Under standard conditions, what reaction occurs, if any, when each of the following operations is performed? a. Crystals of \(\mathrm{I}_{2}\) are added to a solution of NaCl. b. \(\mathrm{Cl}_{2}\) gas is bubbled into a solution of NaI. c. A silver wire is placed in a solution of \(\mathrm{CuCl}_{2}\) d. An acidic solution of \(\mathrm{FeSO}_{4}\) is exposed to air. For the reactions that occur, write a balanced equation and calculate \(\mathscr{E}^{\circ}, \Delta G^{\circ},\) and \(K\) at \(25^{\circ} \mathrm{C}\)

In the grand scheme of chemistry, redox reactions play a crucial role as they are the processes that involve the transfer of electrons between elements or compounds. Such reactions are essential in both biological systems, such as cellular respiration, and industrial applications, like battery operation. Redox is a shortened form of reduction-oxidation. All redox processes involve two simultaneous changes: reduction, where a substance gains electrons, and oxidation, where a substance loses electrons. The substance that donates electrons is called the reducing agent and is oxidized, while the substance that accepts electrons is the oxidizing agent and is reduced.

To identify redox reactions in an exercise, one must first discern the possible half reactions that can take place between reactants. A half-reaction splits the redox process into two parts and allows you to see the oxidation and reduction separately. You'll generally see substances either gaining or losing electrons, signified by a change in oxidation state. Understanding redox reactions is integral to solving problems such as those posed in the exercise, where you must determine whether a reaction will occur and, if so, calculate related values such as standard cell potential, Gibbs free energy, and equilibrium constants.

To discuss standard electrode potentials, we must firstly comprehend that these are measures of the inherent tendency of a redox species to gain or lose electrons and become reduced or oxidized, respectively. They are measured under standard conditions, which is typically at a pressure of 1 atm, a concentration of 1 M for all solutions, and a temperature of 25°C (298 K). Electrode potentials are tabulated as standard reduction potentials, and each half-cell reaction has its own standard electrode potential, symbolized as \(E^°\).

When faced with predicting whether a redox reaction will occur, like in the exercise scenarios, one must reference a table of standard electrode potentials. This step involves determining for each half-reaction in a scenario, using the given reactants. The discrepancies in these potentials determine the direction of electron flow and thus the feasibility of the reaction. When calculating the standard cell potential for the reaction (\(\mathscr{E}^°\)), the potential of the reduction half-reaction (with higher \(E^°\) value) is subtracted from the potential of the oxidation half-reaction. A positive \(\mathscr{E}^°\) indicates a spontaneous reaction under standard conditions.

The concept of Gibbs free energy \(\Delta G^°\) is central to understanding the spontaneity of chemical reactions, which is our capacity to predict if a particular reaction might occur without the need for external energy. For a reaction under standard conditions, a negative value of \(\Delta G^°\) indicates that the process is spontaneous. Conversely, a positive \(\Delta G^°\) signals a non-spontaneous reaction, where external energy is needed to drive it.

Linking Gibbs free energy to redox reactions and standard electrode potentials, there's an elegant formula that ties these concepts together: \(\Delta G^° = -nFE^°\), where \(n\) is the number of moles of electrons exchanged in the reaction, \(F\) is Faraday's constant (96485 C/mol), and \(\mathscr{E}^°\) is the standard cell potential. This relationship allows us to calculate the feasibility of the reactions in the exercise in terms of energy change. If we have a positive standard cell potential, the Gibbs free energy change will be negative, indicating a spontaneous reaction.

The equilibrium constant (\(K\)) is another thermodynamic parameter that is invaluable when studying chemical reactions. It quantifies the ratio of the concentrations of products to reactants at equilibrium, where the rate of the forward reaction equals the rate of the reverse reaction. For reactions where \(\Delta G^°\) is negative, indicating a spontaneous reaction, the value of \(K\) will be greater than 1, signifying that, at equilibrium, there's a greater concentration of products. Conversely, when \(\Delta G^°\) is positive, \(K\) will be less than 1, which means the reactants are favored at equilibrium.

There's an intrinsic tie between Gibbs free energy and the equilibrium constant, described by the equation \(\Delta G^° = -RT \ln K\), where \(R\) is the universal gas constant and \(T\) is the temperature in Kelvin. This equilibrium constant can thus be calculated from the standard Gibbs free energy change, as seen in the final step of the exercise solutions, allowing us to infer the extent to which a reaction will proceed under standard conditions.