Question

A small amount of $CaC{O_3}$ completely neutralizes $525ml$ of $0.1N$ $HCl$ and no acid is left in the end. After converting all calcium chloride to $CaS{O_4}$ how much plaster of Paris can be obtained?

Answer 1

Hint:Metal carbonates act as strong alkalis and react with acids to form salt and water with brisk effervescence due to formation of carbon-dioxide gas also the reaction is a type of exothermic reaction making the vessel used for the reaction hot.
Formula Used:
Mass of plaster of Paris obtained $\left( x \right)$$ = \dfrac{{N \times E \times V}}{{1000}}gm$
Here $N$ is normality of plaster of Paris
$E$ is Equivalent mass of plaster of Paris
$V$ is the volume of solution

Complete step by step answer:
As we know that metal carbonates and acids reaction is a type of neutralization reaction which produces a salt, water and carbon dioxide in a similar way $CaC{O_3}$ a metal carbonate reacts with $HCl$ an acid as follow
$CaC{O_3} + 2HCl \to CaC{l_2} + {H_2}O + C{O_2}$
Now as mentioned in the question that acid is completely neutralized therefore
$525ml$ Of $0.1N$$HCl$$ = 525ml$ Of $0.1N$ $CaC{l_2}$
$ = 525ml$ Of $0.1N$ Plaster of Paris

Now as we know that formula of plaster of Paris is $CaS{O_4}.\dfrac{1}{2}{H_2}O$
Hence its molecular mass $\left( M \right)$ is $145gm$
But we need equivalent mass $\left( E \right)$ of it so using the formula
$E = \dfrac{M}{n}$
Where $n$ is total charge


Here $n = 2$
Hence $E = \left( {\dfrac{{145}}{2}} \right)$ grams per equivalent
$E = 72.5$ grams per equivalent
As the formula is
Mass of plaster of Paris obtained $\left( x \right)$$ = \dfrac{{N \times E \times V}}{{1000}}gm$
Putting all the values in the above formula as follow
$x = \dfrac{{0.1 \times 72.5 \times 525}}{{1000}}gm$
$x = 3.806gm$

Additional information:
Plaster of Paris, quick-setting gypsum plaster made up of a fine white powder (calcium sulfate hemihydrate), which hardens when moisture is applied and allowed to dry. Since ancient times, plaster of Paris is so called because of its preparation from the abundant gypsum found near Paris.
$CaC{O_3}$ is a white insoluble powder-like substance which is found naturally in minerals, chalk, marble, limestone, calcite, shells and pearl. It is used as an antacid or as a calcium supplement.

Note:
When we mention equivalence, it is the number of moles of reactive units present in a compound.
Molecular weight and equivalent weight are completely two different things so do remember to convert molecular weight into equivalent weight whenever doing calculations considering normality.
Also normality varies with temperature so the calculations are done considering temperature as constant.