Question

which equation represents the standard enthalpy of formation, \\( \delta h_{f}^{\circ} \\), of \\( \mathrm{hno}_{2}(\mathrm{aq}) \\) at \\( 25^{\circ} \mathrm{c} \\)?
\\( \mathrm{h}_{2}(\mathrm{~g})+\mathrm{n}_{2}(\mathrm{~g})+\mathrm{o}_{3}(\mathrm{~g}) \to \mathrm{hno}_{3}(\mathrm{aq}) \\)
\\( \mathrm{hno}_{2}(\mathrm{aq}) \to \frac{1}{2} \mathrm{h}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{~n}_{2}(\mathrm{~g})+\mathrm{o}_{2}(\mathrm{~g}) \\)
\\( \mathrm{hno}_{2}(\mathrm{aq}) \to \mathrm{h}(\mathrm{g})+\mathrm{n}(\mathrm{g})+2 \mathrm{o}(\mathrm{g}) \\)
\\( \mathrm{h}(\mathrm{g})+\mathrm{n}(\mathrm{g})+\mathrm{o}_{2}(\mathrm{~g}) \to \mathrm{hno}_{2}(\mathrm{aq}) \\)
\\( \frac{1}{2} \mathrm{h}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{~n}_{2}(\mathrm{~g})+\mathrm{o}_{2}(\mathrm{~g}) \to \mathrm{hno}_{2}(\mathrm{aq}) \\)

Explanation:

The standard enthalpy of formation ($\Delta H_f^{\circ}$) is defined as the change in enthalpy when one mole of a compound is formed from its elements in their standard states.

• For the first option: The product is $HNO_3$ (not $HNO_2$) and $O_3$ is not the standard state of oxygen (standard state of oxygen is $O_2$).
• For the second option: It is a decomposition reaction (not formation of $HNO_2$ from elements).
• For the third option: It is a decomposition of $HNO_2$ into atoms (not formation from elements in standard states).
• For the fourth option: $H$ and $N$ are not in their standard states (standard states of hydrogen is $H_2(g)$, of nitrogen is $N_2(g)$).
• For the fifth option: $\frac{1}{2}H_2(g)$ (standard state of hydrogen), $\frac{1}{2}N_2(g)$ (standard state of nitrogen) and $O_2(g)$ (standard state of oxygen) combine to form one mole of $HNO_2(aq)$. This follows the definition of standard enthalpy of formation.

Answer:

$\frac{1}{2}H_2(g)+\frac{1}{2}N_2(g)+O_2(g)\longrightarrow HNO_2(aq)$