Consider the reaction: CaCO3(s) → CaO(s) + CO2(g). Estimate ΔG° for this reaction at each temperature and predict whether or not the reaction is spontaneous. (Assume that ΔH° and ΔS° do not change too much within the given temperature range.) a. 298 K b. 1055 K c. 1455 K.

Verified step by step guidance

1. Identify the given reaction: \( \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) \). This is a decomposition reaction.
2. Recall the Gibbs free energy equation: \( \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ \).
3. Determine the standard enthalpy change (\( \Delta H^\circ \)) and the standard entropy change (\( \Delta S^\circ \)) for the reaction from standard tables.
4. For each temperature (298 K, 1055 K, 1455 K), substitute the values of \( \Delta H^\circ \), \( \Delta S^\circ \), and the given temperature \( T \) into the Gibbs free energy equation to calculate \( \Delta G^\circ \).
5. Analyze the sign of \( \Delta G^\circ \) for each temperature: if \( \Delta G^\circ < 0 \), the reaction is spontaneous; if \( \Delta G^\circ > 0 \), the reaction is non-spontaneous.

Key Concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ΔG indicates that a reaction is spontaneous, while a positive ΔG suggests non-spontaneity. The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

Enthalpy (ΔH) and Entropy (ΔS)

Enthalpy (ΔH) is the heat content of a system at constant pressure, reflecting the energy changes during a reaction. Entropy (ΔS) measures the disorder or randomness in a system. Both ΔH and ΔS are crucial for determining the spontaneity of a reaction through their influence on ΔG. For the reaction in question, knowing the values of ΔH and ΔS allows for the calculation of ΔG at different temperatures.

Temperature's Effect on Spontaneity

Temperature plays a significant role in determining the spontaneity of a reaction as it influences the ΔG value through the term TΔS in the Gibbs Free Energy equation. As temperature increases, the impact of entropy (ΔS) becomes more pronounced, potentially making a reaction spontaneous that was not at lower temperatures. Therefore, evaluating ΔG at various temperatures helps predict the behavior of the reaction under different thermal conditions.