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Ch.20 - Electrochemistry
All textbooksBrown 15th EditionCh.20 - ElectrochemistryProblem 68
Chapter 20, Problem 68

A voltaic cell utilizes the following reaction: Al1s2 + 3 Ag+1aq2 ¡ Al3+1aq2 + 3 Ag1s2 What is the effect on the cell emf of each of the following changes? (a) Water is added to the anode half-cell, diluting the solution.

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Identify the anode and cathode reactions in the voltaic cell. In this case, aluminum (Al) is oxidized at the anode, losing electrons to form Al3+ ions. At the cathode, silver ions (Ag+) gain electrons to form solid silver (Ag).
Understand the role of ion concentration in the Nernst equation, which describes the cell potential. The equation is E = E^0 - (RT/nF) * ln(Q), where E^0 is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is the Faraday constant, and Q is the reaction quotient.
Recognize that diluting the anode solution with water increases the volume of the solution, thereby decreasing the concentration of Al3+ ions. This change affects the reaction quotient Q in the Nernst equation.
Analyze how a decrease in the concentration of Al3+ ions at the anode affects the reaction quotient Q. Since Al3+ is a product in the anode half-reaction, decreasing its concentration shifts Q to a smaller value.
Conclude that decreasing the concentration of Al3+ ions by diluting the anode solution will increase the cell emf (E), according to the Nernst equation, because the ln(Q) term becomes more negative, making the entire term (RT/nF) * ln(Q) less positive.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Voltaic Cell and Electrode Reactions

A voltaic cell generates electrical energy through spontaneous redox reactions. In this context, the anode is where oxidation occurs (Al is oxidized to Al3+), while the cathode is where reduction takes place (Ag+ is reduced to Ag). Understanding these processes is crucial for analyzing how changes in concentration affect the cell's electromotive force (emf).
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Galvanic Cell Electrodes

Nernst Equation

The Nernst equation relates the cell potential (emf) to the concentrations of the reactants and products in a redox reaction. It shows that changes in concentration can shift the emf of the cell, allowing for predictions about how dilution or concentration adjustments will impact the overall voltage produced by the cell.
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The Nernst Equation

Effect of Dilution on Reaction Quotient

Diluting the solution in the anode half-cell decreases the concentration of Al3+ ions, which affects the reaction quotient (Q) of the cell. According to Le Chatelier's principle, this dilution can shift the equilibrium position, potentially increasing the emf if the reaction favors the formation of products. Understanding this principle helps predict how the cell's performance will change with concentration adjustments.
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Related Practice
Textbook Question

A voltaic cell is constructed that uses the following reaction and operates at 298 K: Zn(s) + Ni2+(aq) → Zn2+(aq) + Ni(s) (b) What is the emf of this cell when [Ni2+] = 3.00 M and [Zn2+] = 0.100 M? (c) What is the emf of the cell when [Ni2+] = 0.200 M and [Zn2+] = 0.900 M?

Textbook Question

A voltaic cell utilizes the following reaction: 4 Fe2+1aq2 + O21g2 + 4 H+1aq2 ¡ 4 Fe3+1aq2 + 2 H2O1l2 (a) What is the emf of this cell under standard conditions?