From the standard electrode potentials in Table 7.2, what...

From the standard electrode potentials in Table $7.2,$ what are the standard Gibbs energies of formation at $25^{\circ} \mathrm{C}$ for $\mathrm{Cl}^{-}(\mathrm{ao}), \mathrm{OH}^{-}(\mathrm{ao}),$ and $\mathrm{Na}^{+}(\mathrm{ao}) ?$

Key Concepts

Standard State Conditions

Standard state conditions provide the reference framework within which thermodynamic quantities are defined and measured. For reactions in solution, this typically means 1 M concentration for solutes, 25°C temperature, and 1 atm pressure for gases. These conditions ensure consistency in the interpretation of electrode potentials and Gibbs free energies across different systems and reactions.

Electrochemical Thermodynamic Relationship

This key concept is the thermodynamic link between electrical work and chemical energy. It is embodied in the relation ?G° = –nFE°, where ?G° is the standard Gibbs free energy change, n is the number of electrons transferred in the reaction, F is Faraday’s constant, and E° is the standard electrode potential. This equation allows one to convert between the electrical potential data and the Gibbs free energy changes, facilitating the calculation of formation energies.

Standard Electrode Potentials

This concept refers to the measured voltage associated with a redox reaction under standard conditions (typically 25°C, 1 atm pressure, and 1 M concentrations for solutions). It is a fundamental parameter in electrochemistry that indicates the tendency of a chemical species to be reduced. In the context of this question, the values from the electrode potential table are used as a basis to calculate derived thermodynamic quantities.

Gibbs Free Energy of Formation

Gibbs free energy of formation is the change in free energy when one mole of a compound is formed from its elements in their standard states. It is an essential thermodynamic parameter that indicates the spontaneity of formation of a species. The values for aqueous ions, such as Cl?(aq), OH?(aq), and Na?(aq), are typically calculated relative to a standard state using thermodynamic data.

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