Question

which statement is true for the reaction below?
k₂o₂(s) → 2k(s) + o₂(g)
δh = 496 kj/mol
the reaction will occur at all temperatures.
the reaction will never occur.
the reaction will occur only at low temperatures.
the reaction will occur only at high temperatures.

Explanation:

To determine the temperature dependence of the reaction \( \text{K}_2\text{O}_2(s)
ightarrow 2\text{K}(s) + \text{O}_2(g) \) with \( \Delta H = 496 \, \text{kJ/mol} \), we analyze the enthalpy (\( \Delta H \)) and entropy (\( \Delta S \)) changes:

1. Enthalpy Change (\( \Delta H \)): The reaction has \( \Delta H = +496 \, \text{kJ/mol} \), meaning it is endothermic (heat is absorbed from the surroundings).
2. Entropy Change (\( \Delta S \)): The reaction produces \( \text{O}_2(g) \) from a solid reactant (\( \text{K}_2\text{O}_2(s) \)). Gases have higher entropy than solids, so \( \Delta S \) is positive (disorder increases).

For a reaction to be spontaneous, the Gibbs free energy change (\( \Delta G \)) must be negative, where \( \Delta G = \Delta H - T\Delta S \).

• At low temperatures: \( T\Delta S \) is small (since \( T \) is low). Thus, \( \Delta G = \text{(positive } \Delta H) - \text{(small } T\Delta S) \) remains positive (non - spontaneous).
• At high temperatures: \( T\Delta S \) becomes large (since \( T \) is high). Thus, \( \Delta G = \text{(positive } \Delta H) - \text{(large } T\Delta S) \) can become negative (spontaneous).

The first option ("occurs at all temperatures") is wrong because \( \Delta H \) is positive (endothermic) and low \( T \) makes \( \Delta G \) positive. The second option ("never occurs") is wrong because high \( T \) can make \( \Delta G \) negative. The third option ("only at low temperatures") is wrong because low \( T \) gives positive \( \Delta G \). Only the fourth option ("only at high temperatures") matches the analysis: high \( T \) makes \( T\Delta S \) large enough to overcome the positive \( \Delta H \), leading to \( \Delta G < 0 \) (spontaneous reaction).

Answer:

The reaction will occur only at high temperatures.