Calculate the free energy change for this reaction at 25 °C. Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) 2 Ca(s) + O₂( g) → 2 CaO(s) ΔH°_rxn = -1269.8 kJ; ΔS°_rxn = -364.6 J/K

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1. Identify the formula for calculating the Gibbs free energy change: \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \).
2. Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 = 298.15 \text{ K} \).
3. Ensure that the units for \( \Delta S^\circ \) are consistent with \( \Delta H^\circ \). Convert \( \Delta S^\circ \) from J/K to kJ/K by dividing by 1000: \( \Delta S^\circ = -364.6 \text{ J/K} = -0.3646 \text{ kJ/K} \).
4. Substitute the values into the Gibbs free energy equation: \( \Delta G^\circ = -1269.8 \text{ kJ} - (298.15 \text{ K} \times -0.3646 \text{ kJ/K}) \).
5. Determine if the reaction is spontaneous by checking the sign of \( \Delta G^\circ \). If \( \Delta G^\circ < 0 \), the reaction is spontaneous.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) for a reaction can be calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates that a reaction is spontaneous under the given conditions.

Standard State Conditions

Standard state conditions refer to a set of specific conditions used to measure the properties of substances, typically defined as 1 bar of pressure and a specified temperature, usually 25 °C (298 K). Under these conditions, the standard enthalpy (ΔH°) and standard entropy (ΔS°) values are determined for reactants and products. These values are essential for calculating the Gibbs Free Energy change for reactions, as they provide a reference point for the thermodynamic properties.

Spontaneity of Reactions

The spontaneity of a reaction refers to whether a reaction can occur without external intervention. A reaction is considered spontaneous if it leads to a decrease in free energy (ΔG < 0). Factors influencing spontaneity include enthalpy (ΔH) and entropy (ΔS) changes; a reaction can be spontaneous at certain temperatures even if it is endothermic (positive ΔH) if the entropy increase (positive ΔS) is sufficiently large to make ΔG negative.