Question

When the calcium carbonate is reacted with an excess amount of hydrochloric acid, how much $CaCO_3$ is required to produce 11.2 litres of $CO_2$ at STP?
(Given molar masses: $CaCO_3$ = 100g/mol, HCl= 36.5g/mol, $CO_2$ = 44.0g/mol)
A) 25.0g
B) 44.0g
C) 50.0g
D) 100.0g
E) None of the above

Answer 1

Hint: Volume of one mole of any gas is called molar volume and is equal to 22.4 L at STP. Molar volume allows conversion between moles and volume of gas at STP.

Complete answer:
We know
$${\text{CaC}}{{\text{O}}_3}{\text{(aq) + 2HCl(aq)}} \to {\text{CaC}}{{\text{l}}_{\text{2}}}{\text{(aq) + }}{{\text{H}}_{\text{2}}}{\text{O (g) + C}}{{\text{O}}_2}(g)$$
The above chemical equation is stoichiometrically balanced
At S.T.P
22.4L of $CO_2$ = 1 mol of $CO_2$
So 11.2L of $CO_2$ = 0.5 mol of $CO_2$
1 mol of $CO_2$ requires 1 mol of $CaCO_3$
So, 0.5 mol of $CO_2$ will require 0.5 mol of $CaCO_3$
According to mole concept
$$
{{\text{1 mol of CaC}}{{\text{O}}_3}{\text{ = molar mass of CaC}}{{\text{O}}_3}} \\
{{\text{0}}{\text{.5 mol of CaC}}{{\text{O}}_{\text{3}}}{\text{ = 100 }} \times {\text{ 0}}{\text{.5}}}
{{\text{0}}{\text{.5 mol of CaC}}{{\text{O}}_{\text{3}}}{\text{ = 50}}g}

$$

Hence, the answer to the above question is option C.

Note: S.T.P - Standard Temperature and Pressure are standard arrangements of conditions for experimental estimations to be set up to permit correlations to be made between different sets of data.
Since 1982, STP has been defined as a temperature of 273.15 K and an absolute pressure of exactly $10^5$ Pa.
Mole - In the SI system, mole (symbol, mol) was introduced as seventh base quantity for the amount of a substance. 1 mol contains as many particles/entities as there are atoms in exactly 12 g of the 12C isotope. No. of entities in 1 mol = $6.02 \times10 ^{-23}$ .
It is called Avogadro constant ($N_A$).

Molar mass - The mass of 1 mol of a substance in grams is called its molar mass. The molar mass in grams is numerically equal to atomic/molecular mass in u.
1 mol = gram formula mass (molar mass)
= $6.02 \times10 ^{-23}$ particles
= 22.4L of a gas at STP .
The molar mass of a polymer is directly related to its properties. As the molecular weight increases, mechanical properties generally increase. Every polymer has an ideal molecular weight at which the balance of different properties (such as processability, strength, brittleness etc.) is optimized.