$\underset{2.76}{\mathrm{A}{\mathrm{g}}_2\mathrm{C}{\mathrm{O}}_3}\stackrel{\mathrm{\Delta }}{\to }\mathrm{A}{\mathrm{g}}_2\mathrm{O}+\mathrm{C}{\mathrm{O}}_2\stackrel{\mathrm{\Delta }}{\to }\underset{\left(\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{u}\mathrm{e}\right)}{2\mathrm{A}\mathrm{g}+\frac{1}{2}{\mathrm{O}}_2}$

Note: $\mathrm{A}{\mathrm{g}}_2\mathrm{O}$ is thermally unstable and decompose on heating liberating oxygen.

Molecular weight of $\mathrm{A}{\mathrm{g}}_2\mathrm{C}{\mathrm{O}}_3=108\times 2+12+16\times 3=276\mathrm{g}$

So 276 g of $\mathrm{A}{\mathrm{g}}_2\mathrm{C}{\mathrm{O}}_3$ on heating gives residue

$=2\times 108=216\mathrm{g}$ of Ag

So 2.76 of $\mathrm{A}{\mathrm{g}}_2\mathrm{C}{\mathrm{O}}_3$ on heating gives $=\frac{216}{276}\times 2.76$

$=2.16\mathrm{g}$ of Ag