Calculate ΔG°rxn for the reaction: CaCO3(s) → CaO(s) + CO2(g). Use the following reactions and given ΔG°rxn values: Ca(s) + CO2(g) + 1/2 O2(g) → CaCO3(s) ΔG°rxn = -734.4 kJ, 2 Ca(s) + O2(g) → 2 CaO(s) ΔG°rxn = -1206.6 kJ.

Verified step by step guidance

1. Identify the target reaction: CaCO3(s) → CaO(s) + CO2(g).
2. Recognize that you need to manipulate the given reactions to derive the target reaction.
3. Reverse the first given reaction: CaCO3(s) → Ca(s) + CO2(g) + 1/2 O2(g), which changes the sign of ΔG°rxn to +734.4 kJ.
4. Divide the second given reaction by 2 to match the stoichiometry of the target reaction: Ca(s) + 1/2 O2(g) → CaO(s), which changes ΔG°rxn to -603.3 kJ.
5. Add the modified reactions together to cancel out intermediate species and obtain the target reaction, then sum the ΔG°rxn values to find ΔG°rxn for the target reaction.

Key Concepts

Gibbs Free Energy (ΔG°)

Gibbs Free Energy (ΔG°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. It indicates the spontaneity of a reaction: a negative ΔG° suggests that the reaction can occur spontaneously, while a positive ΔG° indicates non-spontaneity. Understanding ΔG° is crucial for predicting whether a reaction will proceed in the forward direction.

Standard Reaction Gibbs Free Energy (ΔG°rxn)

Standard Reaction Gibbs Free Energy (ΔG°rxn) is the change in Gibbs Free Energy for a reaction under standard conditions (1 bar pressure, 1 M concentration, and a specified temperature, usually 298 K). It is calculated using the Gibbs Free Energy values of the reactants and products. This concept is essential for determining the favorability of a reaction and for performing calculations involving multiple reactions.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction, regardless of the pathway taken. This principle can be applied to Gibbs Free Energy calculations, allowing us to combine the ΔG°rxn values of known reactions to find the ΔG°rxn for a target reaction. It is a powerful tool in thermodynamics for deriving the energy changes in complex reactions.