Predict the conditions (high temperature, low temperature, all temperatures, or no temperatures) under which each reaction is spontaneous. a. H₂O(g) → H₂O(l) b. CO₂(s) → CO₂(g) c. H₂(g) → 2 H(g) d. 2 NO₂(g) → 2 NO(g) + O₂(g) (endothermic)

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1. Identify the sign of the enthalpy change (\(\Delta H\)) for the reaction. Since the reaction is described as endothermic, \(\Delta H\) is positive.
2. Consider the entropy change (\(\Delta S\)) of the reaction. Since the reaction involves the decomposition of two moles of NO₂ into three moles of gas (2 NO and 1 O₂), the entropy increases, making \(\Delta S\) positive.
3. Use the Gibbs free energy equation, \(\Delta G = \Delta H - T\Delta S\), to analyze the spontaneity of the reaction. Here, \(T\) represents the temperature in Kelvin.
4. Since both \(\Delta H\) and \(\Delta S\) are positive, the sign of \(\Delta G\) depends on the relative magnitudes of \(\Delta H\) and \(T\Delta S\). As temperature increases, \(T\Delta S\) becomes more significant.
5. Conclude that the reaction is spontaneous at high temperatures where \(T\Delta S\) outweighs \(\Delta H\), making \(\Delta G\) negative.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction at constant temperature and pressure. A reaction is spontaneous if the change in Gibbs Free Energy (ΔG) is negative. The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) is given by the equation ΔG = ΔH - TΔS, where a negative ΔG indicates a spontaneous process.

Endothermic Reactions

Endothermic reactions absorb heat from their surroundings, resulting in a positive change in enthalpy (ΔH > 0). For such reactions to be spontaneous, the increase in entropy (ΔS) must be sufficiently large to overcome the positive ΔH when multiplied by the temperature (T). This means that at higher temperatures, the entropy term becomes more significant, potentially making the reaction spontaneous.

Entropy and Temperature

Entropy (S) is a measure of the disorder or randomness in a system. In the context of chemical reactions, an increase in entropy (ΔS > 0) favors spontaneity. For endothermic reactions, higher temperatures can enhance the impact of entropy on Gibbs Free Energy, making it more likely for the reaction to be spontaneous as temperature increases, thus favoring the formation of products.