Equilibrium Electrochemistry
Equilibrium Electrochemistry Dr. David J. Fermín (S123) [email protected] Lecture notes at: www.chm.bris.ac.uk/pt/electrochemistry Aim of the course: This course provides the thermodynamic tools for understanding electrochemical reactions and devices. Starting from the concept of the electrochemical potential of charged species, this course will cover the thermodynamic relationships associated with electrochemical cells and various devices such as batteries and sensors. The potential distribution across electrified metal|electrolyte interfaces will also be discussed. 1
Global Picture – Energy Sources Primary Energy Use
Electricity Production
toe: “tonnes of oil equivalent” = 42 GJ UNDP – World Energy Assessment 2004
2
Unbalanced Energy Economy Primary Energy Use
3
Environmental Impact Radiative Forcing: Impact in energy balance RF > 0: Warming CO2, CH4, NOx: Industrial development Air pollution: 800 k deaths/year Damages in Agriculture, forests, fishing, infrastructure
4 IPCC report – Executive summary Feb. 2007
5
Sustainable Energy Worldwide 2007: 6.5 billion people – 13 TW energy consumption 2100: Energy demand up to 40 TW Carbon neutral energy sources – Global warming Reliable carbon sequestration: 25 billion Ton of CO2 a year with less than 1% loss Nuclear: 1GW plant / week for 50 years. Uranium source to deplete in 10 years Renewable: Hydroelectric - 0.5 TW Tidal – 2 TW
SOLAR: 120000 TW
Geothermal – 10 TW Wind – 2 TW
Target: Harvest – Transform – Store 6
Electrochemistry Electrons Ions Electrical potential Electrodes
Dissolution / Deposition Corrosion Electro-chromic Electro-luminescent systems
Nature 2001
http://p2library.nfesc.navy.mil/index.html
7
Learning Objectives Electrochemical potential Chemical potential in condensed phases The activity of ions in solution The Galvani potential
Ecell and useful constants
Standard potential Calculating thermodynamic parameters, activity coefficient and solubility products
Thermodynamic of ions
Electroanalysis and devices
Standard Enthalpy, Entropy and Gibbs energy of formation Gibbs energy of solvation Debye-Hückel theory
Redox titration Ion selective electrodes Membrane electrodes (pH) Batteries
Electrochemical cells
Electrochemical double layer
The Galvani potential difference Conventional Electrochemical cells Cell reactions and electromotive force The Nernst Equation
The structure of the metal|electrolyte interface The Helmholtz layer The diffuse layer The potential distribution 8
Electrochemical Potential Chemical potential in gas phase
Chemical potential in liquid phase
The electrostatic potential of condensed phases
The electrochemical potential of charged species 9
1.1 Chemical potential Fundamental Equation of Chemical Thermodynamics:
dG = Vdp − SdT + ∑ µidni
eqn. 1.1
i
∂G µi = ∂ni T ,P ,nj≠i eqn. 1.2
10
1.2 Chemical potential in liquid phase Reversible work required for changing the activity of the solute in solution
µi ( l ) = µio ,ideal-dil + RT ln ( xi ) + RT ln ( γ i ) = µio ,ideal-dil + RT ln ( ai ) eqn. 1.12
RT ln γ i
the reversible work associated with interaction between solutes
ai = γ i xi
is defined as the activity of the solute i.
µio ,ideal-dil
Henry’s reference state for solutes: “i” only interacts with solvent (eq. 1.11)
µio ,ideal
Raoult’s reference state for liquids: “i” in its pure state (eq. 1.8)
11
eqn. 1.11
ideal dilute solution eqn. 1.8
ideal solution
Fig. 1.2 Variation of the chemical potential and the definition of the standard chemical potential at 298 K in the scale of mole fractions for an ideally diluted solution [Girault 2001]. 12
1.3 Molality and Molarity scales Both concentration scales used for diluted solutions
ni mi = nsMs
eqn. 1.13
mol × kg-1
ni ci = V
ni number of moles of the solute ns number of moles of the solvent Ms molar mass of the solvent
mol × dm-3
V solution volume From eqn. 1.12,
µi = µio ,c + RT ln γ ic
ci c o
eqn. 1.16
µio ,c = µio ,ideal-dil + RT ln ( c oVM,s )
c o standard molarity 1 mol dm-3 VM,s molar volume of the solvent
eqn. 1.17
Relationship between activity coefficient in the molar and molal scales
d smi γ =γ ci c i
m i
eqn. 1.18
ds density of the pure solvent 13
1.4 Electrostatic potential of condensed phases In the case of charged species, the chemical potential also depends on the electrostatic inner potential associated with the liquid (condensed) phase:
r
x
+
ψ (x) =
q
χ
q
eqn. 1.19
4πεε 0 ( x + r )
surface dipoles – e.g. water molecules
Table 1.1 Relative permittivity
q the charge of the condensed phase
ψ outer potential (Volta potential)
solvent
εr at 293 K
Water
80.1
χ surface potential
Nitrobenzene
35.6
εr relative permittivity
Ethanol
25.3
Benzene
2.3
Cyclohexane
2.0
ε permittivity of free space (8.854×10-12 J-1 C2 m-1)
14
Volta potential (ψ): phase is charged too – dependent on distance (x). The surface potential (χ): differential work for bringing the charge into the phase.
ψ (x) =
q 4πεε 0 ( x + r )
r
+ x q
χ
Galvani potential
φ =ψ + χ If the phase is neutral, ψ = 0 and φ = χ
eqn. 1.20
χ = 0.13 V for water (Trasatti 1980) 15
1.5 Electrochemical potential of charged species The star equation of the day: Electrochemical potential
µ%i = µi + RT ln ( ai ) + ziFφ o
eqn. 1.22
Vacuum
zF i ψ G
Outer potential
bulk
µi
zi F χ
µ% i
16
Summary Chemical potential (µi) – reversible work for transferring one mol of a component from vacuum to a given phase at constant T and p o Standard states ( µi ) are defined for the solvent and solute
Activity (ai) accounts for “non-ideal” behaviour of solute The Galvani potential (φ) is determined by the “charge” of the solvent and surface dipoles
µ%i = µi + RT ln ( ai ) + ziFφ o
17
Giants of the day
Josiah Willard Gibbs American Engineer 1839 - 1903
François-Marie Raoult French Chemist 1830 - 1901
William Henry English Chemist 1775 - 1836
18
Global Picture – Energy Sources Primary Energy Use
Electricity Production
toe: “tonnes of oil equivalent” = 42 GJ UNDP – World Energy Assessment 2004
2
Unbalanced Energy Economy Primary Energy Use
3
Environmental Impact Radiative Forcing: Impact in energy balance RF > 0: Warming CO2, CH4, NOx: Industrial development Air pollution: 800 k deaths/year Damages in Agriculture, forests, fishing, infrastructure
4 IPCC report – Executive summary Feb. 2007
5
Sustainable Energy Worldwide 2007: 6.5 billion people – 13 TW energy consumption 2100: Energy demand up to 40 TW Carbon neutral energy sources – Global warming Reliable carbon sequestration: 25 billion Ton of CO2 a year with less than 1% loss Nuclear: 1GW plant / week for 50 years. Uranium source to deplete in 10 years Renewable: Hydroelectric - 0.5 TW Tidal – 2 TW
SOLAR: 120000 TW
Geothermal – 10 TW Wind – 2 TW
Target: Harvest – Transform – Store 6
Electrochemistry Electrons Ions Electrical potential Electrodes
Dissolution / Deposition Corrosion Electro-chromic Electro-luminescent systems
Nature 2001
http://p2library.nfesc.navy.mil/index.html
7
Learning Objectives Electrochemical potential Chemical potential in condensed phases The activity of ions in solution The Galvani potential
Ecell and useful constants
Standard potential Calculating thermodynamic parameters, activity coefficient and solubility products
Thermodynamic of ions
Electroanalysis and devices
Standard Enthalpy, Entropy and Gibbs energy of formation Gibbs energy of solvation Debye-Hückel theory
Redox titration Ion selective electrodes Membrane electrodes (pH) Batteries
Electrochemical cells
Electrochemical double layer
The Galvani potential difference Conventional Electrochemical cells Cell reactions and electromotive force The Nernst Equation
The structure of the metal|electrolyte interface The Helmholtz layer The diffuse layer The potential distribution 8
Electrochemical Potential Chemical potential in gas phase
Chemical potential in liquid phase
The electrostatic potential of condensed phases
The electrochemical potential of charged species 9
1.1 Chemical potential Fundamental Equation of Chemical Thermodynamics:
dG = Vdp − SdT + ∑ µidni
eqn. 1.1
i
∂G µi = ∂ni T ,P ,nj≠i eqn. 1.2
10
1.2 Chemical potential in liquid phase Reversible work required for changing the activity of the solute in solution
µi ( l ) = µio ,ideal-dil + RT ln ( xi ) + RT ln ( γ i ) = µio ,ideal-dil + RT ln ( ai ) eqn. 1.12
RT ln γ i
the reversible work associated with interaction between solutes
ai = γ i xi
is defined as the activity of the solute i.
µio ,ideal-dil
Henry’s reference state for solutes: “i” only interacts with solvent (eq. 1.11)
µio ,ideal
Raoult’s reference state for liquids: “i” in its pure state (eq. 1.8)
11
eqn. 1.11
ideal dilute solution eqn. 1.8
ideal solution
Fig. 1.2 Variation of the chemical potential and the definition of the standard chemical potential at 298 K in the scale of mole fractions for an ideally diluted solution [Girault 2001]. 12
1.3 Molality and Molarity scales Both concentration scales used for diluted solutions
ni mi = nsMs
eqn. 1.13
mol × kg-1
ni ci = V
ni number of moles of the solute ns number of moles of the solvent Ms molar mass of the solvent
mol × dm-3
V solution volume From eqn. 1.12,
µi = µio ,c + RT ln γ ic
ci c o
eqn. 1.16
µio ,c = µio ,ideal-dil + RT ln ( c oVM,s )
c o standard molarity 1 mol dm-3 VM,s molar volume of the solvent
eqn. 1.17
Relationship between activity coefficient in the molar and molal scales
d smi γ =γ ci c i
m i
eqn. 1.18
ds density of the pure solvent 13
1.4 Electrostatic potential of condensed phases In the case of charged species, the chemical potential also depends on the electrostatic inner potential associated with the liquid (condensed) phase:
r
x
+
ψ (x) =
q
χ
q
eqn. 1.19
4πεε 0 ( x + r )
surface dipoles – e.g. water molecules
Table 1.1 Relative permittivity
q the charge of the condensed phase
ψ outer potential (Volta potential)
solvent
εr at 293 K
Water
80.1
χ surface potential
Nitrobenzene
35.6
εr relative permittivity
Ethanol
25.3
Benzene
2.3
Cyclohexane
2.0
ε permittivity of free space (8.854×10-12 J-1 C2 m-1)
14
Volta potential (ψ): phase is charged too – dependent on distance (x). The surface potential (χ): differential work for bringing the charge into the phase.
ψ (x) =
q 4πεε 0 ( x + r )
r
+ x q
χ
Galvani potential
φ =ψ + χ If the phase is neutral, ψ = 0 and φ = χ
eqn. 1.20
χ = 0.13 V for water (Trasatti 1980) 15
1.5 Electrochemical potential of charged species The star equation of the day: Electrochemical potential
µ%i = µi + RT ln ( ai ) + ziFφ o
eqn. 1.22
Vacuum
zF i ψ G
Outer potential
bulk
µi
zi F χ
µ% i
16
Summary Chemical potential (µi) – reversible work for transferring one mol of a component from vacuum to a given phase at constant T and p o Standard states ( µi ) are defined for the solvent and solute
Activity (ai) accounts for “non-ideal” behaviour of solute The Galvani potential (φ) is determined by the “charge” of the solvent and surface dipoles
µ%i = µi + RT ln ( ai ) + ziFφ o
17
Giants of the day
Josiah Willard Gibbs American Engineer 1839 - 1903
François-Marie Raoult French Chemist 1830 - 1901
William Henry English Chemist 1775 - 1836
18
