Question

Calculate the mass of residue obtained on strongly heating 2.76g of $A{{g}_{2}}C{{O}_{3}}$.
$A{{g}_{2}}C{{O}_{3}}\xrightarrow{\Delta }2Ag+C{{O}_{2}}+\dfrac{1}{2}{{O}_{2}}$

Answer 1

Approach this question by using mole concept which will help us to find the moles of silver carbonate and this will be further useful in calculation of moles of the residue on the basis of the given reaction. The reaction must be balanced.
Formula used:
We will use the following formulas in this solution:-
$n=\dfrac{\text{ mass}}{\text{molar mass}}$
where n is the number of moles of a substance.

Complete answer:
Let us first discuss about the silver carbonate as follows:-
Silver carbonate: It is a metallic carbonate whose chemical formula is $A{{g}_{2}}C{{O}_{3}}$.It is quite basic in nature and when it is heated at high temperature, it produces silver element along with the liberation of carbon dioxide and oxygen gas.
-Calculation of moles of silver carbonate ( $A{{g}_{2}}C{{O}_{3}}$):-
Atomic mass of silver = 108 g/mol
Atomic mass of carbon = 12 g/mol
Atomic mass of oxygen = 16 g/mol
Molar mass of $A{{g}_{2}}C{{O}_{3}}$= 2(108 g/mol) + 12 g/mol +3(16 g/mol) =276g/mol
Given mass of $A{{g}_{2}}C{{O}_{3}}$= 2.76g
$\begin{aligned} & \Rightarrow n=\dfrac{\text{ mass}}{\text{molar mass}} \\\ & \Rightarrow n=\dfrac{2.76g}{\text{276g/mol}} \\\ & \Rightarrow n=0.01moles \\\ \end{aligned}$
-The strong heating of $A{{g}_{2}}C{{O}_{3}}$gives the following reaction:-
$A{{g}_{2}}C{{O}_{3}}\xrightarrow{\Delta }2Ag+C{{O}_{2}}+\dfrac{1}{2}{{O}_{2}}$
As we can see that the residue produced is a silver element. It is clear that 1 mole of silver carbonate produced 2 moles of silver. So 0.01 mole of silver carbonate will produce 0.02 moles of silver.
-Calculation of mass of silver obtained as follows:-
$n=\dfrac{\text{ mass}}{\text{molar mass}}$
Rearrange the formula for further calculations:-
$\begin{aligned} & \Rightarrow \text{ mass}=n\times \text{molar mass} \\\ & \Rightarrow \text{ mass}=0.02mole\times 108g/mol \\\ & \Rightarrow \text{ mass}=2.16g \\\ \end{aligned}$
-The mass of residue (Ag) obtained is 2.16grams.

Note:
-Always remember to balance the reaction (if not balanced in the question) before solving such types of questions because it would give correct information regarding the amount or moles of substance produced, combusted, oxidized or reduced in a reaction.