To determine the nature of the reaction
[tex]\[2 \text{NH}_3(g) \rightarrow \text{N}_2(g) + 3 \text{H}_2(g), \Delta H = 92.4 \, \text{kJ}/\text{mol}\][/tex]
we need to consider the value and sign of [tex]\(\Delta H\)[/tex].
### Step-by-Step Solution:
1. Understanding [tex]\(\Delta H\)[/tex]:
- [tex]\(\Delta H\)[/tex] represents the enthalpy change of the reaction. It indicates the amount of heat absorbed or released during a chemical reaction at constant pressure.
2. Significance of [tex]\(\Delta H = 92.4 \, \text{kJ}/\text{mol}\)[/tex]:
- The given value of [tex]\(\Delta H\)[/tex] is [tex]\(92.4 \, \text{kJ}/\text{mol}\)[/tex].
- The sign of [tex]\(\Delta H\)[/tex] is positive.
3. Interpreting the Positive [tex]\(\Delta H\)[/tex]:
- When [tex]\(\Delta H\)[/tex] is positive, it means that the system absorbs heat from the surroundings. This is characteristic of an endothermic reaction.
- An endothermic reaction requires energy input to proceed, as it consumes heat.
4. Conclusions Based on [tex]\(\Delta H\)[/tex]:
- Since [tex]\(\Delta H = 92.4 \, \text{kJ}/\text{mol}\)[/tex] and is positive, we can conclude that:
B. The reaction is endothermic.
### Final Answer:
[tex]\[
\boxed{B. \text{The reaction is endothermic.}}
\][/tex]
The positive value of [tex]\(\Delta H\)[/tex] confirms that the reaction absorbs heat, fitting the description of an endothermic process.
