Unlike other metal carbonates that usually decomposes into metal
oxides liberating carbon dioxide, silver carbonate on heating
decomposes into elemental silver liberating mixture of carbon
dioxide and oxygen gas as : M
$ Ag_2CO_3 \, _{\longrightarrow \, \, \, \, }^{Heat} 2Ag (s) + CO_2(g) + \frac{1}{2} O_2(g) $
MW = 276 g $ \hspace26mm $ 2 x 108 = 216 g
Hence, 2.76 g of $Ag_2CO_3 $ on heating will give
$ \frac{216}{216 } \times 2.76 $ = 2.16g Ag as residue.