Question

Based on the description of the nickel-cadmium cell on page \(1053,\) and with appropriate data from Appendix \(D\), estimate \(E^{\circ}\) for the reduction of \(\mathrm{NiO}(\mathrm{OH})\) to \(\mathrm{Ni}(\mathrm{OH})_{2}\)

Short answer

The standard cell potential \(E^\circ\) for the reduction of \(\mathrm{NiO}(\mathrm{OH})\) to \(\mathrm{Ni}(\mathrm{OH})_{2}\) must be calculated through the Nernst equation, using the standard potentials of the half reactions revealed in the Appendix D. The precise numeric value, however, requires the exact values of the standard potentials, which the exercise didn't provide.

Step-by-step solution

Identify the Half Reactions

The given process is a reduction, meaning there are two half reactions taking place. The first is the reduction of nickel hydroxide to form nickel hydroxide ion and an electron. The second half reaction is the oxidation of a cadmium ion to cadmium and two electrons. We must identify these reactions and their standard electrode potentials from the information given in the Appendix D.

Calculate the Cell Potential

Once the standard potentials for each of the half reactions have been identified, we can calculate the overall cell potential. According to the Nernst equation, the standard cell potential is the difference between the standard reduction potential of the cathode and the anode. We substitute the values into the equation, \(E^\circ_{cell} =E^\circ_{cathode}-E^\circ_{anode}\), to obtain the cell potential.

Identify the Cell Potential for NiO(OH)

Finally, we need to estimate the cell potential for the reduction of \(\mathrm{NiO}(\mathrm{OH})\) to \(\mathrm{Ni}(\mathrm{OH})_{2}\). As the cell potential we calculated in Step 2 is for the entire nickel-cadmium cell, the potential for the reduction from \(\mathrm{NiO}(\mathrm{OH})\) to \(\mathrm{Ni}(\mathrm{OH})_{2}\) needs to be extracted from this value.

Key concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are processes where electrons are transferred between atoms, ions, or molecules. This transfer results in a change in the oxidation states of the reacting species. In a redox reaction, one substance undergoes oxidation (loss of electrons) while another undergoes reduction (gain of electrons).

Understanding redox reactions is pivotal because they underpin various chemical processes, including the functioning of batteries, corrosion of metals, and even cellular respiration in biology. In an educational context, grasping the balance of electron flow is crucial for students to predict the products of chemical reactions and to comprehend how energy is converted in electrochemical processes.

Nernst Equation

The Nernst Equation is a fundamental principle in electrochemistry used to calculate the electric potential of an electrochemical cell under non-standard conditions. It correlates the standard electrode potential, temperature, and concentrations of the reacting species. The equation is expressed as:
\[ E = E^\circ - \frac{RT}{nF}\ln\left(\frac{\text{Products}}{\text{Reactants}}\right) \]
Where \( E \) is the cell potential, \( E^\circ \) is the standard cell potential, \( R \) is the gas constant, \( T \) is the temperature in Kelvin, \( n \) is the number of moles of electrons exchanged, and \( F \) is the Faraday's constant.

In the textbook problem, the Nernst equation helps us to understand how to estimate cell potential under standard conditions by excluding the concentration terms, thus simplifying it to a difference in standard reduction potentials.

Chemical Cells

Chemical cells, often called electrochemical cells, are devices that convert chemical energy into electrical energy through chemical reactions. There are two types: galvanic (or voltaic) cells that generate electricity spontaneously, and electrolytic cells that use electrical energy to drive chemical reactions.

In the context of the nickel-cadmium cell described in the exercise, we're dealing with a galvanic cell where the spontaneous redox reactions provide electrical power. Students should understand that the setup includes two half-cells – one for oxidation and one for reduction. Each half-cell contains an electrode and an electrolyte, where the interplay of reactions at the electrodes results in the flow of electrons through an external circuit, producing electric current.

Electrochemistry

Electrochemistry is the study of chemical processes that cause electrons to move, resulting in the generation of an electric current. It is a branch of chemistry that deals with the interrelation of electrical and chemical phenomena. Electrochemistry encompasses the study of batteries, fuel cells, electrolysis, and corrosion among other topics. Knowledge in electrochemistry is critical for the understanding of how batteries function, as well as for advancing technologies in energy storage and conversion.

With relevance to our textbook exercise, understanding electrochemistry involves recognizing redox reactions at the electrodes, knowing how to use the Nernst equation to predict cell potentials, and appreciating the design and function of various types of chemical cells. This foundational knowledge is vital in fields such as materials science, engineering, and renewable energy technologies.