Question

Volume at NTP of oxygen required to completely burn 1 kg of coal (100 % carbon) is:
(A) $22.4$L
(B) $22.4 \times {10^3}$L
(C) $1.86 \times {10^3}$L
(D) $1000$L

Answer 1

Hint: First find out the moles of carbon. Then write the combustion reaction of coal and see the amount of oxygen required for combustion of 1 mole of carbon. Then use the unitary method to find out the amount of oxygen required. At NTP conditions 1 mole of a gas occupies 22.4 L of volume.

Complete step by step solution:
-First of all, let us find out the number of moles associated with 1 kg of carbon.
The weight of coal given in the question is = 1 kg
= 1000 g
We know that number of moles = $\dfrac{{wt.}}{{Mol.wt.}}$
= $\dfrac{{1000}}{{12}}$
= 83.333 moles
-Now we will see the combustion reaction of coal (100 % carbon):
$C + {O_2} \to C{O_2}$
From the above combustion reaction we can see that 1 mole of carbon requires 1 mole of oxygen (${O_2}$) for its complete combustion.
So, for combustion of 83.333 moles of carbon, we will require 83.333 moles of oxygen (${O_2}$).
At NTP conditions, 1 mole of a gas occupies 22.4 L of volume.
Hence, 83.333 moles of oxygen (${O_2}$) gas will occupy= 22.4 × 83.333 L
= 1866.659 L
= $1.866 \times {10^3}$ L of volume of oxygen (${O_2}$)
So, for combustion of 1 kg of coal, we will require 83.333moles of oxygen (${O_2}$) which occupies $1.866 \times {10^3}$ L of volume at NTP.

So, the correct option will be: (C) $1.86 \times {10^3}$L.

Note: The burning of coal is an oxidation reaction. It is also exothermic which means it releases heat energy. If carbon or coal undergoes incomplete combustion, it produces carbon monoxide (CO) which is highly poisonous. The carbon monoxide ($C{O_2}$) released during complete combustion causes a rise in atmospheric temperature. This leads to global warming.