Chapter 21 Electrochemistry 21.2 Half-Cells and Cell Potentials 21.1 Electrochemical Cells 21.2 Half-Cells and Cell Potentials 21.3 Electrolytic Cells Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU How can you calculate the electrical potential of a cell in a laptop battery? Batteries provide current to power lights and many kinds of electronic devices—such as the laptop shown here. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What causes the electrical potential of an electrochemical cell? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What causes the electrical potential of an electrochemical cell? The electrical potential of a voltaic cell is a measure of the cell’s ability to produce an electric current. Electrical potential is usually measured in volts (V). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The potential of an isolated half-cell cannot be measured. Electrical Potential The potential of an isolated half-cell cannot be measured. You cannot measure the electrical potential of a zinc half-cell or of a copper half-cell separately. When these two half-cells are connected to form a voltaic cell, however, the difference in potential can be measured. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The electrical potential of a cell results from a competition for electrons between two half-cells. The half-cell that has a greater tendency to acquire electrons is the one in which reduction occurs. Oxidation occurs in the other half-cell. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The tendency of a given half-reaction to occur as a reduction is called the reduction potential. The half-cell in which reduction occurs has a greater reduction potential than the half-cell in which oxidation occurs. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The difference between the reduction potentials of the two half-cells is called the cell potential. cell potential = – reduction potential of half-cell in which reduction occurs reduction potential of half-cell in which oxidation occurs or Ecell = Ered – Eoxid Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The standard cell potential (E0cell) is the measured cell potential when the ion concentrations in the half-cells are 1M, any gases are at a pressure of 101 kPa, and the temperature is 25°C. E0cell = E0red – E0oxid Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The standard hydrogen electrode is used with other electrodes so the reduction potentials of the other cells can be measured. The standard reduction potential of the hydrogen electrode has been assigned a value of 0.00 V. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The standard hydrogen electrode consists of a platinum electrode immersed in a solution with a hydrogen-ion concentration of 1M. The solution is at 24°C. Hydrogen gas at a pressure of 101 kPa is bubbled around the platinum electrode. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The half-cell reaction that occurs at the platinum black surface is as follows: 2H+(aq, 1M) + 2e– H2(g, 101kPa) E0H+ = 0.00 V The double arrows in the equation indicate that the reaction is reversible. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electrical Potential The half-cell reaction that occurs at the platinum black surface is as follows: 2H+(aq, 1M) + 2e– H2(g, 101kPa) Whether this half-cell reaction occurs as a reduction or as an oxidation is determined by the reduction potential of the half-cell to which the standard hydrogen electrode is connected. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the standard reduction potential of the standard hydrogen electrode? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the standard reduction potential of the standard hydrogen electrode? E0H+ = 0.00 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials How can you determine the standard reduction potential of a half-cell? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials A voltaic cell can be made by connecting a standard hydrogen half-cell to a standard zinc half-cell. To determine the overall reaction for this cell, first identify the half-cell in which reduction takes place. Reduction takes place at the cathode, and oxidation takes place at the anode. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials A voltmeter gives a reading of +0.76 V when the zinc electrode is connected to the negative terminal and the hydrogen electrode is connected to the positive terminal. The zinc is oxidized, which means that it is the anode. Hydrogen ions are reduced, which means that the hydrogen electrode is the cathode. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials You can now write the half-reactions and the overall cell reaction. Oxidation: Zn(s) → Zn2+(aq) + 2e– (at anode) Reduction: 2H+(aq) + 2e– → H2(g) (at cathode) Cell reaction: Zn(s) + 2H+(aq) → Zn2+(aq) + H2(g) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials You can determine the standard reduction potential of a half-cell by using a standard hydrogen electrode and the equation for standard cell potential. In the zinc-hydrogen cell, zinc is oxidized and hydrogen ions are reduced. E0cell = E0red – E0oxid E0cell = E0H+ – E0Zn2+ Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials You can determine the standard reduction potential of a half-cell by using a standard hydrogen electrode and the equation for standard cell potential. The cell potential (E0cell) is measured at +0.76 V. E0H+ always equals 0.00 V. E0cell = E0H+ – E0Zn2+ +0.76 V = 0.00 V – E0Zn2+ E0Zn2+ = –0.76 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Standard Reduction Potentials You can determine the standard reduction potential of a half-cell by using a standard hydrogen electrode and the equation for standard cell potential. The standard reduction potential for the zinc half-cell is –0.76 V. The value is negative because the tendency of zinc ions to be reduced to zinc metal in this cell is less than the tendency of hydrogen ions to be reduced to hydrogen gas. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Reduction Potentials at 25°C with 1M Concentrations of Aqueous Species Interpret Data Reduction Potentials at 25°C with 1M Concentrations of Aqueous Species Electrode Half-reaction E0 (V) Least tendency to occur as a reduction Greatest tendency to occur as a reduction Li+/Li Li+ + e– → Li –3.05 Pb2+/Pb Pb2+ + 2e– → Pb –0.13 K+/K K+ + e– → K –2.93 Fe3+/Fe Fe3+ + 3e– → Fe –0.036 Ba2+/Ba Ba2+ + 2e– → Ba –2.90 H+/H2 2H+ + 2e– → H2 0.000 Ca2+/Ca Ca2+ + 2e– → Ca –2.87 Cu2+/Cu Cu2+ + 2e– → Cu +0.34 Na+/Na Na+ + e– → Na –2.71 Cu+/Cu Cu+ + e– → Cu +0.52 Al3+/Al Al3+ + 3e– → Al –1.66 I2/I– I2 + 2e– → 2I– +0.54 Zn2+/Zn Zn2+ + 2e– → Zn –0.76 Fe3+/Fe2+ Fe3+ + e– → Fe2+ +0.77 Cr3+/Cr Cr3+ + 3e– → Cr –0.74 Hg22+/Hg Hg22++ 2e– → 2Hg +0.79 Fe2+/Fe Fe2+ + 2e– → Fe –0.44 Ag+/Ag Ag+ + e– → Ag +0.80 Cd2+/Cd Cd2+ + 2e– → Cd –0.40 Hg2+/Hg Hg2++ 2e– → Hg +0.85 Co2+/Co Co2+ + 2e– → Co –0.28 Br2/Br– Br2+ 2e– → 2Br– +1.07 Ni2+/Ni Ni2+ + 2e– → Ni –0.25 Cl2/Cl– Cl2+ 2e– → 2Cl– 1.36 Sn2+/Sn Sn2+ + 2e– → Sn –0.14 F2/F– F2+ 2e– → 2F– +2.87 Increasing tendency to occur as a reduction (stronger oxidizing agent) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU What do you need to know to calculate the electrical potential of a cell in a laptop battery? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

CHEMISTRY & YOU What do you need to know to calculate the electrical potential of a cell in a laptop battery? In order to determine the electric potential, you need to know the reactions occurring in each half-cell, and the standard reduction potentials for those half-cell reactions. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

In a voltaic cell in which one half-reaction is Fe3+ + 3e– → Fe, which of the following half-reactions would occur as an oxidation? A. 2H+ + 2e– → H2 B. Al3+ + 2e– → Al C. Br2 + 2e– → 2Br– D. Fe3+ + e– → Fe2+ Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

In a voltaic cell in which one half-reaction is Fe3+ + 3e– → Fe, which of the following half-reactions would occur as an oxidation? A. 2H+ + 2e– → H2 B. Al3+ + 2e– → Al C. Br2 + 2e– → 2Br– D. Fe3+ + e– → Fe2+ Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating Standard Cell Potentials How can you determine if a redox reaction is spontaneous? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating Standard Cell Potentials In an electrochemical cell, the half-cell reaction having the more positive (or less negative) reduction potential occurs as a reduction in the cell. You can use the known standard reduction potentials for the half-cells to: predict the half-cells in which reduction and oxidation will occur. find the E0cell value without having to actually assemble the cell. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating Standard Cell Potentials If the cell potential for a given redox reaction is positive, then the reaction is spontaneous as written. If the cell potential is negative, then the reaction is nonspontaneous. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Determining Reaction Spontaneity Sample Problem 21.1 Determining Reaction Spontaneity Show that the following redox reaction between zinc metal and silver ions is spontaneous. Zn(s) + 2Ag+(aq) → Zn2+(aq) + 2Ag(s) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 21.1 Analyze List the knowns and the unknown. 1 Identify the half-reactions, and calculate the standard cell potential (E0cell = E0red – E0oxid). If E0cell is positive, the reaction is spontaneous. KNOWNS Cell reaction: Zn(s) + 2Ag+(aq) → Zn2+(aq) + 2Ag(s) UNKNOWN Is the reaction spontaneous? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 21.1 Calculate Solve for the unknown. 2 First identify the half-reactions. Oxidation: Zn(s) → Zn2+(aq) + 2e– Reduction: Ag+(aq) + e– → Ag(s) Write both half-cells as reductions with their standard reduction potentials. Zn2+(aq) + 2e– → Zn(s) E0Zn2+ = –0.76 V Ag+(aq) + e– → Ag(s) E0Ag+ = +0.80 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 21.1 Calculate Solve for the unknown. 2 Calculate the standard cell potential. E0cell = E0red – E0oxid = E0Ag+ – E0Zn2+ = +0.80 V – (–0.76 V) = +1.56 V E0cell > 0, so the reaction is spontaneous. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Evaluate Does the result make sense? Sample Problem 21.1 Evaluate Does the result make sense? 3 Zinc is above silver in the activity series for metals. It makes sense that zinc is oxidized in the presence of silver ions. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Writing the Cell Reaction Sample Problem 21.2 Writing the Cell Reaction Determine the cell reaction for a voltaic cell composed of the following half-cells: Fe3+(aq) + e– → Fe2+(aq) E0Fe3+ = +0.77 V Ni2+(aq) + 2e– → Ni(s) E0Ni2+ = –0.25 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze Identify the relevant concepts. Sample Problem 21.2 Analyze Identify the relevant concepts. 1 The half-cell with the more positive reduction potential is the one in which reduction occurs (the cathode). The oxidation reaction occurs at the anode. Add the half-reactions, making certain that the number of electrons lost equals the number of electrons gained. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Solve Apply the concepts to this problem. Sample Problem 21.2 Solve Apply the concepts to this problem. 2 First identify the cathode and the anode. The Fe3+ half-cell has the more positive reduction potential, so it is the cathode. The Ni2+ half-cell has the more negative reduction potential, so it is the anode. Thus the voltaic cell, Fe3+, is reduced and Ni is oxidized. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Solve Apply the concepts to this problem. Sample Problem 21.2 Solve Apply the concepts to this problem. 2 Write the half-cell reactions in the direction in which they actually occur. Oxidation: Ni(s) → Ni2+(aq) + 2e– (at anode) Reduction: Fe3+(aq) + e– → Fe2+(aq) (at cathode) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Solve Apply the concepts to this problem. Sample Problem 21.2 Solve Apply the concepts to this problem. 2 If necessary, multiply the half-reactions by the appropriate factor(s) so that the electrons cancel when the half-reactions are added. Ni(s) →Ni2+(aq) + 2e– 2[Fe3+(aq) + e– → Fe2+(aq)] Multiply the Fe3+ half-cell equation by 2 so that the electrons are present in equal numbers on both sides of the equation. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Solve Apply the concepts to this problem. Sample Problem 21.2 Solve Apply the concepts to this problem. 2 Add the half-reactions. Ni(s) → Ni2+(aq) + 2e– 2Fe3+(aq) + 2e– → 2Fe2+(aq) Ni(s) + 2Fe3+(aq) → Ni2+(aq) + 2Fe2+(aq) The electrons lost by the species that is oxidized must be equal to the electrons gained by the species that is reduced. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating the Standard Cell Potential Sample Problem 21.3 Calculating the Standard Cell Potential Calculate the standard cell potential for the voltaic cell described in Sample Problem 21.2. The half-reactions are as follows: Fe3+(aq) + e– → Fe2+(aq) E0Fe3+ = +0.77 V Ni2+(aq) + 2e– → Ni(s) E0Ni2+ = –0.25 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown. Sample Problem 21.3 Analyze List the knowns and the unknown. 1 Use the equation E0cell = E0red – E0oxid to calculate the standard cell potential. UNKNOWN KNOWNS E0cell = ? E0Fe3+ = +0.77 V E0Ni2+ = –0.25 V anode: Ni2+ half-cell cathode: Fe3+ half-cell Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown. Sample Problem 21.3 Calculate Solve for the unknown. 2 First write the equation for the standard cell potential. E0cell = E0red – E0oxid = E0Fe3+ – E0Ni2+ Substitute the values for the standard reduction potentials and solve the equation. E0cell = +0.77 V – (–0.25 V) = +1.02 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Evaluate Does the result make sense? Sample Problem 21.3 Evaluate Does the result make sense? 3 The reduction potential of the reduction is positive, and the reduction potential of the oxidation is negative. Therefore, E0cell must be positive. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Fe3+(aq) + 3e– → Fe(s) E0cell = –0.036 V Determine the cell reaction for a voltaic cell composed of the following half-cells. Fe3+(aq) + 3e– → Fe(s) E0cell = –0.036 V Al3+(aq) + 3e– → Al(s) E0cell = –1.66 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Fe3+(aq) + 3e– → Fe(s) E0cell = –0.036 V Determine the cell reaction for a voltaic cell composed of the following half-cells. Fe3+(aq) + 3e– → Fe(s) E0cell = –0.036 V Al3+(aq) + 3e– → Al(s) E0cell = –1.66 V Oxidation: Al(s) → Al3+(aq) + 3e– (at anode) Reduction: Fe3+(aq) + 3e– → Fe(s) (at cathode) Al(s) + Fe3+(aq) → Al3+(aq) + Fe(s) Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Key Concepts The electrical potential of a cell results from a competition for electrons between two half-cells. You can determine the standard reduction potential of a half-cell by using a standard hydrogen electrode and the equation for standard cell potential. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Key Concepts & Key Equation If the cell potential for a given redox reaction is positive, then the reaction is spontaneous as written. If the cell potential is negative, then the reaction is nonspontaneous. E0cell = E0red – E0oxid Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Glossary Terms electrical potential: the ability of a voltaic cell to produce an electric current reduction potential: a measure of the tendency of a given half-reaction to occur as a reduction (gain of electrons) in an electrochemical cell cell potential: the difference between the reduction potentials of two half-cells Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Glossary Terms standard cell potential (E0cell): the measured cell potential when the ion concentrations in the half-cells are 1.00M at 1 atm of pressure and 25°C standard hydrogen electrode: an arbitrary reference electrode (half-cell) used with another electrode (half-cell) to measure the standard reduction potential of that cell; the standard reduction potential of the hydrogen electrode is assigned a value of 0.00 V Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

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