Calculate the standard reaction Gibbs free energy for the following cell reactions: (a) \(2 \mathrm{Ce}^{++}(\mathrm{aq})+3 \mathrm{I}^{-}(\mathrm{aq}) \longrightarrow 2 \mathrm{Ce}^{3+}(\mathrm{aq})+\mathrm{I}_{3}^{-}(\mathrm{aq})\) \(E_{\mathrm{cell}^{\circ}}=+1.08 \mathrm{~V}\) (b) \(6 \mathrm{Fe}^{3+}(\mathrm{aq})+2 \mathrm{Cr}^{3+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow 6 \mathrm{Fe}^{2+}(\mathrm{aq})+\) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq})+14 \mathrm{H}^{+}(\mathrm{aq}), E_{\text {cell }}{ }^{\circ}=-1.29 \mathrm{~V}\)

Electrochemistry is a branch of chemistry that deals with the interrelation of electrical currents and chemical reactions. It involves the study of the movement of electrons from one substance to another, a process fundamental to many types of electrochemical cells.

Electrochemical reactions can be used for a variety of applications, including energy storage in batteries, electroplating, and the industrial production of chemicals like chlorine and sodium hydroxide. The transfer of electrons during these reactions leads to changes in the oxidation state of the atoms and ions involved, which is key to understanding how electrochemical cells operate.

Galvanic cells, also known as voltaic cells, are a type of electrochemical cell that converts chemical energy into electrical energy through spontaneous redox reactions. They consist of two half-cells, each containing an electrode in contact with an electrolyte.

Each half-cell has its own separate redox reaction, with the overall cell reaction being the sum of these half-reactions. Electrons flow from the anode, where oxidation occurs, to the cathode, where reduction takes place. The potential difference between the two electrodes can be measured and is a source of electric power. Galvanic cells are the basis for common batteries.

The standard cell potential (\( E^{\text{\textdegree}} \)) is a crucial value in electrochemistry representing the potential difference between two electrodes of a galvanic cell when all components are at their standard states, usually 1 M concentration for solutes and 1 atm pressure for gases at 25°C. It is measured in volts (V).

The standard cell potential provides insight into the cell's ability to perform work when electrons transfer through the external circuit. A positive standard cell potential indicates that a reaction is spontaneous, while a negative value suggests a non-spontaneous reaction under standard conditions.

The Gibbs free energy equation connects thermodynamics and electrochemistry, allowing us to predict the spontaneity of a reaction. Given by the formula \( \Delta G^{\text{\textdegree}} = -nFE^{\text{\textdegree}} \), where \( \Delta G^{\text{\textdegree}} \) is the standard Gibbs free energy change, \( n \) is the number of moles of electrons transferred in the reaction, \( F \) is the Faraday constant (approximately 96485 C/mol), and \( E^{\text{\textdegree}} \) is the standard cell potential.

A negative value of \( \Delta G^{\text{\textdegree}} \) implies that the reaction is spontaneous under standard conditions. This fundamental equation bridges the gap between the electrochemical behavior of a cell and its thermodynamic properties and is key to solving problems related to galvanic cells and their energy changes.