21.2 Half-Cells and Cell Potentials > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Chapter 21 Electrochemistry 21.1 Electrochemical

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

21.2 Half-Cells and Cell Potentials >21.2 Half-Cells and Cell Potentials >

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Chapter 21Electrochemistry

21.1 Electrochemical Cells

21.2 Half-Cells and Cell Potentials

21.3 Electrolytic Cells



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How can you calculate the electrical potential of a cell in a laptop battery?

CHEMISTRY & YOUCHEMISTRY & YOU

Batteries provide current to power lights and many kinds of electronic devices—such as the laptop shown here.



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Electrical PotentialElectrical Potential

Electrical Potential

What causes the electrical potential of an electrochemical cell?



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Electrical Potential

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).



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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.



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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.



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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.



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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



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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 = E0

red – E0oxid



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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.



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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.



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• E0H+ = 0.00 V

• The double arrows in the equation indicate that the reaction is reversible.

The half-cell reaction that occurs at the platinum black surface is as follows:

2H+(aq, 1M) + 2e– H2(g, 101kPa)



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• 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.

The half-cell reaction that occurs at the platinum black surface is as follows:

2H+(aq, 1M) + 2e– H2(g, 101kPa)



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What is the standard reduction potential of the standard hydrogen electrode?



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What is the standard reduction potential of the standard hydrogen electrode?

E0H+ = 0.00 V



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Standard Reduction Standard Reduction PotentialsPotentials

Standard Reduction Potentials

How can you determine the standard reduction potential of a half-cell?



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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.



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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.



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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)



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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 = E0

red – E0oxid

E0cell = E0

H+ – E0

Zn2+



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• The cell potential (E0cell) is measured at

+0.76 V.

• E0H

+ always equals 0.00 V.

E0cell = E0

H+ – E0

Zn2+

+0.76 V = 0.00 V – E0Zn

2+

E0Zn

2+ = –0.76 V




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• 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.




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Interpret DataInterpret Data

Reduction Potentials at 25°C with 1M Concentrations of Aqueous Species

Electrode Half-reaction E0 (V) 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 Hg2

2++ 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

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What do you need to know to calculate the electrical potential of a cell in a laptop battery?




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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.



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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+



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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+



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Calculating Standard Calculating Standard Cell PotentialsCell Potentials

Calculating Standard Cell Potentials

How can you determine if a redox reaction is spontaneous?



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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.



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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.



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Show that the following redox reaction between zinc metal and silver ions is spontaneous.

Sample Problem 21.1Sample Problem 21.1

Determining Reaction Spontaneity

Zn(s) + 2Ag+(aq) → Zn2+(aq) + 2Ag(s)



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Analyze List the knowns and the unknown.1


KNOWNS

UNKNOWNIs the reaction spontaneous?

Identify the half-reactions, and calculate the standard cell potential (E0

cell = E0red – E0

oxid). If E0

cell is positive, the reaction is spontaneous.

Cell reaction: Zn(s) + 2Ag+(aq) → Zn2+(aq) + 2Ag(s)



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• First identify the half-reactions.

Calculate Solve for the unknown.2


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) E0Zn

2+ = –0.76 V

Ag+(aq) + e– → Ag(s) E0Ag

+ = +0.80 V



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• Calculate the standard cell potential.



E0cell = E0

red – E0oxid = E0

Ag+ – E0

Zn2+

= +0.80 V – (–0.76 V) = +1.56 V

E0cell > 0, so the reaction is spontaneous.



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• Zinc is above silver in the activity series for metals.

• It makes sense that zinc is oxidized in the presence of silver ions.

Evaluate Does the result make sense?3




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Determine the cell reaction for a voltaic cell composed of the following half-cells:


Writing the Cell Reaction

Fe3+(aq) + e– → Fe2+(aq) E0Fe

3+ = +0.77 V

Ni2+(aq) + 2e– → Ni(s) E0Ni

2+ = –0.25 V



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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.



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First identify the cathode and the anode.

Solve Apply the concepts to this problem.2


• 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.



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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)



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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.



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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.



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Calculate the standard cell potential for the voltaic cell described in Sample Problem 21.2. The half-reactions are as follows:


Calculating the Standard Cell Potential

Fe3+(aq) + e– → Fe2+(aq) E0Fe

3+ = +0.77 V

Ni2+(aq) + 2e– → Ni(s) E0Ni

2+ = –0.25 V



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Analyze List the knowns and the unknown.1


KNOWNS UNKNOWNE0

cell = ?

Use the equation E0cell = E0

red – E0oxid to calculate

the standard cell potential.

E0Fe

3+ = +0.77 V

E0Ni

2+ = –0.25 V

anode: Ni2+ half-cell

cathode: Fe3+ half-cell



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• First write the equation for the standard cell potential.



E0cell = E0

red – E0oxid = E0

Fe3+ – E0

Ni2+

E0cell = +0.77 V – (–0.25 V) = +1.02 V

• Substitute the values for the standard reduction potentials and solve the equation.



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• The reduction potential of the reduction is positive, and the reduction potential of the oxidation is negative.

• Therefore, E0cell must be positive.

Evaluate Does the result make sense?3




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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



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Oxidation: Al(s) → Al3+(aq) + 3e– (at anode)

Reduction: Fe3+(aq) + 3e– → Fe(s) (at cathode)

Al(s) + Fe3+(aq) → Al3+(aq) + Fe(s)

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



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Key ConceptsKey Concepts

The electrical potential of a cell results from a competition for electrons between two half-cells.




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Key Concepts & Key Concepts & Key Equation 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 = E0

red – E0oxid



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Glossary TermsGlossary 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



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Glossary TermsGlossary 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



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END OF 21.2END OF 21.2

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21.2 Half-Cells and Cell Potentials > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Chapter 21 Electrochemistry 21.1 Electrochemical