Question

Formation of $\text{NO}_{2(g)}$ from $\text{N}_{2(g)}$ and $\text{O}_{2(g)}$ is an endothermic process. Which of the following is true for this reaction?

• A. $\Delta H = 0$
• B. $\Delta H \lt 0$
• C. $\Delta H = \Delta U$
• D. $\Delta H \gt 0$

Hint:

Do not spend valuable time computing things like $\Delta n_g$ or comparing $\Delta H$ and $\Delta U$ using $\Delta H = \Delta U + \Delta n_g RT$ unless absolutely necessary. The term "endothermic" strictly and fundamentally dictates that $\Delta H \gt 0$ under any circumstances.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem states that the synthesis of nitrogen dioxide gas ($\text{NO}_{2}$) from fundamental nitrogen and oxygen gases absorbs energy, and requires us to deduce the correct sign convention or mathematical condition for enthalpy change ($\Delta H$).

Step 2: Key Formula or Approach:
By definition, thermodynamic processes are classified according to heat exchange:

Exothermic processes release heat into the surroundings, resulting in a net decrease in enthalpy: $\Delta H \lt 0$.

Endothermic processes absorb heat from the surroundings, resulting in a net increase in enthalpy: $\Delta H \gt 0$.

Step 3: Detailed Explanation:
The chemical reaction describing the formation of $\text{NO}_{2(g)}$ can be written as: $$\text{N}_{2(g)} + 2\text{O}_{2(g)} \rightarrow 2\text{NO}_{2(g)}$$ Since the problem explicitly specifies that this reaction pathway is

endothermic, system heat content is actively gained. Consequently, the enthalpy change ($\Delta H$) associated with the formation step must carry a positive mathematical sign. Therefore, $\Delta H \gt 0$.

Step 4: Final Answer:
For an endothermic process, $\Delta H \gt 0$, which is represented by option (D).