Electrochemistry

Why Do Chemicals Trade Electrons?

Galvanic (Voltaic) Cells

• Remember oxidation reduction reactions

• Good, you can do half reactions no problem

• Because you practiced them, over and over

• Until they were easy

• Lucky, because otherwise you would have to learn them now in addition to all the rest of the stuff in this chapter

Electrochem

• Oxidation involves loss of electrons (OIL)– Increase of oxidation number

• Reduction involved gain of electrons (RIG)– Reduction of oxidation number

• Oxidation agent is the one that’s reduced

• Reducing agent is the one that’s oxidized

• Potassium permanganate is added to an acidified solution of iron (II) chloride.

• Write the net ionic reaction

MnO4- +H+ + Fe+2 Mn+2 + H2O + Fe+3

• Write the half reactions

8H+ + MnO4- + 5e- Mn+2 + 4 H2O

5(Fe+2 Fe+3 + e-)

8H+ + MnO4- + 5Fe+2 Mn+2 + 4 H2O + 5Fe+3

Galvanic Cell• A device that changes chemical energy to

electrical energy.

• The difference between a redox reaction and a cell– Instead of mixing the chemicals in a flask and letting

the electrons move to a new substance– Separate the chemicals– Use moving electrons to do work– Need to allow ions to flow!

• Or will only work for a moment

Voltaic Cells (Galvanic Cells)

• A voltaic cell is a chemical concept that led to the manufacture of batteries.

• There are three major components to a voltaic cell:– Anode – oxidation reaction– Cathode – reduction reaction– Salt bridge – replaces ions to keep solutions

neutral

Salt bridge or porous disk Allows ions to move

Oxidation occurs Reduction Occurs

Red CatAn OX

Cell Potential• Between the anode and the cathode, electrons have a

difference in energy – the cathode is a lower energy state for the electrons, so they will naturally “flow” there.

• This is a form of electrical potential energy.– There is a “force” behind electrons moving

– Electromotive force (emf) or cell potential

• This potential can be measured with a potentiometer• Like all chemical reactions there is a driving force.

– Which thermodynamic concept do you think would work here?

Zn(s) + Cu+2 => Zn+2 + Cu(s)

• What is the anode half reaction?Zn Zn+2 + 2 e-

• What is the cathode half reaction?Cu+2 + 2e- Cu

Cells• The maximum amount of electrons that can move

(Current in Amps) is based on:– Voltage – Volts - Pond on top of hill, water flows downhill.– Resistance – Ohms - Things in its way slow the water down.

• Galvanic cell consists of two half reactions– Trading electrons– The force driving them is called

“voltage”• Or potential

Water in a tank has a forceThat pushes it out a pipe

Which pipe would have a higher water pressure?

Analogous to a cell with more electromotive force. It has a higher voltage

Electromotive Force (EMF)

• The potential difference between anode and cathode is called the electromotive force (the force “pushing” electrons”), or emf.

• Ecell = emf

• EMF is measured in volts, where – 1 Volt = 1 Joule per Coulomb– 1 e- = 1.60 x 10-19 C

• To compute the value of the cell potential– The maximum voltage– Need a standard for all half cells– Use hydrogen at [H+] = 1M, PH2 = 1 atm– All half cells are compared to hydrogen.

• Hydrogen half cell is assigned a value of zero.Zero

Determining Relative Agent Strengths

• The strongest oxidizers (or oxidizing agents) are those which have the most positive Eo

red values. (they are the most easily reduced)

• The strongest reducing agents have the most negative Eo

red values.

• F2 is the strongest oxidizing agent, while Li is the strongest reducing agent.

Zn(s) + Cu+2 => Zn+2 + Cu(s)• What is the anode half reaction? (An Ox)

Zn Zn+2 + 2 e- E° = +0.76

• What is the cathode half reaction? (Red Cat)• Cu Cu+2 + 2e- E ° = -0.34

• Eocell = Eo

red(cathode) – Eored(anode)

• We subtract the anode’s Eored because oxidation happens at

the anode, and we are technically using the reverse reaction.

• The cell potential is 0.76 + 0.34 = 1.10V • What kind of reaction is this?

– We called this a single replacement reaction!

– Remember the activity series?• Why are some substances more active then others?

Standard Reduction Potentials

• Calculate the standard emf for the voltaic cell based on the reaction:

• Cr2O72- + 14 H+ + 6 I- 2 Cr3+ + 3 I2 + 7 H2O

– Eored (Cr2O7

2- + 14 H+ + 6 e- Cr3+ + 7 H2O) = +1.33 V

– Eored (I2 + 2 e- 2 I-) = +0.54 V

• Note: even though there are coefficients, you do NOT multiply emfs by them. EMFs are an intensive property of matter and are not subject to the same rules as joules, grams, etc.

Line NotationAnode Cathode

Mg(s) Mg+2(aq) Al+2

(aq) Al(s)

Mg + Al+2 Mg+2 + Al

For reactions producing/using gases or ions a platinum electrode is used

Pt(s) ClO3-, ClO4

-, H+ H+, MnO4-, Mn+2 Pt(s)

Two Cents Worth of Physics

• A galvanic cell consists of two half reactions

• The “difference” in cell potentials is the electromotive force E

• This force is related to the ability to do work and ideally equal to the free energy change

Equations

• emf = potential difference (V) = Work (J) charge (C)

• Work is viewed from the point of view of the system!• E = -w qWhere E = electromotive force (voltage)

-w = work done (system lost energy) q = charge (number of electrons x charge)

Free Energy

• Without the derivation!∆G = -nF E n = moles of electrons F = 96,485 C/mol (the constant FARADAY) E = emf = electromotive forceUnder standard conditions∆G° = -nF E ° (25 °C, 1 atm, [1M])

Units in Electrochem

• F = Faraday = 1 mole e-

• charge on mole of electrons• F = 96,485 Coulombs / mol e- • Coulomb = C (unit of charge)• q = amount of charge in coulombs• E = electromotive force = EMF• E° = standard EMF• E = joule / C

Predicting Spontaneity

• ∆G for spontaneous reactions < 0 (negative)

• ∆G = -nF E

• Any process with a positive E Will have a negative ∆GWill be spontaneous, ∆G < 0, negativeK>1

Calculate ∆G° for the reaction• Cu+2 + Fe → Fe+2 + Cu

• The half reactions are: Cu+2 + 2e- → Cu E ° = 0.34 V

Fe → Fe+2 + 2 e- E ° = 0.44 V

• The E ° is 0.78 V so the delta G is

∆G ° = -nF E ° = -2 * 96500 * 0.78 = -15.1 kJ

What is the Voltage of a Cell?

• There are several different types of cells

• Each has its uses

• Some are batteries

• Some are electrodes (pH meter)

• Fuel cells use electrochemistry– Instead of combustion

Concentration CellsA galvanic cell can be made with the anode

and cathode with the same half reaction.

Porous disk

0.1M Ag+ 1.0 M Ag+

Which direction willElectrons flow?

Nature will try to makethe concentrationOn both sidesThe same

Ag Ag

Which is the cathode?

Which side plates silver metal?Cathode

Concentration Cells• If the Eº of both the cells is the same, how

can a voltage be formed?

• Eº are at 1M concentrations

• So there is a potential difference between the half cells

0.1M Ag+ 1.0 M Ag+

The Nernst Equation

• The cell potential is dependent on concentration

• Free energy is dependent on concentration

• Remember

G = Gº + RT lnQ

• Q and the concentration affects G

Nernst Again

G = -nFE• Replacing the G’s with –nFE’sE = E - RT lnQ

nF

At 25º C

E = E - 0.0591 log (Q)

n

2Al + 3Mn+2 2Al+3 + 3Mn

• [Mn+2] = 0.50M [Al+3] = 1.50M– Remember heterogeneous equilibria – and half reactions!

E = E - 0.0591 log (Q)

nAl Al+3 +3e- Mn+2 +2e- Mn n = 6 (3 x 2)

E = 0.48V – 0.0591 log (1.50)2 = 0.48 – 0.01 = 0.47V

6 (0.50)3

What is a Dead Battery?

• The cell will spontaneously discharge

• When the Q = K, the reaction is at equilibrium

• There is no longer a driving force

• The two cells have the same free energy

• E cell = G = 0

Lets Consider The Reaction

VO2+1 and Zn react.

2VO2+ + Zn 2VO+2 + Zn+2

Use half reaction method to get equation

2VO2+ +4H+ + Zn 2VO+2 +2H2O + Zn+2

What is the cell potential?

VO2+ +2H+ + e- VO+2 +H2O E = 1.00V

Zn 2 e- + Zn+2 E = 0.76V

2VO2+ +4H+ + Zn 2VO+2 +2H2O + Zn+2

Where T = 25 C, [VO2+] = 2.0M, [H+] = 0.50M

[VO+2] = 1.0x 10-2M [Zn+2]= 1.0 x 10-1M• Not at standard conditions, n = ? (number of electrons)

E = 1.76 - 0.0591 log ([VO+2]2[Zn+2]) = 1.76 + 0.13 = 1.89V

2 [VO2+]2 [H+]4

Ion Selective Electrodes

• pH electrodes are an example– Sensitive to the H+ ion– Others available

• Cd+2, Ca+2,Cu+2, K+1. Ag+1, Na+1

• Cl-1, Br-1, CN-1, F-1, NO3-1, S-2

• Works like a concentration cell– Inside electrode is a half cell of known concentration– Measures the potential difference

Equilibrium Constants

E = E - 0.0591 log (Q)

n

When Q = K, E = 0

E = +0.0591 logK

n

Solve for K.

K is typically large for a redox reaction.

(The useful ones anyway)

Electrolytic Cells

• An electrolytic cell consists of two electrodes in a molten salt or a solution.– Electrolysis is the decomposition of a molecule

using electricity.

• Example: – 2 NaCl(l) 2 Na(l) + Cl2(g)

• Unlike a voltaic cell, electrolytic cells require a voltage source (battery) to function.

Electroplating

• Electrolysis can be used for the industrial practice of electroplating – that is, plating one metal on another.

• Example: Copper plating of a quarter.

The Ampere

• An ampere is a coulomb per second– It is the unit of electric current.

• 1 A = 1 C/s

• We can calculate the extent of electrolysis given the electric current and time.

Moles of Electrons• When you have total charge in coulombs, you

can use Faraday’s constant to convert to moles of electrons.

• Faraday’s constant = 96,483 C/mol e-

• This will allow us to then use stoichiometry to solve for the amount of substance oxidized/reduced.

Practice Problems

• Calculate the number of grams of aluminum produced in 1.00 hour by the electrolysis of molten AlCl3 if the electrical current is 10.0 A (amperes).

Electrical Work• Gibbs’ free energy is the extra energy that can be used

to power other devices.• ΔG = -nFEcell

• Therefore, the maximum amount of useful electrical work (energy) from a voltaic cell is– wmax = -nFEcell

• Or, if you are applying an external potential (like in an electrolytic cell)…– w = nFEext (positive because you are putting energy into the

system)

• q=nF• wmax = qE

Electrical Work and Efficiency

• The unit of electrical work is the kilowatt-hour (kWh).

• Based on the watt (1 J/s), a unit of electrical power.

• 1 kWh = 3.6 x 106 J

• Efficiency = w x 100%

wmax

Practice

• Calculate the number of kilowatt-hours of electricity required to produce 1.0 x 103 kg of aluminum by electrolysis of Al3+ if the applied voltage is 4.50 V.