Electrochemistry Lecture 2 Flashcards
What are the steps that describe the mechanism of electron transformation at the electrode?
The mechanism of a simple electron transfer without chemical transformation can be described using the following steps:
- Diffusion of the species to where the reaction occurs (described by a mass transfer coefficient kd).
- Rearrangement of the ionic atmosphere (10-8 s)
- Reorientation of the solvent dipoles (10^-11 s)
- Alterations in the distances between the central ion and the ligands (10^-14 s)
- Electron transfer (10^-16 s)
- Relaxation following the previous steps in the opposite order
A diagram showing this is in the lecture notes. In the figure [Ox]∞ and [Red]∞ refer to the bulk concentration of Ox and Red while [Ox]0 and [Red]0 refer to the concentration of Ox and Red at the electrode interface. Steps 2 to 5 are
included in the charge transfer rate constant kc or ka, which includes adsorption and desorption of soluble species. This makes since since steps 2-5 provide a different pathway to go to [Red]0
What is the rate equation for electrode reactions?
Look at written notes
What is overpotential?
The potential as calculated from the standard potentials and the Nernst equation is a thermodynamic limit of the system (The highest potential a cell can have).
Operating an electrochemical system will always require more energy, as the activation energy barrier must be overcome(due to resistance, charge transfer limitations, and diffusion effect). When expressed in terms of potential, we call the additional energy the overpotential 𝜂.
The overpotential is defined as follows:
𝜂 ≡ 𝐸observed − 𝐸Nernst(or E0)
Visualization of this definition is shown in the reader
How does this overpotential affect our current understanding of the galvanic and electrolytic cells?
With overpotential, we are now representing real systems. This means:
- In Galvanic cells, the actual voltage is always lower than the Nernst potential due to overpotentials (𝜂) from resistance, slow reaction kinetics, and other inefficiencies.
- in Electrolytic cells, the actual voltage required to drive the reaction is always higher than the Nernst potential because extra energy is needed to overcome activation barriers
What is overpotential used for?
The performance of different electrodes can be characterized and compared to each other using the overpotential, as a lower overpotential is indicative of that electrode being able to facilitate the reaction better. However, this does not tell the full story. The figure in the reader compares two electrodes, A and B, on which the same reaction occurs. Electrode A shows a
lower overpotential than electrode B, meaning that it takes less potential to start the reaction. However, the (absolute value of the) current density on electrode B increases more quickly with increasing potential compared to electrode A. Past a given potential, electrode B is the better option, as less potential needs to be applied to reach a given current density
Break moment
We are now going to attempt to derive an expression that relates the current density to the applied potential! First, we will show how the applied potential affects the gibbs free energy landscape of the system, and then how it affects the reaction rate.
What equation can we use to describe the rate constant (Trauma from oral)?
The rate constant can be described using the Arrhenius equation:
𝑘 = 𝐴 exp (−𝐸𝐴/ 𝑅𝑇)
With 𝐴 the pre-exponential factor or frequency factor and 𝐸𝐴 the activation energy. Even though this equation oversimplifies the situation, they do carry an essence of truth and allow us to grasp how reactions proceed and how they are affected by system parameters.
What is the definition of activation energy? LOL ;)
The activation energy can be understood as the change in standard internal energy from one of the minima (product or reactant) to the maximum (known as the transition state or activated complex). This is often referred to as the standard internal activation energy, Δ𝐸 ‡.
A reaction coordinate diagram is shown in the reader, which shows how products or reactants are minimums and so on
.
Based on the definition of activation energy what would the enthalpy of activation be defined as, and how will this affect the Arrhenius equation?
Look at written notes
What is the transition state theory?
It is a theory of kinteics that has been developed to to elucidate the factors controlling reaction rates. Central to the theory is the idea that reactions proceed through a well-defined transition state or activated complex, as described in the reaction coordinate diagram in the reader.
The standard Gibbs free energy change going from the reactant to the complex is ΔGf ‡, while the standard Gibbs free energy change from the activated complex to the product is denoted by ΔGb ‡. Transition state theory allows
us to derive the following expressions for the forward and backward rate constant:
𝑘𝑓 =(𝜅𝑘′/2)exp (−Δ𝐺𝑓‡/𝑅𝑇 )
and
𝑘𝑏 =(𝜅𝑘′/2)exp (−Δ𝐺𝑏‡/𝑅𝑇 )
With 𝜅 the transmission coefficient and 𝑘′ a combined rate constant related to the decay of the transition state into either the reactant or product. Statistical mechanics can be used to predict a value for 𝜅𝑘′⁄2, however, for simple cases 𝑘′ is shown to be equal to 2𝑘𝐵𝑇⁄ℎ. Thus both rate constants may be expressed as:
𝑘 =(𝜅𝑘𝐵𝑇/ℎ) exp (−Δ𝐺‡/𝑅𝑇 ) = 𝐵𝑐 exp (−Δ𝐺‡/𝑅𝑇 )
With 𝑘𝐵 the Boltzmann constant and ℎ the Planck constant.
How does potential affect the energy of the product and reactant species?
consider the following reaction:
Ox + e ⇋ Red
The figure in the reader shows reaction coordinate diagrams for three cases. The first case is when the applied potential is equal to the potential at equilibrium. As the system is at equilibrium the energy levels of the product and reactant are the same.
If the applied potential is increased above the potential at equilibrium, the energy of the reactant electron is lowered* which means that its Gibbs free energy curve drops with respect to the product. This increases the energy barrier for reduction (distance between Ox + e− and
transition state), which means that oxidation occurs more readily. This means that a net anodic current will flow.
Applying a potential lower than the potential at equilibrium does the opposite. The energy of the electron is raised*, which decreases the energy barrier towards reduction. As such reduction will occur more prominently, meaning a net cathodic current will flow.
*There is a relation between the energy of the electron, Gibbs energy and potential that hasn’t discussed in this course (up till now at least) that states that a more positive potential means a lower electron energy, while a more negative potential means a higher electron energy
When developing a theory of electrode kinetics, how is a reference point defined?
When developing a theory of electrode kinetics, it is useful to express the potential relative to a point that is significant to the chemistry of the system, rather than using arbitrary external references such as a reference electrode. There are two natural
reference points: the equilibrium potential of the system and the standard (or formal) potential of the redox couple under consideration. The equilibrium potential can only be used as a reference point when both components of the redox couple are present, so that an equilibrium can be defined. The more general reference point, therefore, is the standard potential and from it we will derive how the potential effects the Gibbs free energy profile!
How does the potential affect Gibb’s free energy profiles?
Look at the figure from the reader.
Suppose that the upper curve on the Ox + e-side holds when the electrode potential is equal to E0. The cathodic and anodic activation energies are then ΔGf‡0 and ΔGb‡0 respectively. If the potential is changed by ΔE to a new value E, the relative energy of the electron on the electrode changes by -F ΔE = -F(E-E0 ), as such the Ox + e− curve shifts up or down with that
amount (Up if the potential is negative since the electron gains energy and down if the potential is positive)
The diagram in the reader shows the effect of a positive ΔE. It can be observed that the
boundary for oxidation ΔGb‡ has become less than ΔGb ‡0 by a fraction of the total energy change. The fraction will be denoted as (1-α), with α the charge transfer coefficient. Expressed as an equation we get:
Δ𝐺𝑏‡ = Δ𝐺𝑏0‡ − (1 − 𝛼)𝐹(𝐸 − 𝐸0)
Δ𝐺𝑓‡ = Δ𝐺𝑓0‡ + 𝛼𝐹(𝐸 − 𝐸0)
What is the derivation of the Butler-Volmer equation?
With everything we have done so far we laid the groundwork to derive the Butler-Volmer equation, the model for electrode kinetics.
The derivation is in the reader
What is the definition of the exchange current density?
The exchange current density is the current density when the system is in equilibrium, i.e. the forward and backward reaction are occurring at the same rate *. The exchange current density can also be determined using the following equation:
𝑗0 = 𝜈𝑒𝐹𝑘0(𝑐Red)^𝛼 * (𝑐Ox)^(1−𝛼)
With 𝑐Red and 𝑐Ox the concentrations of Red and Ox in the bulk. If 𝑐Red = 𝑐Ox the equation can be simplified to:
𝑗0 = 𝜈𝑒𝐹𝑘0𝑐∞
*Gain intuition. It makes since that J0 is at equilibrium, as it holds for the standard Gibbs energy (G0) which occurs at equilbruim
Plotting the current denstiy against overpotential
Plotting the current density versus
the overpotential for α = 0.5 results
in the plot in the reader.
At positive overpotentials the current density will be dominated by the anodic part meaning that the Butler-Volmer equation can be estimated as j= jo exp((1-α)F*𝜂 )/(RT))
at negative overpotentials, the observed current density will be dominated by the cathodic part meaning j= jo exp((α)F*𝜂 )/(RT))
What is a symmetry factor and how does it differ from the charge transfer coefficient? (Just read it will never be asked)
In literature the charge transfer coefficient and symmetry factor (β) have been used
interchangeably. However, there is a major distinction between the symmetry factor and charge transfer coefficient. The symmetry factor β is strictly defined for a single step reaction and is related to the shape of the energy barrier and to the position of the activated complex along the reaction coordinate. A symmetry factor of 0.5 means that the activated complex is
exactly halfway between the reactant and product on the reaction coordinate, with its structure reflecting the reactant and product equally. For values of the symmetry factor smaller than 0.5,
the activated complex resembles the product more, while for values larger than 0.5, the complex resembles the reactant more (Shown in the reader).
To describe a multistep process, β must be replaced by an experimental parameter, called the charge transfer coefficient, α. For simplicity, the equations used in this course have been adjusted to only use the charge transfer coefficient.
What is the Tafel analysis and the Tafel equation?
The Tafel analysis is a technique that allows to obtain kinetic performance parameters of a system, being the charge transfer coefficient, exchange current density and the Tafel slope. The Tafel equation can
be written as:
𝜂 = 𝑎 + 𝑏 log |𝑗|, With 𝑎 and 𝑏 empricial constant.
In a Tafel analysis, the overpotential is plotted against the logarithm of the absolute value of the current density.
This results in a Tafel plot, as shown in the reader. At large enough overpotentials (|𝜂| > ~0.1 V), the Tafel plot becomes linear, which is the region where we can apply the Tafel equation. Other conditions which need to be met for the Tafel equation to be applicable are no mass transport limitations, uniform current distribution and no interference by film formation
What does the empirical parameter b mean in the tafel equation?
The empirical parameter 𝑏 has been termed the Tafel slope (often shortened to TS), commonly expressed in the units mV dec−1, with the dec referring to the current density in A cm−2. The
Tafel slope expresses how many volts of the potential need to be applied to increase the current density 10-fold or by a dec (which is shoer for decay)!
what is the derivation of the Tafel equation(imp)?
Using the Butler-Volmer equation we can derive the Tafel equation from theory. Assuming large enough overpotentials we can simplify the Butler-Volmer equation for two cases: large positive overpotentials and large negative overpotentials as shown in written notes.
Back to FC:
Note two things:
The observant reader will have noticed that for the simplification at large negative
overpotentials a minus sign (in front of 𝑗0) has disappeared after taking the natural logarithm of both sides of the equation. The minus sign has disappeared as the absolute value of the current density is taken within the natural logarithm, i.e. the minus sign has no significance anymore. When rewriting this equation to calculate the cathodic overpotential, one has to
remember that the cathodic current density is by definition smaller than 0. To account for this, one either needs to add back in the minus sign or take the absolute bars along.
𝜂𝑐𝑎𝑡 = −𝑅𝑇/𝛼𝐹 ln (−𝑗/𝑗0) or 𝜂𝑐𝑎𝑡 = −𝑅𝑇/𝛼𝐹 ln (|𝑗|/𝑗0)
Fitting the Logmertirc equation (not the final one) to a Tafel plot (albeit one with the axes switched), one can obtain the exchange of the current density from the y-intercept and the charge transfer coefficient from the slope. Look at the reader!!
How does the Tafel slope change with different mechanisms?
The table (in reader) shows examples of values for different mechanisms. It allows to determine the reaction mechanism up to the rate determining step. The reactions after the rate determining step do not influence the value of the Tafel slope, meaning that E, EC, ECE, EEC, etc. mechanisms will result in the same Tafel slope.
