculate number of moles: 62.1 g / 164.0 g/mol = 0.3786 moles of N₂O₇.
- Calculate number of molecules: 0.3786 moles x 6.022 x 10²³ molecules/mol.
- Calculate number of atoms: Number of molecules x 9 atoms/molecule.
By carrying out these calculations, we will be able to find the exact number of individual atoms in the given mass of dinitrogen heptoxide.