Problem 106 - General Chemistry: Principles and Modern Applications

Question

Consider two cells involving two metals \(X\) and \(Y\) $$\begin{aligned} \mathrm{X}(\mathrm{s})\left|\mathrm{X}^{+}(\mathrm{aq})\right|\left|\mathrm{H}^{+}(\mathrm{aq}), \mathrm{H}_{2}(\mathrm{g}, 1 \mathrm{bar})\right| \mathrm{Pt}(\mathrm{s}) & \\\ \mathrm{X}(\mathrm{s})\left|\mathrm{X}^{+}(\mathrm{aq}) \| \mathrm{Y}^{2+}(\mathrm{aq})\right| \mathrm{Y}(\mathrm{s}) \end{aligned}$$ In the first cell electrons flow from the metal \(X\) to the standard hydrogen electrode. In the second cell electrons flow from metal \(X\) to metal Y. Is \(E_{x^{+} / x}^{\circ_{+}}\) greater orless than zero? Is \(E_{x^{+} / x}^{\circ}>E_{\mathrm{Y}^{2+}},_{\mathrm{Y}} ?\) Explain.

Step-by-Step Solution

Answer

\(\(E_{x^{+} / x}\) is less than zero and also \(\(E_{x^{+} / x}\) is less than \(E_{\mathrm{Y}^{2+}},_{\mathrm{Y}}\). This is because in both cells metal X is acting as the anode i.e., it is getting oxidized which means it has lesser standard reduction potential.

Step 1: Understand the electron flow in cells

In the first cell, the flow of electrons is from metal X to a standard hydrogen electrode, meaning metal X is getting oxidized. In other words, it is losing electrons. In the second cell, the electron flow is from metal X to metal Y, signifying that X acts as the anode, or again, it is oxidized.

Step 2: Determine \(\(E_{x^{+} / x}\) value

Since metal X is getting oxidized in both cells, this implies that the standard reduction potential \(E_{x^{+} / x}\) of X is less than the standard reduction potential of hydrogen electrode (0.00 V). Therefore, \(\(E_{x^{+} / x}\) is less than zero. This is also indicative that metal X is more easily oxidized than hydrogen.

Step 3: Compare \(\(E_{x^{+} / x}\) and \(E_{\mathrm{Y}^{2+}},_{\mathrm{Y}}\)

In the second cell, as electron flow is from metal X to metal Y, this illustrates that metal X is more easily oxidized than metal Y. Thus, the standard reduction potential \(E_{x^{+} / x}\) of X is less than the standard reduction potential \(E_{\mathrm{Y}^{2+}},_{\mathrm{Y}}\) of Y.

Key Concepts

Electrochemistry

Electrochemistry is an essential branch of chemistry that deals with the interconversion of electrical energy and chemical energy. This field of study encompasses a variety of reactions called redox reactions, where oxidation (loss of electrons) and reduction (gain of electrons) occur simultaneously. Typically, these reactions occur in electrochemical cells, where two electrodes, the anode and the cathode, are immersed in an electrolyte and separated by a salt bridge or porous membrane.

In such a cell, electrons flow through an external circuit while ions move within the electrolyte, maintaining the electrical neutrality. This movement of electrons generates an electric current, which can be harnessed for practical uses. The understanding of the standard reduction potential is crucial in electrochemistry because it provides information about the tendency of a species to gain or lose electrons. The standard hydrogen electrode (SHE) serves as a universal reference with a set potential of 0.00 V, against which all other electrode potentials are measured. An important application of electrochemistry is in the development of batteries, galvanic cells, fuel cells, and electrolysis processes.

Oxidation and Reduction

Oxidation and reduction are chemical processes that are at the core of electrochemistry. Oxidation involves the loss of electrons from an atom or molecule, while reduction refers to the gain of electrons. These processes always occur together; when one species is oxidized, another is simultaneously reduced, hence the term 'redox' reactions.

To remember which is which, the mnemonic 'LEO says GER' can be helpful, standing for 'Loss of Electrons is Oxidation' and 'Gain of Electrons is Reduction'. In an electrochemical cell, the electrode at which oxidation occurs is known as the anode, while the electrode where reduction happens is termed the cathode. By convention, electrons flow from the anode to the cathode. The standard reduction potential helps us predict the direction of electron flow and determine which half-reaction will be oxidation and which will be reduction in a given chemical reaction.

Galvanic Cells

Galvanic cells, also known as voltaic cells, are a type of electrochemical cell that convert chemical energy into electrical energy through spontaneous redox reactions. They consist of two half-cells connected by a salt bridge or porous membrane, each containing an electrode in contact with its own electrolyte solution. One metal tends to lose electrons (oxidized) and the other tends to gain them (reduced).

The cell potential, or electromotive force (EMF), of a galvanic cell is the difference in standard reduction potentials of the cathode and the anode. If the standard reduction potential of the cathode is higher, electrons will flow to the cathode from the anode, creating an electrical current. In the exercise mentioned, since electrons flow from metal X to the standard hydrogen electrode in one cell, and from metal X to metal Y in another cell, we infer that metal X has a lower standard reduction potential than both hydrogen and metal Y. This suggests that X is a good reducing agent and will act as the anode in a galvanic cell.