Step 1: Understanding the Concept:
Silver carbonate decomposes on heating to silver, CO\(_2\), and O\(_2\).
Step 2: Detailed Explanation:
\(2\mathrm{Ag}_2\mathrm{CO}_3 \xrightarrow{\Delta} 4\mathrm{Ag} + 2\mathrm{CO}_2 + \mathrm{O}_2\)
Molar mass of Ag\(_2\)CO\(_3\) = \(2 \times 108 + 12 + 48 = 276\) g/mol.
2 mol (552 g) Ag\(_2\)CO\(_3\) gives 4 mol (432 g) Ag.
So, \(2.76\) g Ag\(_2\)CO\(_3\) gives Ag = \(\frac{432}{552} \times 2.76 = 0.7826 \times 2.76 = 2.16\) g.
Step 3: Final Answer:
2.16 g