You're asking about the number of moles of ammonium ions in a 22.5 gram sample of ammonium carbonate. Here's how to solve this:

1. Write the chemical formula:

* Ammonium carbonate is (NH₄)₂CO₃

2. Find the molar mass:

* Molar mass of (NH₄)₂CO₃ = (2 * 18.04 g/mol) + (12.01 g/mol) + (3 * 16.00 g/mol) = 96.09 g/mol

3. Calculate the moles of ammonium carbonate:

* Moles = mass / molar mass

* Moles = 22.5 g / 96.09 g/mol = 0.234 moles of (NH₄)₂CO₃

4. Determine the moles of ammonium ions:

* Each mole of (NH₄)₂CO₃ contains 2 moles of ammonium ions (NH₄⁺).

* Moles of NH₄⁺ = 0.234 moles (NH₄)₂CO₃ * 2 moles NH₄⁺ / 1 mole (NH₄)₂CO₃ = 0.468 moles of NH₄⁺

Therefore, a 22.5 gram sample of ammonium carbonate contains 0.468 moles of ammonium ions.