What are \(E_{\text {cell }}^{\circ}\) and \(\Delta G^{\circ}\) of a redox reaction at \(25^{\circ} \mathrm{C}\) for which \(n=2\) and \(K=65 ?\)

A redox reaction, short for reduction-oxidation reaction, involves the transfer of electrons between two species. During this process, one substance gets oxidized (loses electrons) while another gets reduced (gains electrons). Understanding redox reactions is essential because they form the basis of many chemical processes and are fundamental in electrochemistry. You can identify redox reactions with changes in oxidation states of the elements involved.

In the context of electrochemistry, redox reactions occur in electrochemical cells where oxidation happens at the anode and reduction at the cathode. These reactions generate electrical energy in galvanic cells or consume electrical energy in electrolytic cells.

Remember, balancing redox reactions requires ensuring both mass and charge are conserved. You may use methods like the half-reaction method to split into oxidation and reduction parts, balance them independently, and then combine them for the full reaction.

Standard cell potential (\(E_{\text{cell}}^\text{o}\)) is a measure of the potential difference between two half-cells under standard conditions (1 M concentration, 1 atm pressure, and 25°C). It determines how much voltage an electrochemical cell can provide. The Nernst equation gives us a useful way to find this potential:

\begin{align*}E_{\text{cell}} = E_{\text{cell}}^\text{o} - \frac{0.0592}{n} \text{log}(Q)\text{/end{align*}In the exercise example, we used a variation of this equation to find the standard cell potential. By knowing the equilibrium constant (\text{K}), we can simplify our work:\begin{align*}E_{\text{cell}}^\text{o} = \frac{0.0592}{n} \times \text{log}(K)//end{align*} where n is the number of moles of electrons transferred. Substituting the given values from the exercise determined the standard cell potential for the reaction.A positive (\text{E\text{cell}}\text{o}) indicates a spontaneous redox reaction.

Gibbs free energy (\text{G}) determines whether a process is spontaneous. For redox reactions, the change in Gibbs free energy (\text{\(\text{Delta} G\)}) links directly to the cell potential using the equation:

\begin{align*}\text{\(\text{Delta} G\)}^\text{o} = -nFE_{\text{cell}}^\text{o}\text{end{align*}\text{Here, F} is the Faraday constant (about 96485 C/mol).Replacing the values from the example into this equation allows us to calculate the Gibbs free energy change for the redox reaction.