Electrochemical Thermodynamics and Concepts Sensitivity of electrochemical measurements Measurements of electrochemical processes are made by measuring electrical currents and voltages. The currents results from the flow of charged ions (positive or negative) and or electrons. Current measurement can be extremely sensitive as small as amps (coulombs per second). Let’s get “feeling” for the sensitivity of such a measurement. monolayer: ≈1.5 x10 15 atoms/cm 2. Suppose each atom on the surface dissolves as a single charged positive ion (i.e., a cation). corresponding to 1.6 x C/atom of charge. Today we can easily measure at the nanoamp scale. Suppose we measure a current density of A cm -2 for 1 s or C. A full monolayer of metal dissolving as a +1 cation results in a charge of 1.6 x C/atom x 1.5 x atoms/cm 2 or ≈ 2.4 x C cm -2. Then C corresponds to only of order 0.01 ML cm A

An electrochemical reaction is a chemical reaction involving electron transfer. An ordinary chemical reaction does not involve electron transfer Chemical reactions: Note the mass balance N 2 +3H 2 = 2NH 3 synthesis of ammonia Electrochemical Reactions: Note the mass and charge balance 2H + +2e - = H 2 Hydrogen ion reduction Zn = Zn e - Zn oxidation

Since electrochemical reactions involve electron transfer we can measure the rate of these processes by designing an appropriate electrical circuit and measuring the flow of an electric current. Faraday’s Law relates the flow of electric current to the mass of metal reacting. m = mass of metal reacting (gm) t =time (s, min, hours, years) I =current (Amps) a = atomic weight of metal n = number of electrons transferred in the reaction F = 96,500 C; Faraday ’ s constant which is equal to the charge associated with 1 mole of electrons.

If, for example, we divide Faraday’s law by the time and area of A dissolving surface, we obtain a relation describing the rate of this process. A = surface area of corroding metal (cm 2 ) i =I/A: the current density (A/cm 2 ) r = Rate measured as a weight per unit area per unit time (gm/cm 2 -s).

Examples Consider the case for steel or iron corrosion. Suppose we make a measurement of the current associated with the corrosion of 100 cm 2 of a steel surface and find a current of 0.1A. Then dividing through by the area of the sample, 0.1 A/100 cm 2 = A/cm 2 = 1 mA/cm 2 current density. i = 1 mA/cm 2 a = g F = 96,500 C n =2

We can convert this to a penetration rate (cm/s) by dividing by the density of Fe.

Next consider:

H 2 at 1Atm porous barrier {H + } =1 {Zn 2+ } =1 Zn Pt V Electrochemical Cells Pt is inert and acts as a catalyst: 2H + + 2e - = H 2 Zn is oxidized: Zn = Zn 2+ +2e - Total reaction: Zn + 2H + = Zn 2+ + H 2 We measure a potential difference of V 2H + + 2e - = H 2 E 0 = V (defined as zero by convention) Zn 2+ +2e - = Zn E 0 = V (NHE) sign taken to be negative since Zn is oxidized.

H 2 at 1Atm porous barrier {H + } =1 {Cu 2+ } =1 Cu Pt V Pt is inert and acts as a catalyst: H 2 = 2H + + 2e - : hydrogen is oxidized Cu plates; Cu 2+ +2e - = Cu Total reactionCu 2+ + H 2 = Cu + 2H + We measure a potential difference of V 2H + + 2e - = H 2 E 0 = V (defined as zero by convention) Cu 2+ +2e - = Cu E 0 = V (NHE) This sign is positive since Cu is reduced. Electrochemical Cells

1 M ZnSO 4 1 M CuSO V If we construct this “cell” we observe the following: Zn dissolves; Zn = Zn 2+ +2e - ; oxidation occurs at the anode Cu plates; Cu 2+ +2e - =Cureduction occurs at the cathode If we connect a voltmeter as shown we measure a voltage of V. Electrochemical Cells

Daniell Cell Zn dissolves; Zn = Zn 2+ +2e - ; oxidation occurs at the anode Cu plates; Cu 2+ +2e - =Cureduction occurs at the cathode For the Cu-Zn cell we measured a voltage difference of V. Zn 2+ +2e - = Zn E 0 = V (NHE) Cu 2+ +2e - = Cu E 0 = V (NHE) V This difference is V

Standard Reduction Potentials: EMF Series Noble Active Cathode Anode Volts (NHE): E 0

Standard conditions Standard states: For a solid; a =1: pure metal, metal oxide, etc. For a gas, 1 Atm pressure is taken as unit activity. For dilute solutes typically found in most instances of corrosion, activity is reasonably approximated by the concentration in M. The standard state is 1 M. Temperature is taken as 25ºC = 298 K definition: pH = -log [H + ]

Thermodynamics of Chemical Equations A, B … reactants X, Y … products a, b, …., x, y,…. Stoichiometric Coefficients defining how many moles of A and B produce moles of X and Y The chemical reaction can proceed as indicated if the energy change is negative. That is if the energy of the products is less then that of the reactants. Mathematically we say aA + bB xX + yY Energy of the standard state Activity or concentration “correction” -non standard state

Chemical Equilibrium aA + bB + … xX + yY + … A, B … reactants X, Y … products a, b, …., x, y,…. Stoichiometric Coefficients Equilibrium is defined by the condition Since ≣ standard free energy change /mole

K is the equilibrium constant for the reaction. Solving for The equilibrium constant is defined by When components are not in standard state: Chemical Equilibrium

Electrochemical Equilibrium Free energy is measured in units of kcal or kJ. 1 calorie=4.186 Joules 1Joule = 6.24 x eV Since 1 Volt = Joule/Coulomb where Q is the total charge. The total charge transferred in an electrochemical reaction will be equal to the number of moles of electrons participating in the reaction times the charge/mole, Q = nF By convention a minus sign relates ΔG and E.

Electrochemical Equilibrium If we flip the numerator and denominator in the argument of the ln function,

Electrochemical Equilibrium Nernst Equation Formal Potential

Electrochemical Equilibrium: pH effects We can write a general metal dissolution reaction in the following way: Here A could correspond to some oxidized species such as Fe 2+ and B would be its reduced form, metallic Fe. Alternatively A could be an oxide such as FeO and B its reduced form, also metallic Fe. The Nernst equation for this general reaction is

It’s convenient at this stage to convert the natural log (Ln) to base 10. In general: Ln (x) = Log (x) Also Electrochemical Equilibrium and Corrosion

The Nernst Equation above can now be rewritten as: Electrochemical Equilibrium and Corrosion

Examples: (1) Consider the reaction First note that for this and all simple metal dissolution reactions there is no H + in the reaction and no dependence of the reaction on pH, m = 0 The Fe 2+ is equivalent to A. Also a =1. The quantity [Fe 2+ ] is the concentration of Fe 2+ in the electrolyte. Fe is equivalent to B. Since Fe is a pure metal [Fe ] = 1 Then: This type of reaction is favored at low values of pH.

Electrochemical Equilibrium and Corrosion ΔE (V) [Fe 2+ ] M For every decade change in ferrous cations there is ~ 30 mV decrease in the equilibrium potential. What is the difference between an open circuit potential (corrosion potential) and an Equilibrium Potential????? – Lab.

Electrochemical Equilibrium and Corrosion (2) Consider Both Al and Al 2 O 3 are solids with unit activity, A=1, B=1. On a complete EMF series one could find that Also note that m = 6, n = 6 so, The equilibrium potential decreases by ~ 60 mV per pH unit. Examples: This type of reaction occurs at some intermediate value of pH.

Electrochemical Equilibrium and Corrosion (3) One other type of corrosion reaction that can occur involves the formation of a soluble metal oxide anion at some high pH, The ΔE for this reaction is a function of both the dissolved ion content and the pH of the electrolyte. Examples:

The above reaction occurs in an acid solution. An equivalent reaction in neutral or alkaline solutions is: Cathode reactions Supporting Corrosion Hydrogen reduction

The above reaction occurs in an acid solution. An equivalent reaction in neutral or alkaline solutions is: Cathode reactions Supporting Corrosion Oxygen reduction

Potential/pH (Pourbaix) Diagram It turns out to be very convenient to represent the results of all these anodic metal oxidation processes and cathodic reduction process on a Map-like “phase diagram”. The map considers the parameters of voltage and solution pH and shows the possible electrochemical/corrosion reactions that can occur for a particular metal such as Fe, Al, Cd, Zn, … and water.

Potential/pH (Pourbaix) Diagram oxygen evolution and acidification hydrogen evolution and alkalization water thermodynamically stable Water

Potential/pH (Pourbaix) Diagram Generic diagram for a metal pH POTENTIAL, E(V) Corrosion Passivation Immunity Corrosion-soluble ions of the metal are stable Passivation- oxides are stable Immunity-reduced form of the metal is stable

Potential/pH (Pourbaix) Diagram Reaction 1: Metal oxidizes to aqueous cations Pourbaix diagram for Al Independent of pH since no H + is involved. Only depends on Al 3+ activity

Potential/pH (Pourbaix) Diagram Reaction 2: Metal reacts to metal hydroxide or oxide Pourbaix diagram for Al At higher pH Al 2 O 3 is formed. At lower pH Al 2 O 3 chemically dissolves to Al 3+ Intersection depends depends on Al 3+ activity (dashed lines are portions of the reactions with no significance)

Potential/pH (Pourbaix) Diagram The reaction rate constant for Pourbaix diagram for Al is known For (Al 3+ )=10 -6, Independent of potential

Potential/pH (Pourbaix) Diagram Reaction 3: Metal reacts to form soluble aqueous anions Pourbaix diagram for Al At higher pH, Al 2 O 3 dissolves to AlO 2 -