Ch 21_Electrochemistry.pdf

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Chapter 21

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Galvanic Cells

Electrochemistry: The area of chemistry concerned with the interconversion of chemical and electrical energy.

In a Galvanic (Voltaic) Cell: A spontaneous chemical reaction generates an electric current.

In an Electrolytic Cell: An electric current drives a

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Galvanic Cells

Cu(s) Cu2+₍_aq_{) + 2 e}–

Reduction half-reaction:

Oxidation half-reaction:

Zn2+₍_aq_{) + Cu(}_s₎

Zn(s) + Cu2+₍_aq₎

Zn2+₍_aq_{) + 2 e}–

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Galvanic Cells

Zn2+₍_aq_{) + Cu(}_s₎

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Galvanic Cells

Anode:

• The electrode where oxidation occurs.

• The electrode where electrons are produced. • The electrode that anions migrate toward.

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Galvanic Cells

Anode:

• The electrode where oxidation occurs.

• The electrode where electrons are produced. • The electrode that anions migrate toward.

• Has a negative sign.

Cathode:

• The electrode where reduction occurs.

• The electrode where electrons are consumed. • The electrode that cations migrate toward.

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Galvanic Cells

Zn2+₍_aq_{) + Cu(}_s₎

Zn(s) + Cu2+₍_aq₎

Cu(s) Cu2+₍_aq_{) + 2 e}–

Zn2+₍_aq_{) + 2 e}–

Zn(s)

Overall cell reaction:

Anode half-reaction:

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Shorthand Notation for Galvanic Cells

Zn2+₍_aq_{) + Cu(}_s₎

Zn(s) + Cu2+₍_aq₎

Cu(s) Cu2+₍_aq_{) + 2 e}–

Zn2+₍_aq_{) + 2 e}–

Zn(s)

Cathode half-reaction:

Zn(s) | Zn2+₍_aq_{) || Cu}2+₍_aq_{) | Cu(}_s₎

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Cell Potentials and Free-Energy Changes for

Cell Reactions

Electromotive Force (emf): The force (or electrical

potential) that pushes the negatively charged electrons away from the anode (– electrode) and pulls them toward the cathode (+ electrode).

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Cell Potentials and Free-Energy Changes for

Cell Reactions

1 J = 1 C × 1 V

volt

SI unit of electric potential

joule

SI unit of energy

coulomb

Electric charge

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Cell Potentials and Free-Energy Changes for

Cell Reactions

∆G° = –nFE°

cell potential free-energy change

number of moles of electrons transferred in the reaction

faraday or Faraday’s constant

the electric charge on 1 mol of electrons

96,500 C/mol e–

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Cell Potentials and Free-Energy Changes for

Cell Reactions

The standard cell potential at 25 °C is 1.10 V for the following reaction:

Calculate the standard free-energy change for this reaction at 25 °C.

Zn2+₍_aq_{) + Cu(}_s₎

Zn(s) + Cu2+₍_aq₎

(1.10 V)

∆G° = –212 kJ

1000 J 1 kJ = –(2 mol e–₎

mol e– 96,500 C

1 C V 1 J

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Standard Reduction Potentials

2 H+₍_aq_{) + Cu(}_s₎

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The standard potential of a cell is the sum of the standard half-cell potentials for oxidation at the anode and reduction at the cathode:

Standard Reduction Potentials

2 H+₍_aq_{) + Cu(}_s₎

H₂(g) + Cu2+₍_aq₎

Cu(s) Cu2+₍_aq_{) + 2 e}–

2 H+₍_aq_{) + 2 e}–

H₂(g)

E°_cell = E°_ox + E°_red

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The standard hydrogen electrode (S.H.E.) has been chosen to be the reference electrode.

2 H+₍_aq_{, 1 M) + 2 e}–

H₂(g, 1 atm)

H₂(g, 1 atm) 2 H+₍_aq_{, 1 M) + 2 e}–

E°_red = 0 V

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2 H+₍_aq_{) + Cu(}_s₎

H₂(g) + Cu2+₍_aq₎

Cu(s) Cu2+₍_aq_{) + 2 e}–

2 H+₍_aq_{) + 2 e}–

H₂(g)

0.34 V = 0 V + E°_red

Cu(s) Cu2+₍_aq_{) + 2 e}–

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Standard Reduction Potentials

H₂(g) + Zn2+₍_aq₎

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H₂(g) + Zn2+₍_aq₎

2 H+₍_aq_{) + Zn(}_s₎

Zn2+₍_aq_{) + 2 e}–

Zn(s)

H₂(g) 2 H+₍_aq_{) + 2 e}–

Zn(s) Zn2+₍_aq_{) + 2 e}–

0.76 V = E°_ox + 0 V

E° = –0.76 V As a standard reduction potential:

Zn2+₍_aq_{) + 2 e}–

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Using Standard Reduction Potentials

2 Ag(s) + Cu2+₍_aq₎

2 Ag+₍_aq_{) + Cu(}_s₎

Ag(s)] 2 x [Ag+₍_aq_{) + e}–

Cu2+₍_aq_{) + 2 e}–

Cu(s)

E° = 0.46 V E° = 0.80 V

E° = –0.34 V

Zn2+₍_aq_{) + Cu(}_s₎

Zn(s) + Cu2+₍_aq₎

Cu(s) Cu2+₍_aq_{) + 2 e}–

Zn2+₍_aq_{) + 2 e}–

Zn(s)

E° = 1.10 V

E° = –(–0.76 V)

E° = 0.34 V

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Cell Potentials Under Nonstandard-State

Conditions: The Nernst Equation

∆G = ∆G° + RT ln Q

Using: ∆G = –nFE and ∆G° = –nFE°

Nernst Equation:

log Q n

0.0592 V E = E° –

or

ln Q nF

RT E = E° –

log Q nF

2.303RT

E = E° –

or

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Cell Potentials Under Nonstandard-State

Consider a galvanic cell that uses the following reaction:

What is the potential of a cell at 25 °C that has the following ion concentrations?

Cu2+₍_aq_{) + 2 Fe}2+₍_aq₎

Cu(s) + 2 Fe3+₍_aq₎

[Fe2+_{] = 0.20 M}

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Cell Potentials Under Nonstandard-State

log Q n

0.0592 V

E = E° –

Calculate E°:

Fe2+₍_aq₎

Fe3+₍_aq_{) + e}–

Cu2+₍_aq_{) + 2 e}–

Cu(s) E° = –0.34 V

E° = 0.77 V

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Cell Potentials Under Nonstandard-State

log

(1.0 x 10–4)2 (0.25)(0.20)2

= 0.43 V –

2

0.0592 V log

[Fe3+_]2

[Cu2+_][Fe2+_]2

E = 0.25 V

n

0.0592 V

E = E° –

log Q n

0.0592 V

E = E° –

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Standard Cell Potentials and Equilibrium

Constants

–nFE° = –RT ln K

∆G° = –RT ln K

and Using ∆G° = –nFE°

log K n

0.0592 V

E° =

log K nF

2.303RT

ln K nF

RT

=

E° =

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Standard Cell Potentials and Equilibrium

Constants

Three methods to determine equilibrium constants:

1. K from concentration data:

2. K from thermochemical data:

3. K from electrochemical data:

K =

[A]a_[B]b

[C]c_[D]d

RT

–∆G° ln K =

RT nFE°

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Batteries

Lead Storage Battery

2 PbSO₄(s) + 2 H₂O(l) Pb(s) + PbO₂(s) + 2 H+_{(aq) + 2 HSO}

4–(aq)

PbSO₄(s) + 2 H₂O(l) PbO₂(s) + 3 H+_{(aq) + HSO}

4–(aq) + 2 e–

PbSO₄(s) + H+_{(aq) + 2 e}– Pb(s) + HSO₄–(aq)

Overall:

Anode:

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Batteries

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Batteries

Dry-Cell Batteries

Leclanché cell

Mn₂O₃(s) + 2 NH₃(aq) + H₂O(l) 2 MnO₂(s) + 2 NH₄+_{(aq) + 2 e}–

Zn2+_{(aq) + 2 e}– Zn(s)

Anode:

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Batteries

Dry-Cell Batteries

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Batteries

Dry-Cell Batteries

Alkaline cell (1.5 V)

Mn₂O₃(s) + 2 OH–(aq) 2 MnO₂(s) + H₂O(l) + 2e–

ZnO(s) + H₂O(l) + 2 e– Zn(s) + 2 OH–(aq)

Anode:

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Batteries

Nickel-Cadmium (“Ni-cad”) Batteries (1.2 V)

Nickel-Metal Hydride (“NiMH”) Batteries (1.2V)

Ni(OH)₂(s) + OH–(aq) NiO(OH)(s) + H₂O(l) + e–

Cd(OH)₂(s) + 2 e– Cd(s) + 2 OH–(aq)

Anode:

Cathode:

M(s) + Ni(OH)₂(s) MH_ab(s) + NiO(OH)(s)

Ni(OH)₂(s) + OH–(aq) NiO(OH)(s) + H₂O(l) + e–

M(s) + H₂O(l) + e– MH_ab(s) + OH–(aq)

Overall:

Anode:

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Batteries

Lithium and Lithium Ion Batteries (3-4 V)

Lithium

Lithium Ion

Li_xMnO₂(s) MnO₂(s) + x Li+_{(soln) + x e}–

x Li+_{(soln) + x e}– x Li(s)

Anode:

Cathode:

LiCoO₂(s) Li_1–_xCoO₂(s) + x Li+_{(soln) + x e}–

x Li+_{(soln) + 6 C(s) + x e}– Li_xC₆(s)

Anode:

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Fuel Cells

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Corrosion

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Corrosion

Prevention of Corrosion

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Corrosion

Prevention of Corrosion

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Corrosion

Prevention of Corrosion

1. Galvanization: The coating of iron with zinc.

When some of the iron is oxidized (rust), the process is reversed since zinc will reduce Fe2+ _{to Fe:}

Fe(s) Fe2+(aq) + 2 e–

Zn(s)

Zn2+₍_aq_{) + 2 e}– _E° = –0.76 V

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Corrosion

Prevention of Corrosion

2. Cathodic Protection: Instead of coating the entire surface of the first metal with a second metal, the second metal is placed in electrical contact with the first metal:

Attaching a magnesium stake to iron will corrode the magnesium instead of the iron. Magnesium acts as a

sacrificial anode.

Mg2+(aq) + 2 e– Mg(s)

Anode:

Cathode:O₂(g) + 4 H+(aq) + 4 e– 2 H₂O(l) _E_{° = 1.23 V}

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Electrolysis and Electrolytic Cells

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Electrolysis and Electrolytic Cells

Electrolysis of Water

2 H₂(g) + O₂(g) + 4 H+ _{+ 4 OH}–_(aq) 6 H₂O(l)

2 H₂(g) + 4 OH–(aq) 4 H₂O(l) + 4 e–

O₂(g) + 4 H+_{(aq) + 4 e}– 2 H₂O(l)

Overall:

Anode:

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Electrolysis and Electrolytic Cells

Electrolysis of Molten Sodium Chloride

2 Na(l) + Cl₂(g) 2 Na+_{(l) + 2 Cl}–_(l)

2 Na(l) 2 Na+_{(l) + 2 e}–

Cl₂(g) + 2 e– 2 Cl–(l)

Overall:

Anode:

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Electrolysis and Electrolytic Cells

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Electrolysis of Aqueous Sodium Chloride

Cl₂(g) + H₂(g) + 2 OH–(aq) 2 Cl–(l) + 2 H₂O(l)

H₂(g) + 2 OH–(aq) 2 H₂O(l) + 2 e–

Cl₂(g) + 2 e– 2 Cl–(aq)

Overall:

Anode:

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Electrolysis and Electrolytic Cells

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Quantitative Aspects of Electrolysis

Moles of e– = Charge (A) ×

Charge (C) = Current (A) × Time (s)

96,500 C 1 mol e–

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Quantitative Aspects of Electrolysis

• An aluminum refining factory draws

2.0x10

6

A of current for 4 hours while

running an electrolytic cell to produce