Question

Minimum amount of $A{{g}_{2}}C{{O}_{3}}\left( s \right)$ required to produce sufficient amount of oxygen for the complete combustion of ${{C}_{2}}{{H}_{2}}$ which produces 11.2 L of $C{{O}_{2}}$ at STP after combustion is⋯⋯
\[A{{g}_{2}}C{{O}_{3}}\left( s \right)\to 2Ag\left( s \right)+C{{O}_{2}}\left( g \right)+\dfrac{1}{2}{{O}_{2}}\left( g \right)\]
\[{{C}_{2}}{{H}_{2}}+\dfrac{5}{2}{{O}_{2}}\to 2C{{O}_{2}}+{{H}_{2}}O\]
(A) 276 g
(B) 345 g
(C) 690 g
(D) 1380 g

Answer 1

Hint: When silver carbonate is subjected to heating, it decomposes into elemental silver along with a liberating mixture of carbon dioxide and oxygen gas. This oxygen formed is used for the combustion of acetylene to form carbon dioxide and water.

Complete step by step solution:
- The idea of moles can be defined in terms of volume. That is at STP (standard pressure and temperature ) conditions, one mole of any gas ( particles) will occupy a volume of 22.4 litres. Therefore the number of moles in 11.2 L of $C{{O}_{2}}$ at STP can be found as given below
\[11.2\text{ }L\text{ }of\text{ }C{{O}_{2}}~~at\text{ }STP=\dfrac{11.2L}{22.4{L}/{mol}\;}=0.5mol\]
 From the stoichiometry of the reaction which involves the combustion of acetylene, we can see that $\dfrac{5}{2}$ moles of ${{O}_{2}}$ is required for the combustion of ${{C}_{2}}{{H}_{2}}$ along with 2 moles of $C{{O}_{2}}$.
  Therefore we can write as follows
\[1\text{ }mole\text{ }of\text{ }C{{O}_{2}}=\dfrac{5}{2\times 2}moles\text{ }of\text{ }{{O}_{2}}\text{ }required\text{ }\]
 Thus $\dfrac{5}{2\times 2}$ moles of ${{O}_{2}}$ is required for the complete combustion of ${{C}_{2}}{{H}_{2}}$. The number of moles of ${{O}_{2}}$ required for 0.5 mol of $C{{O}_{2}}$ can be found as below
\[\text{0}\text{.5}mole\text{ }of\text{ }C{{O}_{2}}=0.5\text{ mol}\times \dfrac{5}{2\times 2}=\dfrac{5}{8}moles\text{ }of\text{ }{{O}_{2}}\text{ }required\text{ }\]
That is $\dfrac{5}{8}$ moles of ${{O}_{2}}$ required for the complete combustion of ${{C}_{2}}{{H}_{2}}$.Now let's look at the reaction which involves the decomposition of silver carbonate ($A{{g}_{2}}C{{O}_{3}}\left( s \right)$).By looking at the stoichiometry of the reaction , we can arrive at the following conclusion
$\dfrac{1}{2}moles\text{ }of\text{ }{{O}_{2}}=1\text{ mole }of\text{ }A{{g}_{2}}C{{O}_{3}}\text{ }required$
\[1\text{ }moles\text{ }of\text{ }{{O}_{2}}=2\text{ mole }of\text{ }A{{g}_{2}}C{{O}_{3}}\text{ }required\]
As we mentioned $\dfrac{5}{8}$ moles of ${{O}_{2}}$ is required for the complete combustion of ${{C}_{2}}{{H}_{2}}$.Therefore we can write as follows
\[\dfrac{5}{8}\text{ }moles\text{ }of\text{ }{{O}_{2}}=2\times \dfrac{5}{8}=\dfrac{5}{4}\text{ }moles\text{ }of\text{ }A{{g}_{2}}C{{O}_{3}}\left( s \right)\text{ }required\]
The molar mass of silver carbonate is 275.5 $gmo{{l}^{-1}}$ and thus the mass of $A{{g}_{2}}C{{O}_{3}}\left( s \right)$ required can be given as follows
\[The\text{ }mass\text{ }of\text{ }A{{g}_{2}}C{{O}_{3}}\left( s \right)\text{ }required=275.5{g}/{mol}\;\times \dfrac{5}{4}mol=345g\]

Therefore the answer is option (B) 345 g

Note: It should be noted that acetylene(${{C}_{2}}{{H}_{2}}$) is a very widely used hydrocarbon and it is the simplest alkyne found in nature. Also, around 20% of ${{C}_{2}}{{H}_{2}}$ is supplied by the industrial gases industry for oxyacetylene gas.