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An endothermic reaction is one where the system absorbs heat from its surroundings. This process involves a positive change in enthalpy (\( \Delta H \gt 0 \) ) since energy is added to the reactants to convert them into products. Although it might seem counterintuitive, endothermic reactions can still be spontaneous under certain conditions. For example, in the reaction: \[ 2 \mathrm{~N}_{2} \mathrm{O}_{5}(s) \longrightarrow 4 \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \], the positive enthalpy indicates that the reaction requires energy input. One might wonder how such reactions proceed spontaneously. The answer lies in other factors, such as entropy changes, which play a crucial role in determining spontaneity. In summary, while endothermic reactions absorb heat, their occurrence depends on the interplay between enthalpy and entropy changes.

Entropy (\( \Delta S \) ) is a measure of the disorder or randomness in a system. In chemical reactions, changes in entropy (\( \Delta S \) ) occur when there is a change in the number of gas molecules, as gases are more disordered compared to solids. In the given reaction, solid \( \mathrm{N}_{2}\mathrm{O}_{5} \) transforms into gaseous \( \mathrm{NO}_{2} \) and \( \mathrm{O}_{2} \).Such a transformation leads to a significant increase in entropy because:

• Gases have higher entropy than solids due to their greater freedom of movement.
• The number of moles of gas increases, indicating higher disorder.

A large positive entropy change (\( \Delta S^{\circ} \gt 0 \) ) helps offset the positive enthalpy change in the reaction. This increase contributes to making the reaction spontaneous at room temperature, explained further through Gibbs free energy.

The spontaneity criterion for a chemical reaction is determined through Gibbs free energy (\( \Delta G \)), a thermodynamic potential that predicts whether a process will occur without outside intervention. The equation: \[ \Delta G = \Delta H - T \Delta S \] represents the relationship between Gibbs free energy, enthalpy (\( \Delta H \)), and entropy (\( \Delta S \) ). For a reaction to be spontaneous, \( \Delta G \) must be negative (\( \Delta G \lt 0 \)).Notably, in the discussed endothermic reaction:

• Enthalpy (\( \Delta H \)) is positive, suggesting the input of heat.
• Entropy (\( \Delta S \)) is positive, facilitating a distribution towards greater disorder.
• The temperature (\( T \)) is a crucial factor, as higher temperatures promote spontaneous endothermic reactions.

The positive entropy change is sufficiently large, multiplied by temperature (\( T \Delta S \)), such that it outweighs the positive \( \Delta H \), ensuring \( \Delta G \) becomes negative. This explanation clarifies why some reactions that might not intuitively seem spontaneous, such as endothermic ones, actually can be under the right temperature conditions.