Consider the following endothermic decomposition of AB2 molecules: (a) What is the sign(+,-, or

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Consider the following endothermic decomposition of AB2...

Consider the following endothermic decomposition of $\mathrm{AB}_{2}$ molecules:
(a) What is the $\operatorname{sign}(+,-, \text { or } 0)$ of $\Delta S^{\circ}$ for the reaction?
(b) Is the reaction more likely to be spontaneous at high temperatures or at low temperatures? Explain.

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. In chemical reactions, an increase in the number of particles or a transition to a more disordered state generally results in a positive change in entropy (?S > 0). When a compound decomposes into multiple products, the system's disorder typically increases, which is a key factor in determining the sign of ?S.

Endothermic Reaction

An endothermic reaction is one that absorbs energy from the surroundings, resulting in a positive enthalpy change (?H > 0). These reactions require an input of heat to proceed, and this characteristic plays a significant role in how temperature influences the spontaneity of the reaction.

Gibbs Free Energy and Spontaneity

The spontaneity of a reaction is determined by the Gibbs free energy change (?G), which is calculated using the equation ?G = ?H - T?S. For a reaction to be spontaneous, ?G must be negative. In reactions where ?H is positive and ?S is also positive, increasing the temperature (T) can make the T?S term more significant, lowering ?G and making the reaction more thermodynamically favorable.

Temperature Dependence of Reaction Spontaneity

The effect of temperature on reaction spontaneity is pivotal in systems where both enthalpic and entropic factors play a role. For an endothermic reaction with a positive entropy change, a higher temperature increases the T?S contribution in the Gibbs free energy equation, thereby favoring spontaneity. This explains why certain reactions become more spontaneous at high temperatures.

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