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Enthalpy change, denoted as \( \Delta H \), is a crucial aspect of understanding chemical reactions. It represents the overall heat absorbed or released during a reaction at constant pressure. Usually measured in kilojoules per mole (\( \mathrm{kJ/mol} \)), a positive \( \Delta H \) suggests the reaction absorbs heat, termed as endothermic.
Conversely, a negative \( \Delta H \) means the reaction releases heat, known as exothermic.Key points about enthalpy change:

• It reflects the energy change in terms of heat.
• Endothermic reactions feel cold to the touch as they absorb heat from the surroundings.
• Exothermic reactions may feel warm or hot as they release heat.

Considering the reaction from the exercise, with \( \Delta H = 15 \mathrm{~kJ/mol} \), it is endothermic. This indicates that heat must be supplied for the reaction to proceed. This value is important when considering reaction spontaneity but must be evaluated alongside entropy changes as well.

Entropy change, represented as \( \Delta S \), measures the disorder or randomness in a system. The unit is usually joules per Kelvin per mole (\( \mathrm{J/K/mol} \)). A positive \( \Delta S \) indicates an increase in disorder, while a negative \( \Delta S \) suggests a decrease.Entropy is a key concept in determining the feasibility of a reaction:

• Greater disorder (higher \( \Delta S \)) usually favors spontaneity, especially at higher temperatures.
• A reaction with a positive entropy change often occurs naturally and more freely.
• Entropy change is especially significant when combined with temperature, impacting the Gibbs free energy.

For the reaction referenced in the exercise, \( \Delta S = 51 \mathrm{~J/K/mol} \). This positive value suggests that the reaction results in increased disorder—a favorable condition for spontaneity.

The concept of reaction spontaneity hinges on the Gibbs free energy change \( \Delta G \), calculated using the formula: \( \Delta G = \Delta H - T \Delta S \), where \( T \) is the temperature in Kelvin.A few critical points about spontaneity:

• The reaction is spontaneous when \( \Delta G < 0 \).
• Temperature plays a vital role in spontaneity, especially when \( \Delta H \) is positive, as seen in the given reaction.
• The inequality \( T > \frac{\Delta H}{\Delta S} \) helps determine the temperature above which the reaction becomes spontaneous.

In the exercise, finding \( T > 294.2 \mathrm{~K} \) means that above this temperature, the negative contribution of \( T \Delta S \) overcomes the positive \( \Delta H \), ensuring \( \Delta G \) is negative. Thus, understanding reaction spontaneity is pivotal for predicting whether a process will occur without external assistance.