1. Identify the compound and the ion:

* The compound is ammonium carbonate (NH₄₂CO₃).

* We are looking for the number of moles of ammonium ions (NH₄⁺).

2. Determine the mole ratio:

* The chemical formula NH₄₂CO₃ tells us that there are two ammonium ions (NH₄⁺) for every one ammonium carbonate molecule (NH₄₂CO₃).

3. Calculate the moles of ammonium ions:

* Since there are 2 moles of NH₄⁺ for every 1 mole of NH₄₂CO₃, we multiply the moles of NH₄₂CO₃ by 2:

4.50 mol NH₄₂CO₃ * (2 mol NH₄⁺ / 1 mol NH₄₂CO₃) = 9.00 mol NH₄⁺

Therefore, there are 9.00 moles of ammonium ions in 4.50 mol of NH₄₂CO₃.