Here's how to break down the number of atoms in one mole of ammonium carbonate ((NH₄)₂CO₃):

1. Identify the Elements:

* Nitrogen (N)

* Hydrogen (H)

* Carbon (C)

* Oxygen (O)

2. Determine the Number of Atoms per Molecule:

* Nitrogen (N): 2 atoms per molecule (because of the subscript 2 outside the parentheses)

* Hydrogen (H): 8 atoms per molecule (2 ammonium ions x 4 hydrogen atoms per ion)

* Carbon (C): 1 atom per molecule

* Oxygen (O): 3 atoms per molecule

3. Avogadro's Number:

* One mole of any substance contains 6.022 x 10²³ particles (atoms, molecules, etc.).

Therefore, in one mole of ammonium carbonate:

* Nitrogen (N): 2 atoms/molecule x 6.022 x 10²³ molecules/mole = 1.2044 x 10²⁴ atoms

* Hydrogen (H): 8 atoms/molecule x 6.022 x 10²³ molecules/mole = 4.8176 x 10²⁴ atoms

* Carbon (C): 1 atom/molecule x 6.022 x 10²³ molecules/mole = 6.022 x 10²³ atoms

* Oxygen (O): 3 atoms/molecule x 6.022 x 10²³ molecules/mole = 1.8066 x 10²⁴ atoms