Question

The number of litres of air required to burn $8$ litres of ${C_2}{H_2}$ is approximately $?$

Answer 1

First we know that the earth's atmosphere/air is composed of about $78\%$ nitrogen, $21\%$ oxygen, $0.9\%$ percent argon, and carbon dioxide, methane, water vapor, and neon are some of the other gases that make up the remaining $0.1\%$ . So, oxygen reacts with ${C_2}{H_2}$ (acetylene) and gives the carbon dioxide ( $C{O_2}$ ) as a main product. First balance the chemical reaction. Then, using Avogadro’s law we can get the number of litres of acetylene is equal to the number of litres of oxygen.

Complete Step By Step Answer:
Avogadro's law state that equal volumes of different gases contain an equal number of molecules under the same conditions of temperature and pressure (STP)
The unbalanced chemical reaction of oxygen with acetylene is written as follows
${C_2}{H_2} + {O_2} \to C{O_2} + {H_2}O$
Then the balanced chemical reaction is written as follows
$2{C_2}{H_2} + 5{O_2} \to 4C{O_2} + 2{H_2}O$
As we can see $2$ moles of acetylene react with $5$ moles of oxygen.
According to Avogadro’s law, we get
$2$ litres of acetylene $= 5$ litres of oxygen.
$\Rightarrow$ One litre of acetylene $= \dfrac{5}{2}\;$ litres of oxygen.
Thus, $8\;L$ of acetylene requires $= \dfrac{5}{2}\; \times 8 = 20\;L$ of oxygen.
Since air contains $21\%$ of oxygen in atmosphere
Then, Air required to burn $8\;L$ of acetylene $= \dfrac{{100}}{{21}}\; \times 20 = 105\;L$
Thus $105\;L$ of air is required to burn $8\;L$ of ${C_2}{H_2}$ .

Note:
Based on the temperature, the atmosphere is divided into five different layers. These layers are the troposphere, stratosphere, mesosphere, thermosphere, and exosphere. Also note that the troposphere contains $75\%$ of the atmosphere's total mass due to earth gravity.