Gay Lussac's Law — Avogadro's Law — Mole Concept — Question 2

[By Lussac's law]

$\begin{matrix} \text{\scriptsize{2C}}_2\text{\scriptsize{H}}_6 & \text{\scriptsize{+}} & \text{\scriptsize{7O}}_2 & \longrightarrow & \text{\scriptsize{4CO}}_2 & \text{\scriptsize{+}} & \text{\scriptsize{6H}}_2\text{\scriptsize{O}} \\ \text{\scriptsize{2 vol.}} & \text{\scriptsize{:}} & \text{\scriptsize{7 vol.}} & \longrightarrow & \text{\scriptsize{4 vol.}} & \text{\scriptsize{:}} & \text{\scriptsize{6 vol.}} \end{matrix}$

To calculate the volume of unused oxygen.

$\begin{matrix} \text{C}_2\text{H}_6 & : &\text{O}_2 \\ 2 & : & 7 \\ 600 & : & x \end{matrix}$

Therefore,

$\dfrac{7}{2} \times 600 = x \\[0.5em] \Rightarrow x = 2100 \text{cc}$

Therefore, volume of unused oxygen = 2500 - 2100 = 400 cc

To calculate the volume of carbon dioxide formed

$\begin{matrix} \text{C}_2\text{H}_6 & : & \text{CO}_2 \\ 2 & : & 4 \\ 600 & : & x \end{matrix}$

Therefore,

$\dfrac{4}{2} \times 600 = x \\[0.5em] \Rightarrow x = 1200 \text{cc}$

Therefore, volume of carbon dioxide formed is 1200 cc