Question

A quantity of 2.76 g of silver carbonate on being strongly heated yields a residue weighing (Ag = 108)
(A)- 2.16 g
(B)- 2.48 g
(C)- 2.32 g
(D)- 2.64 g

Answer 1

Hint: The thermal decomposition of the metal carbonate takes place with the release of gases like carbon-dioxide and oxygen. So, from the balanced equation, the moles of the carbonate and the residue produced by it can be obtained from the stoichiometry.

Complete step by step answer:
Firstly, the silver carbonate on heating undergoes thermal decomposition along with the evolution of gases. The reaction is as follows:
$A{{g}_{2}}C{{O}_{3}}(s)\to 2Ag(s)+C{{O}_{2}}(g)+\dfrac{1}{2}{{O}_{2}}(s)$
So, the silver carbonate on decomposition leaves behind the silver metal residue along with carbon dioxide and oxygen gas. Then, from the above balanced equation, it can be seen that 1 moles of silver carbonate produces 2 moles of silver metal residue. Now, we will see how much moles do 2.76g of silver carbonate make. So, the molecular mass of silver carbonate is $A{{g}_{2}}C{{O}_{3}}=(2\times 108)+12+(3\times 16)=276\,g$
Then, the number of moles of silver carbonate will be $=\dfrac{weight}{molecular\,mass}=\dfrac{2.76}{276}=0.01\,\,moles$. Now, using the unitary method, If 1moles of silver carbonate gives 2 moles of silver metal residue, then 0.01 moles will produce $=0.01\times 2=0.02\,moles$ .
Given the atomic mass of $Ag=108\,g/mol$ , the weight of silver present in 0.02 moles will be $0.02\times 108=2.16\,g$ .

Therefore, the quantity of 2.76 g of silver carbonate on being strongly heated yields a residue weighing option (A)- 2.16 g.

Note: Unlike, the other metal carbonates in the reactivity series, which on thermal decomposition form oxides and carbon-dioxide. The silver carbonates being lower down in the reactivity series, need lower temperature for the decomposition.
Also, the oxide formed is unstable, and on applying more heat, it breaks down into the elemental metal and the oxygen.