Electrochemistry

박준원 교수(포항공과대학교 화학과)

General Chemistry

• Electrochemical cells

• Cell potentials and the Gibbs free energy

• Concentration effects and the Nernst equation

이번 시간에는!

Electrochemistry (I)

박준원 교수(포항공과대학교 화학과)

General Chemistry

Electrochemistry is the branch of chemistry

concerned with the interconversion of chemical and electrical

energy through oxidation-reduction reactions.

Bulk commodity chemicals, such as chlorine, and most metals

are produced using large-scale electrochemical processes, and

another important practical application has been the

development of batteries, solar cells, fuel cells.

Electrochemical cells

Galvanic cell

Electrolytic cells:

1

The Gibbs free energy made available in spontaneous redox

reactions can be converted in electrical energy.

Electrical work done on the system by an electrical power

supply provides a source of free energy to drive redox

reactions that are not normally spontaneous.

<Galvanic cells>

Let’s begin by considering the following redox reaction.

The reaction may be written as the sum of two half-reactions:

Cu 𝑠 + 2 Ag+ 𝑎𝑞 → Cu2+ 𝑎𝑞 + 2 Ag(𝑠)

Cu 𝑠 → Cu2+ 𝑎𝑞 + 2𝑒−

2 Ag+ 𝑎𝑞 + 2𝑒− → 2 Ag(𝑠)

The beaker on the left contains a strip of

copper metal immersed in an aqueous solution

of Cu(NO3)2 , while the beaker on the right

contains a strip of silver metal immersed in an

aqueous solution of AgNO3. A wire connects the

two metal electrodes, the ionic conductor

connecting the cells is called salt bridge.

Anode: the electrode at which oxidation occurs.

Cathode: the electrode at which reduction

occurs.

A shorthand notation: Cu|Cu2+||Ag+|Ag [ F I G U R E 1 7 . 2 ]

Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7th ed.; Cengage Learning: Boston, 2012; p 765.

It is customary in electrochemistry to measure the difference

between the electrostatic potential of the electrons at the

cathode and the anode, and the electrostatic potential is defined

as the electrostatic potential energy per unit positive charge:

𝐸 = 𝐸P/𝑒, 𝐸P is the symbol for the electrostatic potential energy

(referred to simply as the potential energy from now on.) and e is

the elementary charge measured in coulombs (C). The SI unit for

potential is the volt: 1 V = 1 JC−1

.

The change of in the potential energy of a unit positive test charge (+e)

that results from a change in potential of 1 V is given by

and the corresponding change that accompanies the transfer of 1 C of

charge through a potential difference of 1 V is

The potential energy of an electron decreases by 1 eV when it moves through a

potential difference of +1 V.

The electrostatic driving force in electrochemistry is expressed in terms of

the potential, rather than the potential energy. Spontaneous processes

are characterized by increase in the potential (∆G = −𝑛𝐹∆𝐸).

∆𝐸P = 𝑒∆𝐸 = (1.602 × 10−19 C)(1 V) = 1.602 × 10−19 J = 1eV

∆𝐸P = ∆𝐸 = (1 C)(1 V) = 1 J

<Faraday’s laws> discovered by Faraday in 1833.

1. The mass of a given substance that is produced or consumed

in an electrochemical reaction is proportional to the quantity

of electric charge passed.

2. Equivalent mass of different substances are produced or

consumed in electrochemical reactions by a given quantity of

electric charge passed.

The charge e on a single electron has been very accurately determined

to be later on,

so the charge of one mole of electron is equal to

We typically measure the total charge passed in electrochemical

experiments by measuring the current and the time. The electric current

is the amount of charge that flows a circuit per second, the ampere in SI

unit. 1 C = (1 A)(1 s)

𝑒 = 1.60217646 × 10−19 C

= (6.0221420 × 1023 mol−1)(1.60217646 × 10−19 C) = 96,485.34 C

Faraday constant 𝐹 = 96,485.34 C mol−1

Electrochemistry (II-1)

박준원 교수(포항공과대학교 화학과)

General Chemistry

It is customary in electrochemistry to refer the difference in potential simply as the cell potential 𝐸cell

The change in the potential energy of the electrons is defined as the electrical work

Eq 17. 2 can be rewritten in terms of the current and the time as

Cell potentials and the Gibbs free energy

∆𝐸P = − ∆𝐸, 𝐸 in joules

∆𝐸P = − 𝐸cell, 𝐸cell in volts

𝑤elec = ∆𝐸P = − 𝐸cell [17.2]

, where 𝐸cell = 𝐸cathode − 𝐸anode

𝑤elec = −𝑖𝑡𝐸cell

2

∆𝐸P = − 𝐸cell, 𝐸cell in volts

𝑤elec = ∆𝐸P = − 𝐸cell [17.2]

, where 𝐸cell = 𝐸cathode − 𝐸anode

at constant 𝑃 and constant 𝑇,

The first law of thermodynamics is

Therefore,

For electrochemical reactions that are run reversibly

Therefore,

For Galvanic cells, 𝐸cell > 0, for electrolytic cells, 𝐸cell < 0

𝐺 = 𝐻 − 𝑇𝑆 = 𝑈 + 𝑃𝑉 − 𝑇𝑆

∆𝐺 = ∆𝑈 + 𝑃∆𝑉 − 𝑇∆𝑆

∆𝑈 = 𝑞 + 𝑤 = 𝑞 + 𝑤elec − 𝑃∆𝑉

∆𝐺 = 𝑞 + 𝑤elec − 𝑃∆𝑉 + 𝑃∆𝑉 − 𝑇∆𝑆 = 𝑞 + 𝑤elec − 𝑇∆𝑆

𝑤elec,rev = ∆𝐺 = −𝑛𝐹𝐸cell (at constant 𝑃 and 𝑇) [17.3]

<Standard states and standard cell potentials>

The standard cell potential 𝐸cell° is defined by

in which all reactants and products are in their standard states

(gases at 1 atm pressure, solutions at 1 M concentration, pure

metals in their most stable states and at a specified temperature).

∆𝐺 = −𝑛𝐹𝐸cell° (reversible) [17.4]

<Standard reduction potentials>

For convenience, we chose one half-reaction as our reference half-

reaction and then measure the cell potentials that result when this

reference half-reaction is coupled to all other half-reactions of interest.

The primary reference electrode has been chosen, by convention, to be

the standard hydrogen electrode (SHE), often called normal hydrogen

electrode (NHE). The SHE consists of a platinum electrode immersed in a

solution in which [H3O+

] = 1 M under a hydrogen partial pressure 𝑝H2= 1

atm (Fig 17.4). The cell potential was set to be 0.00 V.

The procedure for finding standard cell potentials for any cell is:

2H3O+

+ 2𝑒−

→ H2(g) + 2H2O(l)

𝐸cell° = 𝐸cathode

° – 𝐸anode°

The standard reduction potentials tabulated in Appendix E are arranged

in order, with the most positive potentials at the top and the most

negative potentials at the bottom (The most strong oxidant is F2(g), and

the most strong reductant is Li(s)).

Example) Find the cell potential for the Zn | Zn2+ || Cu2+ | Cu

The overall reaction is

The standard reduction potentials of the two half-reactions (Appendix E)

are:

Zn 𝑠 + Cu2+ 𝑎𝑞 → Cu 𝑠 + Zn2+(𝑎𝑞)

Zn2+ 𝑎𝑞 + 2 𝑒− → Zn(𝑠) 𝐸° = −0.76 V

Cu2+ 𝑎𝑞 + 2 𝑒− → Cu(𝑠) 𝐸° = 0.34 V

and so the standard cell potential for the cell is

The change in the Gibbs free energy is

Suppose we want to find the standard reduction potential for a half-reaction

that is not listed in Appendix E.

Using the following standard reduction potentials from Appendix E.

𝐸cell° = 𝐸cathode

° – 𝐸anode° = 0.34 V − −0.76 V = 1.10 V

∆𝐺° = −𝑛𝐹𝐸°cell = (−2 mol)(96,500 C mol−1)(1.10 V) = −212 kJ

Cu2+ + 𝑒− → Cu+ 𝐸3°(Cu2+ |Cu+) = ?

Cu2+ + 2 𝑒− → Cu 𝐸1° = 𝐸°(Cu2+ |Cu) = 0.340 V

Cu+ + 𝑒− → Cu 𝐸2° = 𝐸°(Cu+ |Cu) = 0.522 V

We calculate the change in the Gibbs free energy as

Therefore, is

∆𝐺3° = ∆𝐺1

° − ∆𝐺2°

−𝑛3𝐹𝐸3° = −𝑛1𝐹𝐸1

° − −𝑛2𝐹𝐸2° = −𝑛1𝐹𝐸1

° + 𝑛2𝐹𝐸2°

𝐸3° =

𝑛1𝐸°1 − 𝑛2𝐸°2

𝑛3

𝐸3° (Cu2+ |Cu+) =

(2 mol)(0.340 V) − (1 mol)(0.522 V)(1 mol)

= 0.158 V

<Reduction potential diagram and disproportionation>

We can summarize the half-reactions of copper in a reduction potential diagram of the form

Diagram like these are very useful in helping us predict which ions are unstable with respect to 𝑑𝑖𝑠𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛𝑎𝑡𝑖𝑜𝑛 . Species will disproportionate if the driving force for reduction is greater than the driving force for oxidation (In other words, the value on the right is bigger than that on the left.).

2 Cu+ → Cu2+ + Cu 𝐸° = 0.522 V − 0.158 V = 0.324 V

Cu2+ Cu+ Cu 0.158 V 0.522 V

0.340 V

<Alternative reference electrode>

The SHE is not particularly convenient to use in practice, so several alternative reference electrodes have been developed. The saturated calomel electrode (SCE) was the most popular alternative reference electrode for many years.

With a reduction potential 𝐸° = 0.242 V.

The Ag/AgCl electrode is a very convenient alternative to both the SHE and SCE reference electrodes. The reduction half-reaction is

With a reduction potentials 𝐸° = 0.197 V.

Hg2Cl2 + 2 𝑒− → 2 Hg + 2 Cl− (saturated)

AgCl + 𝑒 → Ag + Cl−

Electrochemistry (II-2)

박준원 교수(포항공과대학교 화학과)

General Chemistry

It is necessary to understand how concentration and pressure affect cell potentials.

Combining this equation with

gives

from which we get

𝐸cell = 𝐸cell° −

𝑅𝑇

𝑛𝐹 ln Q [17.6] (Nernst equation)

[17.7] 𝐸cell = 𝐸cell

° −0.0592 V

𝑛log10Q

Concentration effects and the Nernst equation

∆𝐺 = ∆𝐺° + RT ln Q (Chapter 14)

3

∆𝐺 = − 𝑛𝐹𝐸cell and ∆𝐺° = − 𝑛𝐹𝐸cell°

−𝑛𝐹𝐸cell = −𝑛𝐹𝐸cell° + RT ln Q

<Measuring equilibrium constants>

Electrochemistry provides a convenient and accurate way to

measure equilibrium constants for many solution-phase reactions:

at equilibrium

so

and

∆𝐺 = 0, ∆𝐺° = −𝑛𝐹𝐸cell° and ∆𝐺° = −𝑅𝑇 ln 𝐾

𝑅𝑇 ln 𝐾 = 𝑛𝐹𝐸cell° , ln 𝐾 =

𝑛𝐹

𝑅𝑇𝐸cell

°

log10 𝐾 =𝑛

0.0592 V𝐸cell

° (at 25℃ ) [17.8]

𝐸cell = 𝐸cell° −

0.0592 V

𝑛 log10 Q

pH meters

Cell potentials are sensitive to pH if one half-cell is the SHE. A

simple cell can be constructed to measure pH as follows:

Pt|H2(1 atm)|H3O+(1 M)||H3O+(aqueous, variable)|H2(1 atm)|Pt

If the half-reactions are written as

2 H3O+(var) + 2 𝑒− → H2(1 atm) + 2 H2O(l) (cathode)

H2(1 atm) + 2 H2O(l) → 2 H3O+(1 M) + 2 𝑒− (anode)

then 𝑛 = 2 and Q = 1/[H3O+(aqueous, variable)]2

The cell potential is

which becomes

The measured cell potential is directly proportional to the pH.

𝐸cell = 𝐸° − 0.0592 V

𝑛 log10Q

𝐸cell = − 0.0592 V

2 log10 1/[H3O+]2

= −0.0592 V log10 H3O+ = −(0.0592 V) pH

- Schematic of an early pH meter utilizing SCE -

Oxtoby, D. W.; Gillis, H. P.; Campion, A., Principles of modern chemistry, 7th ed.; Cengage Learning: Boston, 2012; p 786.

[ F I G U R E 1 7 . 1 0 ]