Explanation:
(I) Mole method:
\({\text{2A}}{{\text{g}}_{\text{2}}}{\text{C}}{{\text{O}}_{\text{3}}}{\text{4Ag + 2C}}{{\text{O}}_{\text{2}}}{\text{ + }}{{\text{O}}_{\text{2}}}\)
\(\,\,\,{\rm{2}}\,\,{\rm{mol}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{4}}\,\,{\rm{mol}}\)
\({\rm{2 \times 276}}\,\,{\rm{g}}\,\,\,\,\,{\rm{4 \times 108}}\,\,{\rm{g}}\)\({\rm{2}}{\mkern 1mu} {\mkern 1mu} {\rm{mol}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\rm{4}}{\mkern 1mu} {\mkern 1mu} {\rm{mol}}\)
\({\rm{2 \times 276}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\rm{4 \times 108}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}\)
\({\rm{2 \times 276}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}{\mkern 1mu} {\mkern 1mu} {\rm{of}}{\mkern 1mu} {\mkern 1mu} {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{o}}_{\rm{3}}}{\mkern 1mu} {\mkern 1mu} {\rm{gives}}{\mkern 1mu} {\mkern 1mu} {\rm{4 \times 108}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}{\mkern 1mu} {\mkern 1mu} {\rm{of}}{\mkern 1mu} {\mkern 1mu} {\rm{Ag}}\)
\({\rm{2}}{\rm{.76}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}{\mkern 1mu} {\mkern 1mu} {\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}{\mkern 1mu} {\mkern 1mu} {\rm{will}}{\mkern 1mu} {\mkern 1mu} {\rm{give}}\)
\(\left( {\frac{{{\rm{4 \times 108 \times 2}}{\rm{.76}}}}{{{\rm{2 \times 276}}}}} \right){\rm{ = 2}}{\rm{.16}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}{\mkern 1mu} {\mkern 1mu} {\rm{of}}{\mkern 1mu} {\mkern 1mu} {\rm{Ag}}{\rm{.}}\)
(II) Principle of Atomic Conservation (POAC) method:
Moles of \({\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}\) = Total moles of Ag as product
2 moles of \({\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}\) = 4 moles of Ag
\({\rm{2 \times 276}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}\) of \({\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}\) = \({\mkern 1mu} {\rm{4 \times 108}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}\) of Ag
2.76 g of \({\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}{\mkern 1mu} \) \({\rm{ = }}\left( {\frac{{{\rm{4 \times 108 \times 2}}{\rm{.76}}}}{{{\rm{2 \times 276}}}}} \right){\rm{ = 2}}{\rm{.16}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}{\mkern 1mu} {\mkern 1mu} {\rm{of}}{\mkern 1mu} {\mkern 1mu} {\rm{Ag}}{\rm{.}}\)
(III) Equivalent Method:
Number of gram - equivalents of \({\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}{\mkern 1mu} \) = Number of gram-equivalents of Ag
\(\frac{{{\rm{2}}{\rm{.76}}{\mkern 1mu} {\mkern 1mu} {\rm{g}}}}{{\left( {\frac{{{\rm{2 \times 276}}{\mkern 1mu} {\mkern 1mu} {\rm{g/mol}}}}{{\rm{1}}}} \right)}}{\rm{ = }}\frac{{{\rm{yg}}}}{{\left( {\frac{{{\rm{4 \times 108g/mol}}}}{{\rm{1}}}} \right)}}\)
\( \Rightarrow {\rm{y = 2}}{\rm{.16g}}\)
[Change in oxidation state of \({\rm{A}}{{\rm{g}}_{\rm{2}}}{\rm{C}}{{\rm{O}}_{\rm{3}}}\) and Ag is 1, respectively]