1. Write the balanced chemical equation:

CrCl₃(aq) + 3AgNO₃(aq) → 3AgCl(s) + Cr(NO₃)₃(aq)

2. Determine the molar masses of the relevant compounds:

* CrCl₃: 158.36 g/mol

* AgCl: 143.32 g/mol

3. Calculate the moles of AgCl produced:

* Moles of AgCl = (mass of AgCl) / (molar mass of AgCl)

* Moles of AgCl = 75.0 g / 143.32 g/mol = 0.523 mol

4. Use the mole ratio from the balanced equation to find the moles of CrCl₃ needed:

* From the balanced equation, 1 mole of CrCl₃ produces 3 moles of AgCl.

* Moles of CrCl₃ = (moles of AgCl) / 3

* Moles of CrCl₃ = 0.523 mol / 3 = 0.174 mol

5. Calculate the mass of CrCl₃ required:

* Mass of CrCl₃ = (moles of CrCl₃) * (molar mass of CrCl₃)

* Mass of CrCl₃ = 0.174 mol * 158.36 g/mol = 27.6 g

Therefore, 27.6 grams of chromium III chloride are required to produce 75.0 g of silver chloride.