Question

What quantity of limestone on heating will give $56{\text{kg}}$ of ${\text{CaO}}$ ?
(A) $1000{\text{kg}}$
(B) $56{\text{kg}}$
(C) $44{\text{kg}}$
(D) $100{\text{kg}}$

Answer 1

To solve this question, we have to find the number of moles of calcium oxide. Then we have to write a balanced chemical reaction and find the number of moles of calcium oxide obtained by heating one mole of limestone.

Complete answer: Limestone consists of calcium carbonate having the chemical formula
${\text{CaC}}{{\text{O}}_{\text{3}}}$. When limestone is heated, calcium oxide and carbon dioxide gas are formed. The reaction is given below:
${\text{CaC}}{{\text{O}}_{\text{3}}}\xrightarrow{{\text{\Delta }}}{\text{CaO + C}}{{\text{O}}_{\text{2}}} \uparrow$
The molar mass of calcium oxide $= 56{\text{ g mo}}{{\text{l}}^{ - 1}}$
The molar mass of calcium carbonate $= 100{\text{ g mo}}{{\text{l}}^{ - 1}}$
The required mass of calcium oxide $= 56{\text{ kg}} = 56000{\text{ g}}$
The number of moles of a given substance is the ratio of the mass of the given substance by the molar mass of the substance.
Number of moles of calcium oxide $= \dfrac{{{\text{mass of CaO}}}}{{{\text{molar mass of CaO}}}}$
$= \dfrac{{56000{\text{ g}}}}{{56{\text{ g mo}}{{\text{l}}^{ - 1}}}}$
$= 1000{\text{ mol}}$
From the balanced chemical reaction,
${\text{CaC}}{{\text{O}}_{\text{3}}}\xrightarrow{{\text{\Delta }}}{\text{CaO + C}}{{\text{O}}_{\text{2}}} \uparrow$
One mole of calcium oxide is obtained by heating one mole of calcium carbonate.
So, $1000$ moles of calcium oxide will be obtained by heating $1000$ moles of calcium carbonate.
Mass of ${\text{CaC}}{{\text{O}}_{\text{3}}} = 1000{\text{ mol}} \times {\text{100 g mo}}{{\text{l}}^{ - 1}} = {10^5}g$
We know that one gram $= {10^{ - 3}}{\text{ kg}}$
So, ${10^5}{\text{g}} = {10^5} \times {10^{ - 3}} = 100{\text{ kg}}$
$100{\text{ kg}}$ of limestone on heating gives $56{\text{kg}}$ of ${\text{CaO}}$
Therefore, option D is the correct answer.

Note:
Remember to check the units of mass and convert them as required. In this question, mass is given in kilograms. We know that molar mass is generally expressed in grams, so we have to convert the mass given into grams. This is done by multiplying the given mass with thousand. And after solving the problem, we have to convert the mass into kilograms as the options are in kilograms. This can be achieved by dividing the mass by thousand.