Question

A $400\text{ cm}^3$ sample of polluted air containing nitrogen dioxide ($\text{NO}_2$), carbon dioxide ($\text{CO}_2$), and unpolluted air components is passed sequentially through two absorption reagents. First, passing the sample through concentrated sodium hydroxide ($\text{NaOH}$) solution absorbs both acidic pollutants ($\text{NO}_2$ and $\text{CO}_2$), reducing the volume of the gas by $40\text{ cm}^3$. The remaining gas mixture is then passed through alkaline pyrogallol, where oxygen ($\text{O}_2$) is completely absorbed, causing a further volume reduction of $75.6\text{ cm}^3$. Assuming oxygen constitutes $21\%$ by volume of the unpolluted portion of the air sample, what is the percentage by volume of nitrogen dioxide ($\text{NO}_2$) in the original polluted air sample?