11

NERNST EQUATIONNERNST EQUATIONChapter 20Chapter 20

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

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Electrical PotentialElectrical Potential

Electrical Potential

What causes the electrical What causes the electrical potential of an potential of an

electrochemical cell?electrochemical cell?

• The The electrical potentialelectrical potential of a voltaic of a voltaic cell is acell is a measure of the cell’s ability measure of the cell’s ability

to produce an electric currentto produce an electric current..

• Electrical potential is usually Electrical potential is usually measuredmeasured in in volts (V)volts (V)..

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

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

Electrical PotentialElectrical Potential

The The standard cell potentialstandard cell potential ( (EE00cellcell) is the ) is the

measured cell potential when the ion measured cell potential when the ion concentrations in the half-cells are concentrations in the half-cells are 11MM, ,

any any gasesgases are at a pressure of are at a pressure of 101 kPa101 kPa, , and the temperature is and the temperature is 25°C25°C..

EE00cellcell = = EE00

redred – – EE00oxidoxid

44

55

RED = REDUCEDRED = REDUCED

BLACK = OXIDIZEDBLACK = OXIDIZED

e-e-CuCu AlAl

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

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SampleSample Problem 21.1Problem 21.1SampleSample Problem 21.1Problem 21.1

Cu2+(aq) + 2e– →Cu(s) E0Cu

2+ = 0.34 V

Al3+(aq) + 3e– → Al(s) E0Al

3+ = -1.66 V

E0cell = E0

red – E0oxid

2.00 V = 0.34 V – (-1.66 V)

77

If Al and Cu are If Al and Cu are separatedseparated work is work is done by the electrons. Voltmeter is done by the electrons. Voltmeter is

used to measure the energyused to measure the energy. .

What What determines determines

the the measuredmeasured

value?value?

88

AP SHEET

99

NERNST EQUATIONNERNST EQUATIONE at Nonstandard ConditionsE at Nonstandard Conditions

E = potential under nonstandard conditions

n = no. of electrons exchanged

ln = “natural log”

If [P] and [R] = 1 mol/L, then E = E˚

E EÞ - 0.0257 V

n ln

[Products][Reactants]

E EÞ - 0.0257 V

n ln

[Products][Reactants]

1010NERNST EQUATIONNERNST EQUATIONE at Nonstandard E at Nonstandard

ConditionsConditions

If [R](bottom) > [P], Q <1, ln is neg

then E is ______________ than E˚

E EÞ - 0.0257 V

n ln

[Products][Reactants]

E EÞ - 0.0257 V

n ln

[Products][Reactants]

greater

less

If [R](bottom) < [P], Q >1, ln is pos

then E is ______________ than E˚

1111

1212

1313

AP Question

1414

Hw

1515

Q = [ Zn2+] [Ag+]2

X X

X

1616

Is E˚ related to ∆G?Is E˚ related to ∆G? YES!YES!

1717

EEoo and ∆G and ∆Goo

Eo is related to ∆Go, the free energy change for the reaction.

∆Go = - n F Eo where F = Faraday constant

= 9.6485 x 104 J/V•mol

and n is the number of moles of electrons transferred

Michael FaradayMichael Faraday1791-18671791-1867

1818

∆∆GGoo = - n F E = - n F Eoo For a product-favored reaction Reactants ----> Products

∆Go < 0 and so Eo > 0

Eo is positiveFor a reactant-favored reaction Reactants <---- Products

∆Go > 0 and so Eo < 0

Eo is negative

1919

2020

∆Go = - n F Eo

Eo = - 0.20 v

2121

HW

2222

Is E˚ related to K?Is E˚ related to K? YES!YES!

2323

AP SHEET

2424

R= 8.31 J/(mol K)

2525