Final answer:
To find the total number of atoms in 36.5 g of hydrazine, we calculate the number of moles based on the molar mass, then use Avogadro's number to get the number of molecules, and finally multiply by the number of atoms per molecule to get the total atoms.
Step-by-step explanation:
To determine the total number of atoms in 36.5 g of hydrazine (N₂H₄), we need to perform a series of calculations. First, we calculate the molar mass of hydrazine.
The molar mass of nitrogen is approximately 14.01 g/mol (for each nitrogen atom) and that of hydrogen is approximately 1.008 g/mol (for each hydrogen atom). Since hydrazine has two nitrogen atoms and four hydrogen atoms, its molar mass is (2 × 14.01 g/mol) + (4 × 1.008 g/mol) = 32.042 g/mol.
Next, we use the molar mass to convert the mass of hydrazine into moles:
Number of moles of hydrazine = Mass of hydrazine ÷ Molar mass of hydrazine
Number of moles of hydrazine = 36.5 g ÷ 32.042 g/mol = 1.139 moles (approximately).
Then, we use Avogadro's number to find out the total number of molecules in the moles we have:
Number of molecules = Number of moles × Avogadro's number = 1.139 moles × 6.022 × 10²³ molecules/mol
Finally, since one molecule of hydrazine contains six atoms (2 nitrogen and 4 hydrogen), we multiply the number of molecules by the number of atoms per molecule:
Total number of atoms = Number of molecules × Atoms per molecule
Total number of atoms = 1.139 moles × 6.022 × 10²³ molecules/mol × 6 atoms/molecule