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Chapter 13: Problem 99

(a) If you were to construct a concentration cell in which one half-cell contains \(1.0 \mathrm{M} \mathrm{CrCl}_{3}\) and the other half-cell \(0.0010 \mathrm{M}\) \(\mathrm{CrCl}_{3}\), and both electrodes were chromium, at which electrode would reduction spontaneously take place? How will each of the following changes affect the cell potential? Justify your answers. (b) Adding \(100 \mathrm{~mL}\) pure water to the anode compartment. (c) Adding \(100 \mathrm{~mL} 1.0 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) to the cathode compartment (Cr \((\mathrm{OH})_{3}\) is insoluble). (d) Increasing the mass of the chromium electrode in the anode compartment.

Short Answer

Expert verified
Reduction occurs spontaneously at the cathode with 1.0 M \(\mathrm{CrCl}_3\). Adding water to the anode increases the cell potential, adding NaOH to the cathode decreases it, and increasing the mass of the chromium electrode in the anode has no effect on the cell potential.

Step by step solution

01

Identify the electrode with spontaneous reduction

To determine at which electrode reduction will spontaneously occur in a concentration cell, identify the half-cell with the higher concentration of metal ions. This is because the more concentrated solution has a higher reduction potential. In this case, the half-cell with 1.0 M \(\mathrm{CrCl}_3\) will have a higher concentration of \(\mathrm{Cr}^{3+}\) ions compared to the 0.0010 M solution, so reduction will spontaneously occur at the electrode with the 1.0 M \(\mathrm{CrCl}_3\), making it the cathode.
02

Effect of adding pure water to the anode compartment

Adding pure water to the anode compartment will dilute the chromic chloride solution, therefore decreasing the concentration of \(\mathrm{Cr}^{3+}\) ions. This will result in a lower anode potential, consequently increasing the overall cell potential, as the difference between the cathode and anode potentials will increase.
03

Effect of adding 1.0 M NaOH(aq) to the cathode compartment

Adding \(1.0 \mathrm{M} \mathrm{NaOH}(\mathrm{aq})\) to the cathode compartment will result in the precipitation of \(\mathrm{Cr}(\mathrm{OH})_3\) due to its low solubility. This reduces the concentration of \(\mathrm{Cr}^{3+}\) ions at the cathode, decreasing the cathode potential. The net potential of the cell decreases, as the difference in potential between the cathode and anode is reduced.
04

Effect of increasing the mass of the chromium electrode in the anode compartment

Increasing the mass of the chromium electrode in the anode compartment will not affect the cell potential directly. The cell potential is driven by the concentrations of the ions in the solution, not the mass of the electrodes. Thus, this change has no impact on the cell potential.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrochemical Cells
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. A classic example is the galvanic or voltaic cell, which turns chemical energy into electrical energy through spontaneous redox (reduction-oxidation) reactions. In the context of a concentration cell, both half-cells contain the same substances at different concentrations, and electrical current flows as the system seeks equilibrium.
Cell Potential
The cell potential, also known as electromotive force (emf), is the driving force behind the electrical current in an electrochemical cell. It is a measure of the energy per unit charge that is available from the redox reactions and is determined by the difference in potential between two half-cells. In concentration cells, the cell potential arises from the concentration gradient between the two half-cell solutions and is calculated based on the reduction potentials of the electrodes and the ion concentrations.
Redox Reactions
Redox reactions are chemical reactions that involve the transfer of electrons from one substance to another. In such reactions, one species is oxidized (loses electrons) while the other is reduced (gains electrons). In the case of an electrochemical cell like the concentration cell, the movement of electrons from the anode to the cathode through an external circuit is facilitated by these redox reactions, generating an electric current.
Half-Cell
A half-cell is one part of a two-part electrochemical cell where either oxidation or reduction occurs, with the entire cell consisting of two such half-cells. In a concentration cell, both half-cells generally involve the same chemical species but at different concentrations, setting up a concentration gradient that drives electron transfer and generates electrical energy.
Nernst Equation
The Nernst equation is integral to understanding the behavior of electrochemical cells, including concentration cells. It allows for the calculation of the cell potential by considering the temperature, the standard cell potential, the concentrations of the reacting species, and the number of moles of electrons exchanged in the redox reaction. This equation highlights how variations in concentration influence the cell potential, crucial for analyzing scenarios affecting the concentration cell.
Electrode Reduction
Electrode reduction is the process by which electrons are gained at an electrode during a redox reaction. In a concentration cell, this typically occurs at the cathode, the electrode towards which positively charged ions migrate to gain electrons. The potential for reduction at this electrode is inherently related to the ion concentration and the intrinsic tendency of the electrode material to undergo reduction.
Chemical Equilibrium
Chemical equilibrium in the context of electrochemical cells refers to the state where the forward and reverse reactions occur at equal rates leading to no net change in the concentration of reactants and products over time. In concentration cells, equilibrium is reached when the concentrations of the reacting species in both half-cells become equal, at which point no further current flows, and the cell potential drops to zero.

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Most popular questions from this chapter

(a) Suggest two metals that could be used for the cathodic protection of a titanium pipeline. (b) What factors other than relative positions in the electrochemical series need to be considered in practice? (c) Often copper piping is connected to iron pipes in household plumbing systems. What is a possible effect of the copper on the iron pipes?

A chromium-plated steel bicycle handlebar is scratched. Will rusting of the iron in the steel be encouraged or retarded by the chromium?

The density of the electrolyte in a lead-acid battery is measured to assess its state of charge. Explain how the density indicates the state of charge of the battery.

When a pH meter was standardized with a boric acid-borate buffer with a pH of \(9.40\), the cell was \(+0.060 \mathrm{~V}\). When the buffer was replaced with a solution of unknown hydronium ion concentration, the cell potential was \(+0.22 \mathrm{~V}\). What is the \(\mathrm{pH}\) of the solution?

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?
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