A \(\mathrm{Zn} / \mathrm{Zn}^{2+}\) concentration cell is constructed in which both electrodes are pure zinc. The \(\mathrm{Zn}^{2+}\) concentration for one cell half is \(1.0 M\), for the other, \(10^{-2} M\). Is a voltage generated between the two cell halves? If so, what is its magnitude and which electrode will be oxidized? If no voltage is produced, explain this result.

Electrochemistry is a branch of chemistry that deals with the relationship between electrical energy and chemical reactions. It involves the study of redox reactions where oxidation and reduction processes occur, often within an electrochemical cell. In an electrochemical cell, chemical energy is converted into electrical energy, which is harnessed to perform work or measure reaction properties. Electrochemistry is fundamental in a variety of applications, from batteries and fuel cells to corrosion prevention and the electroplating of metals.

In the context of a concentration cell, like the \(\mathrm{Zn} / \mathrm{Zn^{2+}}\) cell mentioned in the exercise, electrochemistry explains how an electrical current can be generated solely by differences in concentration of the same species at the two electrodes. The flow of electrons through an external circuit, and ions through a salt bridge, equalizes the concentrations, creating electrical potential in the process. Understanding electrochemistry is essential to grasp why a voltage is created in such a cell, and why one electrode will undergo oxidation while the other undergoes reduction.

The Nernst equation is a mathematical expression that relates the voltage (potential) of an electrochemical cell to the standard electrode potential, temperature, and the concentrations of the chemical species involved. The equation is given as:

\[E = E° - \frac{0.0592}{n}\log Q\]
where \(E\) is the cell potential, \(E°\) is the standard cell potential, \(n\) is the number of electrons transferred in the redox reaction, and \(Q\) is the reaction quotient which represents the ratio of the concentrations of reactants and products at any point in time. For a concentration cell, the equation adapts to differences in concentration for the same species as seen in the provided homework exercise.

Applying the Nernst equation allowed the determination of the voltage generated in the concentration cell. Despite having a standard cell potential of zero, the different concentrations of \(\mathrm{Zn^{2+}}\) ions resulted in a measureable cell potential, which indicates that a spontaneous redox reaction can still occur, driven by the concentration gradient between the two half-cells.

Redox reactions are chemical reactions involving the transfer of electrons between two substances. 'Redox' is a portmanteau of 'reduction' and 'oxidation,' which occur simultaneously during such reactions. Oxidation refers to the loss of electrons, while reduction is the gain of electrons. In electrochemistry, redox reactions are central to the operation of electrochemical cells, including batteries and concentration cells.

In the exercise provided, oxidation happens at the anode where the \(\mathrm{Zn}\) metal loses electrons and reduction happens at the cathode where the \(\mathrm{Zn^{2+}}\) ions gain electrons to form \(\mathrm{Zn}\) metal. Despite the simple reaction appearing to achieve no net change, the difference in ion concentrations drives the spontaneous reaction, confirming that a redox process is indeed occurring. Understanding how these reactions work is crucial to grasping why electrons flow through an external circuit, thus generating an electric current in a concentration cell as seen in the exercise.