Question

samples of gases containing nitrogen and oxygen were decomposed by electricity and the volume of each gas produced was measured. based on these results, which is the correct chemical formula for sample 2?
gas samples

sample	volume of nitrogen (l)	volume of oxygen (l)
2	1.01	1.99
3	1.00	4.99
4	1.00	1.02

a) no
b) n₂o₅
c) n₂o
d) no₂

Explanation:

Step1: Recall Avogadro's law

At the same temperature and pressure, the ratio of volumes of gases in a chemical reaction is equal to the ratio of their coefficients in the balanced - chemical equation. For the decomposition of nitrogen - oxygen compounds into nitrogen ($N_2$) and oxygen ($O_2$), the ratio of the volume of $N_2$ to $O_2$ gives the ratio of the number of moles of $N_2$ to $O_2$ in the decomposition reaction.

Step2: Calculate the ratio of nitrogen to oxygen volumes for Sample 2

For Sample 2, the volume of nitrogen ($V_{N_2}$) is $1.01$ L and the volume of oxygen ($V_{O_2}$) is $1.99\approx2$ L. The ratio of the volume of nitrogen to oxygen is $\frac{V_{N_2}}{V_{O_2}}=\frac{1.01}{1.99}\approx\frac{1}{2}$.

Step3: Determine the chemical formula

In the decomposition of a nitrogen - oxygen compound $N_xO_y$ into $N_2$ and $O_2$, the general reaction is $N_xO_y
ightarrow\frac{x}{2}N_2+\frac{y}{2}O_2$. The ratio of the number of moles of $N_2$ to $O_2$ (which is the same as the volume ratio at constant $T$ and $P$) is $\frac{\frac{x}{2}}{\frac{y}{2}}=\frac{x}{y}$. Since the volume ratio of $N_2$ to $O_2$ for Sample 2 is approximately $\frac{1}{2}$, the ratio of $N$ to $O$ in the compound is $1:2$, and the chemical formula is $NO_2$.

Answer:

D. $NO_2$