Define (a) the standard free-energy change, ∆G°, for a reaction, and (b) the standard free energy of formation, ∆G°f, of a substance.

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1. Step 1: Define the standard free-energy change, \( \Delta G^\circ \), for a reaction. It is the change in Gibbs free energy when reactants in their standard states are converted to products in their standard states at a specified temperature, usually 298 K (25°C).
2. Step 2: Explain that the standard state refers to the pure form of a substance at 1 bar of pressure and a specified temperature, typically 298 K.
3. Step 3: Describe that \( \Delta G^\circ \) is used to predict the spontaneity of a reaction. If \( \Delta G^\circ < 0 \), the reaction is spontaneous under standard conditions; if \( \Delta G^\circ > 0 \), it is non-spontaneous.
4. Step 4: Define the standard free energy of formation, \( \Delta G^\circ_f \), of a substance. It is the change in Gibbs free energy when one mole of a compound is formed from its elements in their standard states.
5. Step 5: Clarify that \( \Delta G^\circ_f \) values are used to calculate \( \Delta G^\circ \) for reactions using the equation: \( \Delta G^\circ = \sum \Delta G^\circ_f (\text{products}) - \sum \Delta G^\circ_f (\text{reactants}) \).