Gay Lussac's Law — Avogadro's Law — Mole Concept — Question 5

[By Lussac's law]

$\begin{matrix} \text{\scriptsize{2C}}_2 \text{\scriptsize{H}}_2 & \text{\scriptsize{+}} & \text{\scriptsize{5O}}_2 & \longrightarrow & \text{\scriptsize{4CO}}_2 & \text{\scriptsize{+}} & \text{\scriptsize{2H}}_2\text{\scriptsize{O}} \\ \text{\scriptsize{2 vol.}} & \text{\scriptsize{:}} & \text{\scriptsize{5 vol.}} & \longrightarrow & \text{\scriptsize{4 vol.}} & \text{\scriptsize{:}} & \text{\scriptsize{2 vol.}} \end{matrix}$

To calculate the volume of air required,

$\begin{matrix} \text{C}_2 \text{H}_2 & : & \text{O}_2 & \\ 2 & : & 5 \\ 50 & : & x \end{matrix}$

Therefore, volume of oxygen (x),

$\dfrac{5}{2} \times 50 = x \\[0.5em] \Rightarrow x = 125 \text{ cm}^3$

When oxygen is 20% then air is 100%
Therefore when, oxygen is 125 cm³ then air is

$\dfrac{100}{20} \times 125 = x \\[0.5em] \Rightarrow x = 625 \text{ cm}^3$

Therefore, volume of air required is 625 cm³.