The absolute magnitudes of the standard potentials of two metals \(\mathrm{M}\) and \(\mathrm{X}\) were determined to be (1) \(\mathrm{M}^{+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{M}(\mathrm{s}) \quad\left|E^{\circ}\right|=0.25 \mathrm{~V}\) (2) \(\mathrm{X}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{X}(\mathrm{s}) \quad\left|E^{\circ}\right|=0.65 \mathrm{~V}\) When the two electrodes are connected, current flows from \(M\) to \(\mathrm{X}\) in the external circuit. When the electrode corresponding to halfreaction 1 is connected to the standard hydrogen electrode (SHE), current flows from \(M\) to SHE. (a) What are the signs of \(E^{\circ}\) of the two half-reactions? (b) What is the standard cell potential for the cell constructed from these two electrodes?

An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or facilitating chemical reactions through the introduction of electrical energy. These cells consist of two electrodes (anode and cathode) immersed in electrolytic solutions, connected by an external circuit and a salt bridge.

In the given exercise, when metal M is connected to X, there's a flow of current, indicating that an electrochemical reaction is taking place. The metal M, having a negative standard potential, acts as the anode where oxidation occurs, giving up electrons. Metal X, on the other hand, has a positive standard potential and acts as the cathode where reduction takes place, gaining electrons. The flow of electrons from anode to cathode through the external circuit is what generates the electric current.

Understanding electrochemical cells is pivotal as they form the basis of batteries and various types of sensors and are fundamental in electroplating, electrorefining, and electrolysis processes.

The Standard Hydrogen Electrode, often abbreviated as SHE, is used as a reference electrode against which the standard electrode potentials of other electrodes are measured. SHE has a defined potential of 0 volts. In practice, it consists of a platinum electrode in contact with 1 M H₂ gas and immersed in 1 M H⁺ aqueous solution.

When M is connected to SHE, as stated in the exercise, current flows from M to SHE. This indicates that M has a lower potential than SHE. Since SHE is the universal reference with a potential of 0 volts, M's potential is assigned a negative sign, depicting that M is undergoing oxidation and releasing electrons to SHE. The SHE serves a crucial role in understanding redox chemistry as it provides a stable comparison for measuring and quantifying the tendency of other half-cells to lose or gain electrons.

Oxidation-reduction reactions, or redox reactions, are chemical processes involving the transfer of electrons between two substances. Oxidation involves the loss of electrons, while reduction involves the gain of these electrons. These reactions are fundamental to the function of an electrochemical cell.

Within the context of our exercise, when metal M loses an electron - it's said to undergo oxidation, represented by the half-equation \(\mathrm{M}^{+}(\mathrm{aq})+\mathrm{e}^{-} \longrightarrow \mathrm{M}(\mathrm{s})\). Conversely, metal X gains electrons and is reduced, described by the half-equation \(\mathrm{X}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow \mathrm{X}(\mathrm{s})\). The overall cell potential is determined by the difference in the potential of these two half-reactions. Recognizing these redox concepts is central to comprehending how batteries produce electricity or how corrosion occurs, among other practical applications.