Overview of electrochemistry

Overview of electrochemistry 1 Homogeneous Heterogeneous Equilibrium electrochemistry (no current flows) Thermodynamics of electrolyte solutions: electrolytic dissociation thermodynamics and activities of ions Thermodynamics of electrodes and Galvanic cells: electrochemical cells cell and electrode potential types of electrodes Dynamic electrochemistry (current does flow) Conductance of electrolytes: electrolytic conduction mobilities of ions Kohlrausch laws Kinetics of electrode reactions: exchange current overpotential Tafel equation Butler-Volmer equation electrolysis batteries HOMOGENOUS DYNAMIC ELECTROCHEMISTRY Simultaneous or coupled transport phenomena I. Conductivity of electrolytes (κ, Λ m, Λ mo ) II. law of the independent migration of ions: Λ m = ν + λ + + ν λ Strong electrolytes: Kohlrausch law: Λ m = Λ mo Kc ½ III. Weak electrolytes: (α < 1, α = Λ m /Λ mo ) Ostwald s dilution law IV. Mobilities of ions, ion transport number 1

I. Conductivity of electrolytes Ionic conductivity: Ohm s law is valid: Conductance G is the reciprocal of R res : I U R G R as T increases, do does κ (opposite to metals). Solution: κ conductivity: Gl / A GC (l: length of cell, A: surface, C: cell constant) Concentration is important, molar conductivity is used: / c The limiting value of Λ m at infinite dilution is Λ m o (limiting molar conductivity). m / res 1/ res I. Conductivity of electrolytes The limiting value of Λ m at infinite dilution is Λ mo (limiting molar conductivity). The conductivity of the electrolyte is obtained by adding the conductivities of ions: law of the independent migration of ions: 0 Λ m λ + and λ - : limiting molar conductivities of (individual) cations and anions ν + and ν - : stoichiometric number of the cation and anion 2

Cell: measuring the conductivity of electrolytes Weak and strong electrolytes: concentration dependence of conductivity II. Strong electrolytes Concept (definition): in a solution of a strong electrolyte dissociation is practically complete independently of the concentration, so α = 1. Degree of dissociation (α): the ratio of dissociated molecules. Conductivity of electrolytes, Kohlrausch law: Λ m Λ 0 m Kc 1 2 K: a constant to be determined experimentally; depends primarily on the type of the electrolyte and not on its identity 3

II. Strong electrolytes Λ m Λ 0 m Kc 1 2 III. Weak electrolytes The degree of dissociation is reflected by the ratio of Λ m and limiting Λ mo : Λ Acid dissociation constant: 2 c K a 1 Ostwald s dilution law: 1 1 1 c 0 2 m m K m Λ a m 0 m 0 m 4

IV. Mobilities of ions drift speed(s) mobilities of ions (u) frictional coefficient(f) mobility (u) and conductivity (λ) transport numbers (t + and t - ) determination methods for transport numbers IV. Mobilities of ions Molecular view: ions with radius a hydr are accelerated in a medium of viscosity η by an electric force of F el, but this is balanced by a counter-force of friction F fric (Stokes law). F el ze A stationary state is established with constant drift speed: ze s u f The drift speed of the ion is the product of electric field ε and ion mobility u. The value of u: ze ze u f 6 F fric a hydr fs 6a hydr s 5

IV. Mobilities of ions Molar conductivities of a few ions at 298 K u ze f ze 6a hydr Ion transport number Ion transport number: the fraction of current transported by the ion: I t I Obviously: t + + t - = 1 Determination methods for transport numbers: moving boundary method, Hittorf s method (measuring concentration change in electrode compartments), comparison of cell potentials with and without liquid junction. 6

Overview of electrochemistry 13 Homogeneous Heterogeneous Equilibrium electrochemistry (no current flows) Thermodynamics of electrolyte solutions: electrolytic dissociation thermodynamics and activities of ions Thermodynamics of electrodes and Galvanic cells: electrochemical cells cell and electrode potential types of electrodes Dynamic electrochemistry (current does flow) Conductance of electrolytes: electrolytic conduction mobilities of ions Kohlrausch laws Kinetics of electrode reactions: exchange current overpotential Tafel equation Butler-Volmer equation electrolysis batteries 14 HETEROGENEOUS DYNAMIC ELECTROCHEMISTRY 1. Observations (current density overpotential, exchange current(s), Tafel equation,...) 2. Interpretation of the observations (the double layer and its models, Galvani and Volta potentials; kinetics of electrode reactions, Butler Volmer equation; lower and upper limits of overpotential, polarization, limiting current) 3. Practical electrochemistry (working galvanic cells, accumulators, fuel cells, polarography, voltammetry, electrolysis, corrosion) 7

Kinetics of electrode processes (heterogeneous dynamic electrochemistry) 15 In equilibrium electrochemistry (thermodynamics of electrolytes, Galvanic cells and electrodes), states of equilibrium are described and the possibility of changes. No current flows in such systems, the Galvanic cell does no useful work, no change occurs on the electrodes. In non-equilibrium electrochemistry [dynamic electrochemistry], dynamic processes are described: the system is not in equilibrium: current flows in the solutions, substances deposit or dissolve on electrodes. In addition to equilibrium electrode potential, overpotential occurs. Kinetics of electrode processes (heterogeneous dynamic electrochemistry) 16 In dynamic electrochemistry, the voltage and current of spontaneous reactions in Galvanic cells or those of forced reactions in electrolysis are described in a temporal and spatial manner. Understanding of the mechanism of electrode processes is necessary for both electrolysis and Galvanic cells. 8

17 Kinetics of electrode processes (heterogeneous dynamic electrochemistry) Macroscopic measurements give important information about the processes on electrode surfaces and also contribute to understanding phenomena occurring at the molecular level. 1. Observations 18 Quantities in dynamic electrochemistry: a) Current-related: The definition of reaction rate in a heterogeneous process: product flux = k[particle] In the two electrode processes: v ox = k c [Ox], and v red = k a [Red] Characterization of the on an electrode: j current density (j) = current / surface [A cm -2 ] [Remark: there is Ohmic resistance in systems like this (it is readily measurable).] 9

1. Observations 19 Quantities in dynamic electrochemistry: b) Potential / voltage related: The original equilibrium electrode potentials (E) are not valid in a working Galvanic or electrolytic cell. The differences are formally described as: On electrodes: η overpotential (polarization potential) Galvanic cells: actual cell potential ( < E) [not necessarily constant, depends on the current] Electrolytic cells: η overpotantial ( > E) [set by the experimenter based on the objectives] All of these quantities are measurable similarly to E. 1. Observations 20 Quantities in dynamic electrochemistry: c) Current density, exchange current(s): Observations show that current density j changes when the overpotential η is changed: increase and decrease, even a sign change are possible. On all electrodes, cathodic j c = Fk c [Ox] And anodic j a = Fk a [Red] current densities are. The actual (and measurable) current density j is the difference of these two: if j a > j c, then j > 0, the net current is anodic, if j a < j c, then j < 0, the net current is cathodic, if j a = j c, then j = 0, the net current is zero. 10

1. Observations 21 Quantities in dynamic electrochemistry: c) Current density, exchange current(s): (a) anodic and (b) cathodic net current density: ja Fk a jc Fk c Red Ox solution / anode solution / cathode 1. Observations 22 Quantities in dynamic electrochemistry: d) Relationship between the overpotential and current density, the Tafel equation: At small overpotential, current density increases linearly with the overpotential: j = j 0 f η (f = F/RT) At intermediate overpotential, the relationship is exponential (logarithmic). This is the observed Tafel 1 f equation: j j e, lnj lnj 0 0 1 f At large overpotential, current density reaches an upper limit, this is the limiting current. If η < 0, then j < 0: ln( j) = ln j 0 α f η 11

1. Observations 23 Quantities in dynamic electrochemistry: d) Cases in the overpotential current density landscape, the Tafel equation: Current density j as a function of overpotential η: 2. Interpretation of observations 24 To interpret the observations, we need: an understanding of the structure of the surface boundary between the electrode and the electrolyte: a description of the electric double layer and the Nernst adsorption layer. the mechanisms of the rate limiting step: the activation free energy Δ # G of the charge transfer step and its possible dependence on the overpotential η. to clarify the role of diffusion and activation. Recognizing the relationship between η and Δ # G is the core issue in the kinetic description of electrode processes. 12

2. Interpretation of observations 25 a) The structure of the electrode /electrolyte boundary: In the bulk solution, the flow of the solute toward (and from) the surface is caused by (fast) convection (stirring). On a solid-liquid boundary, there is always a highly adhesive liquid layer (not only for electrolytes and not only on electrodes) : this is the Nernst δ diffusion layer. In this layer, transport of matter is only possible by (slow) diffusion, so a concentration gradient forms in it. There is no specific structure in it. Its width depends on the intensity of stirring or rotation 10-3 -10-2 mm. [On a rotating disc electrode: δ = D 1/3 η 1/6 ω -1/2 ]. 2. Interpretation of observations 26 a) The structure of the electrode /electrolyte boundary: Gouy Chapman diffusion model Helmholtz planar capacitor model Stern model 13

100 nm 2. Interpretation of observations 27 a) The structure of the electrode /electrolyte boundary: Within the double layer, the electric field is characterized by the potential of a unit charge (e - ) vs. the surface. On approaching from a large distance, the potential increases exponentially, then remains constant close to the (quasiplanar) surface (ψ Volta potential). A sudden jump on the surface (χ surface potential potential). Together: φ Galvani potential. Only the Galvani potential is available experimentally, it is the same as the electrode potential. 2. Interpretation of observations 28 b) Kinetics of electrode processes, the Butler Volmer equation: 1. If in the electrode reaction Ox + e - = Red (cathodic reduction), the electrode becomes more positive (is polarized), the activation free energy of the electrode process increases: G c G 0 F 2. In a Red e - = Ox oxidation (anodic) process, the effect of polarization: G G 0 1 F With these two modified values of activation free energy, the net current density is obtained, which connects j and η. This is called the Butler Volmer equation: a c a 14

29 b) Kinetics of electrode processes, the Butler Volmer equation: 1. If in the electrode reaction Ox + e - = Red (cathodic reduction), the electrode becomes more positive (is polarized), the activation free energy [- Gaof (1 the )F ]/RT electrode a c process increases: a[re ]e G c Gc [- 0 G F 2. In a Red e - c F ]/RT = Ox FB oxidation c[ Ox(anodic) ]e process, the effect of polarization: G G 0 1 F j j j FB d 2. Interpretation of observations With these two modified values of activation free energy, the net current density is obtained, which connects j and η. This is called the Butler Volmer equation: a a 2. Interpretation of observations 30 b) Kinetics of electrode processes, the Butler Volmer equation: activation profiles of reduction-oxidation = 1 = 0 normal reaction profile potential difference between the inner and outer Helmholtz layer the electron transport appears either in the activation or in the reaction free energy 15

2. Interpretation of observations 31 b) Kinetics of electrode processes, the Butler Volmer equation: Without any overpotential (η = 0), the formula gives the exchange current density j 0 arising from the equilibrium cell potential E cell without current: j 0 = j a = j c Δ Ga 1 αfe /RT ja FBa[Red]e Δ Gc αfe /RT j FB [Ox]e c c Exchange current density j 0 is not measurable directly, but can be extrapolated based on the Tafel equation (η 0). The introduction of j 0 gives a simpler from for the Butler Volmer equation: (1 ) f f j j0 [ e e ] 2. Interpretation of observations 32 c) Limits of the overpotential: The lower limit of overpotential: At low overpotentials of η << 0.01 V, i.e. fη << 1, series expansion (e x = 1 + x + ) gives: j = j 0 [1 + (1 α) fη + 1 ( αfη) ] j 0 fη Ohm law is valid in this regime, and in agreement with the observations a linear relationship is valid between j and η. j j 0 [ e (1 ) f e f ] 16

2. Interpretation of observations 33 c) Limits of the overpotential: Upper limit of the overpotential: At η > 0.12 V (intermediate overpotential), the second term in the Butler Volmer equation becomes negligible, so j = j 0 e (1 α)fη, i.e.: ln j = ln j 0 + (1 α)fη. At η < 0.12 V (intermediate cathodic overpotential), the first term becomes negligible, so j = j 0 e αfη, i.e.: ln ( j) = ln j 0 αfη. These are the same as the Tafel equation. The transfer coefficient α and exchange current density j 0 can be determined in this way. (1 ) f f j j0 [ e e ] 2. Interpretation of observations 34 d) Limiting current: At high overpotentials, the Nernst diffusion layer quickly becomes depleted because of the fast charge transfer (metal deposition). A further increase in η cannot increase the current density any more, as diffusion across the Nernst layer becomes the limiting step. This is characterized by the j lim limiting current density. Its value only depends on on the concentration gradient dc/dx, diffusion constant D, and layer thickness δ: j lim zfj lim zfdc 17

3. Practical electrochemistry 35 a) The practical significance of overpotential: Ion reactions do not really start at the reversible potentials. For cations, more negative, for anions, more positive potentials are needed. E.g. H 2 production on Pt: 0 V, on Pb 0.6 V, on Hg: 0.8 V. O 2 production on Pt: 0.4 V, on Pb: 0.3 V. The overpotential adds to the energy needs of electrolysis, so minimizing it is an important objective. 3. Practical electrochemistry 36 b) Working Galvanic cells: In working Galvanic cells (I > 0), the cell potential E is always smaller than the equilibrium potential E cell without current (I = 0) (electromotive force): E = ΔΦ J ΔΦ B = E cell + η J η B IR s. The term IR s (Ohmic term) gives the heat production within the solution as a result of the current. This causes energy loss in the Galvanic cell. 18

3. Practical electrochemistry 37 c) Electrolysis: In an electrolytic cell, the potential necessary to force the reaction is larger than the equilibrium potential (overpotential). Faraday s laws of electrolysis: I. The electric charge necessary to force 1 mol of electron is F = 96485 C (Faraday constant. II. The mass of the substance produced by electrolysis is directly proportional to the current and the electrolysis time: m = F I t (coulombmetry). 3. Practical electrochemistry 38 d) Practical applications: NaCl (common salt) electrolysis in industry (Hg cathode, diaphragm) electrolysis of molten Al 2 O 3 production of Al galvanization, (protective) metal layers Anodic oxidation of Al layers: metal protection 19

3. Practical electrochemistry 39 e) Electrochemical corrosion: O 2 is reduced, gains electrons from the metal local cell anode: iron dissolves (internal part, little O 2 ) cathode: H + is reduced. O 2 depolarizes sacrificial anode Different states of matter (different phases) and their properties, similarities and differences Transport processes Diffusion: transport of matter Thermal conductivity: transport of energy Viscosity: transport of momentum Interpretation of transport processes with the kinetic theory of gases Effusion Barometric formula 40 20

Properties of gases (overview) State of matter: GAS (g) LIQUID (l) SOLID (s) Fixed shape no no yes Fixed volume no yes yes An example of phenomenological description. State of matter: The particles' potential energy GAS (g) LIQUID (l) SOLID (s) small medium large kinetic energy large medium small ordering no yes? yes An example of (qualitative) interpretation. 41 Similarities and differences: diffusion and thermal conduction exist in all three states of matter (all three phases): there is a gradient in c or T which tends to zero with transport on the molecular level (not a macroscopic convection); the equations describing these two processes are similar. viscosity exists only in fluid and gas phase, not in crystals ion conduction: can be detected only in electronic force gradient (voltage). Exists only in solutions and melts. In solid phase, there is electronic conduction instead. In gas phase, there is electric discharge. 42 21

Similarities and differences: the pressure: In gases: molecules have large kinetic energy. The moment changes when they collide with the wall. This results in the pressure on all walls of the container (up, down, sides!) This exist without gravity. In liquids: there is small kinetic energy, this cannot result in any pressure directly. In a gravity field, the mass of the liquid causes pressure on the bottom of the container which is transported to the side walls by molecular motions. In solids: pressure can be measured only on the bottom of the container in gravity field. 43 Transport phenomena Phenomenon gradient transport Diffusion concentration matter thermal conduction temperature energy viscosity velocity momentum ionic conduction electronic potential charge Transport processes can be found in all three phases (with some exceptions. In transport processes, only the molecules are in motion. The system and its macroscopic parts are not. There is no convection or mixing. 44 22

Transport phenomena Diffusion: particle transport Thermal conduction: energy transport Electrolytic conduction: charge transport Viscosity: momentum transport 45 Transport phenomena Common concepts in transport phenomena: gradient: one of the parameters (T, c, E...) is inhomogeneously distributed in space, at least in one direction. flux: the quantity of a given property (m, v...) passing through a given area in a given time interval divided by the area and the duration of the interval. Symbol: J(matter, charge ). dn J matter dz N: the number density of particles with units number per cubic meter 46 23

Diffusion: transport of matter (molecular level) dn [J]: m -2 s -1 flux of matter J matter D [D]: m 2 s -1 diffusion coefficient dz dn/dz: m -4 concentration gradient Fick s first law of diffusion: diffusion will be faster when the concentration varies steeply with position than when the concentration is nearly uniform. Different concentrations mean different chemical potentials (since μ depends on c), Practical importance: motion of matter in soils. Convection: macroscopic! 47 Thermal conduction: transport of energy dt [J]: J m -2 s -1 flux of energy J energy [κ]: J K dz -1 m -1 s -1 coefficient of thermal conductivity dt/dz: K m -1 temperature gradient Energy migrates down a temperature gradient. The connection between flux and gradient is similar to Fick s first law of diffusion. Good thermal conductors: metals (Ag, Cu, Au, Al), marble, diamond Good thermal insulators: vacuum, CO2, plastic, wood Practical importance: thermal insulation of houses. There is molecular heat conduction, macroscopic (convective) heat flow and heat radiation. 48 24

J Viscosity: transport of momentum momentum z dvx dz Because the retarding effect depends on the transfer of the x- component of linear momentum into the layer of interest, the viscosity depends on the flux of this x-component in the z- direction. [J]: kg m -1 s -2 flux of momentum [η]: kg m -1 s -1 coefficient of viscosity (or simply the viscosity ) dv x /dz: s -1 velocity gradient 49 Data for gases: diffusion coefficients: 10-4 m 2 s -1 coefficients of thermal conductivity: 0.01-0.1 J K -1 m -1 s -1 coefficients of viscosity: 1-210 -5 kg m -1 s -1 50 25

Kinetic theory of gases: Molecules in the gaseous phase (macroscopic equilibrium). The gas particles (with m mass) move continuously in a straight line with constant speed and they collide. The collisions are perfectly elastic (there is no change in the shape of the molecule). The gas molecules have only m mass and v velocity, so, momentum (mv) and kinetic energy (1/2 mv 2 ). 51 Kinetic theory of gases - results: Mean free path: σ: collision cross-section k B T 2p p and T have opposite effects on λ. Mean speed of a particle with m mass (i.e. M=N A m 1/ 2 1/ 2 molar mass): 8kBT 8RT c m M The mean speed is directly proportional with T 1/2 and inversely proportional to M 1/2. p Collision frequency: Z w 1 / 2mk 2 BT Z w : the number of collisions made by one molecule divided by the time interval during which the collisions are counted 52 26

The transport constants from the kinetic theory of gases: diffusion coefficient: coefficient of thermal conductivity: coefficient of viscosity: 1 D c 3 1 3 cc V,m 1 cmn 3 A 53 Time and diffusion: the diffucion equation (Fick s 2nd law) At a given position x, the concentrations change is given as: 2 c c D 2 t x Some solutions of the diffusion equation: An initial value and two boundary conditions are needed: At t = 0, the concentration is N 0 in the x, y plane No reactions in the system Concentration are always finite. Sugar at the bottom of the tea cup: diffusion in space 54 27

D t relative time scale A solution of the diffusion equation: 2 x 4Dt n0e c 1 / A Dt 2 Concentration distributions above different planes At different values of relative time D t 55 Effusion: Effusion: gas slowly escapes through a small hole into an external vacuum (a tire becomes flat slowly if the hole is small [Vacuum is relative: the essence is the unidirectional diffusion.] Graham s law of effusion: the rate of effusion is inversely proportional to the square root of the molar mass (an old determination method for molar mass): 1 rate of effusion M 56 28

Inhomogeneity in gas pressure in an external force field: In a force field (e.g. gravity field of Earth), the pressure is not uniform (e.g. atmosphere): there is an exponential decrease in pressure with the elevation. This is described by the barometric formula : p Mgh RT p 0 e The phenomenon can be observed in n an artificial gravity field (centrifuge) as well, and the distribution (which depend on the molar mass) can be used in separating different isotopes. 57 29