Question

The shell of a chicken’s egg makes up \[5%\]of the mass of an average egg. An average egg has a mass of \[50g.\] Assume the egg shell is pure calcium carbonate. How many complete chickens egg shells would be needed to neutralize \[50\text{ }c{{m}^{3}}\]of \[2.0mol\text{ }d{{m}^{-3}}\]ethanoic acid?
A.$1$
B.$2$
C.$3$
D.$4$

Answer 1

Hint: We know that In order to solve the given problem first we will understand the chemical composition of egg shells further we will understand the chemical reaction of the egg shell with the solution and the gas evolved we will try to find out the acid involved in the reaction i.e. ethanoic acid.

Complete step by step answer:
Let’s discuss the stepwise answer to this question; Egg-shells are made up of calcium carbonate. When we add egg-shell to nitric acid, the Nitric acid reacts with calcium carbonate (which is present in the egg-shell) to form calcium nitrate, carbon dioxide gas, and water. The carbon dioxide gas released from this reaction turns lime-water milky.
Here we can see in the reaction calcium nitrate is one of the products. Calcium nitrate is mainly produced as a fertilizer and for wastewater treatment. Calcium nitrate is a source of both calcium and nitrogen, for plants.
Reaction of ethanoic acid with calcium carbonate: \[2C{{H}_{3}}COOH+CaC{{O}_{3}}\xrightarrow{{}}{{\left( C{{H}_{3}}COO \right)}_{2}}Ca+C{{O}_{2}}+{{H}_{2}}O\]
For an average egg, Weight of shell \[=0.05\times 50=2.5g~\]; Molecular mass of \[CaC{{O}_{3}}=100g\]
No. of moles of \[CaC{{O}_{3}}\] ​ in chicken's egg shell \[=\dfrac{2.5}{100}=0.025~mol~\]
Now, \[50c{{m}^{3~}}\]of \[2.0mol/d{{m}^{3}}=\dfrac{50\times 2}{1000}=0.1~mol\] of ethanoic acid.
Now, from the above equation, \[2\] moles of ethanoic acid reacts with $1$ mole of \[CaC{{O}_{3}}.\] Hence \[0.05~\] mole of calcium carbonate would be required to react with \[0.1~\] mole of ethanoic acid.
Therefore, Number of chicken's eggshells required \[=\dfrac{0.05}{~0.025}=2.\]

Therefore, the correct answer is option B.

Note:
Remember that In order to solve such problems students must remember the test for different chemical compounds one of which is mentioned in the solution. Students must remember the chemical composition of some practical materials. Before reaching to some conclusion students must remember to check for all the parts of the problem.