Electrochemical methods : Fundamentals and Applications ... · PDF file10.03.2014 · Kwang Kim Yonsei University [email protected] Electrochemical methods : Fundamentals and Applications

Kwang Kim

Yonsei University

[email protected]

Electrochemical methods : Fundamentals and Applications

Introduction

March 05, 2014

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Y88.91

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O16.00

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I126.9

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Se78.96

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N14.01

Electrochemical Cell

A dc electrochemical cell consists of two electrical conductors called electrodes, each immersed in a suitable electrolyte solution. For a current to develop in a cell, it is necessary (1) that the electrodes be connected

externally by means of a metal conductor,

(2) that the two electrolyte solutions be in contact to permit movement of ions from one to the other, and

(3) that an electron transfer reaction can occur at each of the two electrodes.


Electrode/electrolytic solution interface


Electrode :

A phase containing

electrons

Electrolytic Solution:

A phase containing

ions

Electron and Ion Charge Transfer Reaction at an electrode solution interface



Electrode :

A phase containing

electrons

Electrolytic Solution:

A phase containing

ions

Electron and Ion Charge Transfer Reaction at an electrode solution interface


Ionics:Concerns ions in solution in terms of material transport, ion distribution ion/solvent,and ion/ion interactions

Electrodics:Concerns the region between an electronic and ionic conductor and the transfer of electric charge across it in terms of electrode potential, polarization, charge transfer kinetics

Reaction at each electrode (half cell reaction)

Differing reactivities of metals of Mg and Cu:

When metals react, they give away electrons and form positive ions. This particular topic sets about comparing the ease with which a metal does this to form hydrated ions in solution ‐ for example, Mg2+(aq) or Cu2+(aq).

OHMe)(OHMe 22 nMezenz

Ions are surrounded by polar water molecules.


Differing reactivities of metals of Mg and Cu:


Oxidation and Reductionequilibrium reaction at a single electrode E° (volts)

‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50

•The more positive the E° value, the further the position of equilibrium lies to the right.

•That means that the more positive the E° value, the more likely the substances on the left-hand side of the equations are to pick up electrons.

•A substance which picks up electrons from something else is an oxidisingagent.

•The more positive the E° value, the stronger the substances on the left-hand side of the equation are as oxidising agents.

•Chlorine gas is the strongest oxidisingagent (E° = +1.36 v).

•A solution containing dichromate(VI) ions in acid is almost as strong an oxidising agent (E° = +1.33 v).

•None of these three are as strong an oxidising agent as Au3+ ions (E° = +1.50 v).

Differing reactivities of metals:




In the magnesium case, there is a lot of difference between the negativeness of the metal and the positiveness of the solution around it. In the copper case, the difference is much less.

This potential difference could be recorded as a voltage ‐ the bigger the difference between the positiveness and the negativeness, the bigger the voltage. Unfortunately, that voltage is impossible to measure!

It would be easy to connect a voltmeter to the piece of metal, but how would you make a connection to the solution? By putting a probe into the solution near the metal? No ‐ it wouldn't work!


Voltmeter Can you measure the potential difference between the metal and the solution directly? How?

V

The potential difference between metal and the probe (usually another metal)


Voltmeter Any probe you put in is going to have a similar sort of equilibrium happening around it. The best you could measure would be some sort of combination of the effects at the probe and the piece of metal you are testing.

M1 M2M1z+

----

--

++

++++

Reference electrode

Suppose you had an optical device for measuring heights some distance away, and wanted to use it to find out how tall a particular person was. Unfortunately, you can't see their feet because they are standing in long grass.

Although you can't measure their absolute height, what you can do is to measure their height relative to the convenient post. Suppose that in this case, the person turned out to be 15 cm taller than the post.You could repeat this for a range of people . . .

Although you don't know any of their absolute heights, you can usefully rank them in order, and do some very simple sums to work out exactly how much taller one is than another.

person height relative to post (cm)

C +20

A +15

B -15


‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50








Oxidation and Reduction

Galvanic CellsThe net cell reaction that occurs in the cell composed of Zn and Cu is the sum of the two half-cell reactions

Zn(s) + Cu2+ Zn2+ + Cu(s)

Cells that are operated in a way that produces electrical energy are called galvanic cells.

copper electrode (Cu metal in CuSO4) coupled with zinc electrode (Zn metal in ZnSO4)

Electrodics:

Concerns the region between an electronic and ionic conductor and the transfer of electric charge across it in terms of electrode potential, polarization, charge transfer kinetics

‐ Electrode potentials‐ Electrochemical potential‐ Potentials and Thermodynamics of cells‐ Electrode potential – the Nernst equation‐ Electrical double layer‐ Electrode kinetics – basic principles ‐ Electrode kinetics – BV and microscopic treatment‐ Adsorption phenomena

Volta potential () or outer potential is the part of total potential difference across metal-electrolyte interface.• Defined as the work required to bring a unit point charge from infinity to a point just outside the surface of the phase by a distance of about 10−5~ 10−3 cm from surface. • Outer potential is a measurable quantity.

Galvani potential () or inner potential is the electrostatic potential which is actually experienced by a charged particle inside the phase.• Defined as the work required to bring a unit point charge from infinity to a point inside the phase.• Inner potential is not measurable.

The inner and outer potential differ by the surface potential ()• Caused by an inhomogeneous charge distribution at the surface• Can not be measured　　　　

(Galvani potential)

(Volta potential)

(surface potential)

Galvani potential and Electrochemical potential

Zero energy–charged particle in vacuum at infinite separation from a charged phase

1. Electrochemical potential (μ) work done when a charged particle is transferred from infinite separation in vacuum to the interior of a charged phase

2. Chemical potential (μ)work done when an uncharged particle is transferred from infinite separation in vacuum to the interior of an uncharged phase stripped from the charged surface layer

3. Inner potential (Galvani potential, φ) work done when a charged particle is transferred from infinite separation in vacuum across a surface shell which contains an excess charge and oriented dipoles

Electrochemical potential

zi is the charge on species i, , the inner potential,is the potential of phase .

iii ez 0

Electrochemical potential

1) If z = 0 (species uncharged)

2) for a pure phase at unit activity

3) for species i in equilibrium between and .

ii ,0

ii

ii

Inner, outer and surface potential

(1) Potential in vacuum:

the potential of certain point is the work done by transfer unitpositive charge from infinite to this point. (Only coulomb force isconcerned).

x xFdx dx

- strength of electric fieldF e

This process can be divided into two separated steps.

Vacuum, infinitecharged sphere

++

++

Electrochemical reaction can be simplified as the transfer of electron from species in solution to inner part of an electrode.

W2 +

10-6 ~ 10-7 m

W1

(2) Potential of solid phase

The work (W1) done by moving a test charge from infinite to 10-6 ~ 10-7 m vicinity to the solid surface (only related to long-distance force) is outer potential.

Outer potential also termed as Volta Potential () is the potential measured just outside a phase.

10-6 ~ 10-7 m

W1

Moving unit charge from vicinity (10 –6 ~10-7 m) into inner of the sphere overcomes surface potential (). Short-distance force takes effect.

W2 +

W2

For hollow ball, can be excluded.

arises due to the change in environment experienced by the charge (redistribution of charges and dipoles at the interface)

(3) Inner, outer and surface potential

W2

10-6 ~ 10-7 m

W1

The total electrical work done for moving unit charge to the innercharged sphere is W1 + W2

= (W1+ W2) / z e0 = + The electrostatic potential within a phase termed the Galvani potential or inner potential ().

If short-distance interaction, i.e., chemical interaction, is taken intoconsideration, the total energy change during moving unite testcharge from infinite to inside the sphere: chemical potential

inner

hollow

10-6~10-7 m

infinitedistance

Work function

work function

the minimum energy (usually measured in electron volts) neededto remove an electron from a solid to a point immediately outside the solid surface or energy needed to move an electron from the Fermi energy level into vacuum.

For two conductors contacting with each other at equilibrium,their electrochemical potential is equal.

e e

0e ee 0e e

e =

eΔ 0 e e

0

Δe

0e e( )e

0 0 0 0e ee e e e

0 0 0 0( ) ( ) ( )e e

e e e e

0eWee

0eW

e

0e

W Δ 0 Δ 0

different metal with different

0e ee 0e e

e =


‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50








Reference Electrode

Standard hydrogen electrode

As the hydrogen gas flows over the porous platinum, an equilibrium is set up between hydrogen molecules and hydrogen ions in solution. The reaction is catalysed by the platinum.

This is the equilibrium that we are going to compare all the others with.

Standard conditions:‐Hydrogen pressure is 1 bar (100 kPa). (You may find 1 atmosphere quoted in older sources.) ‐Temperature is 298 K (25°C).‐ All ions concentrations are taken as being 1 mol dm‐3.

There is a major difference between the charge on the two electrodes ‐ a potential difference which can be measured with a voltmeter. The voltage measured would be 2.37 volts and the voltmeter would show the magnesium as the negative electrode and the hydrogen electrode as being positive.

The copper is the more positive (less negative) electrode. The voltage measured would be 0.34 volts The voltmeter will show the hydrogen electrode as the negative one and the copper electrode as positive.

VoltmeterYou may have noticed that the voltmeter was described as having a "high input resistance". Ideally, it wants to have an infinitely high input resistance.

This is to avoid any flow of current through the circuit. If there was a low resistance in the circuit, electrons would flow from where there are a lot of them (around the magnesium, for example) to where there are less (on the hydrogen electrode).

If any current flows, the voltage measured drops. In order to make proper comparisons, it is important to measure the maximum possible voltage in any situation. This is called the electromotive force or emf.

The emf of a cell measured under standard conditions is given the symbol E°cell.

You read E° as "E nought" or "E standard".

There is a major difference between the charge on the two electrodes ‐ a potential difference which can be measured with a voltmeter. The voltage measured would be 2.37 volts and the voltmeter would show the magnesium as the negative electrode and the hydrogen electrode as being positive.

The copper is the more positive (less negative) electrode. The voltage measured would be 0.34 volts The voltmeter will show the hydrogen electrode as the negative one and the copper electrode as positive.


‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50








Standard Hydrogen Electrode (SHE)Hydrogen gas electrodes were widely used not only as reference electrodes but also as indicator electrodes for the determination of pH.The composition of this type of electrode can be represented as

Pt, H2(p atm) H+(aH+ = x)

The potential at the platinum surface depends upon the hydrogen ion activity of the solution and upon the partial pressure of the hydrogen used to saturate the solution. Hydrogen is oxidized to hydrogen ions when the electrode is an anode; the reverse reaction takes place as a cathode.

For the standard hydrogen electrode call for a hydrogen ion activity of unity and a partial pressure for hydrogen of exactly one atmosphere. By convention, the potential of this electrode is assigned the value of exactly zero volt at all temperatures.

Standard Hydrogen Electrode (SHE)

Cell conventions

SHE

Typical electrochemical cells and their notations

Zn Ag PtH2 Ag

Practical Reference ElectrodesThe standard hydrogen electrode is of great fundamental importance, the difficulty in preparing the electrode surface and controlling the activities of the reactants make it impractical enough.

Reference electrodes that are simple to prepare, more rugged, and easier to use are normally substituted for the hydrogen gas electrode.

One of the most common of these is the silver/silver chloride electrode. This electrode can be prepared by applying an oxidizing potential to a silver wire immersed in a dilute solution of hydrochloric acid.The potential of this electrode is about 0.2 V positive with respect to the standard hydrogen electrode. The electrode half-reaction is

2AgCl(s) + e - Cl - + 2Ag(s)

A second widely used reference electrode is the saturated calomel electrode (SCE), which consists of a pool of mercury in contact with a solution that is saturated with mercury(I) chloride (calomel) as well as potassium chloride. The potential of this reference is about 0.24 V positive. The electrode reaction is

Hg2Cl2(s) + 2e - 2 Cl - + 2Hg(l)

Standard Hydrogen Electrode (SHE), or Normal Hydrogen Electrode (NHE)

Reference electrodes

Saturated Calomel Electrode (SCE)

Silver-silver Chloride Electrode

E0 = 0 V ASSUMED

E0 = 0.241 V

E0 = 0.197 V


‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50








Ideal polarizable electrode vs. ideal nonpolarizable electrode

An ideal polarized electrode shows a verylarge change in potential upon the passage of a small current. Ideal polarizability is characterized by a horizontal region of an i-E curve

Ideal nonpolarizable electrode is an electrode whose potential does not change upon passage of current.Nonpolarizability is characterized by a vertical region on an i-E curve.

i

E

i

E

(a) Non-Faradaic Process : Double Layer Charge/Discharge

(b) Faradaic Process : Charge Transfer Reaction, Redox reaction

Electrode Solution

:Electric Double Layer Capacitance

: Charge Transfer Resistance

Non‐Faradaic Current

Faradaic Current

Electrode/Solution Interface

Ideal polarizable electrode

An ideal polarized electrode shows a verylarge change in potential upon the passage of a small current. Ideal polarizability is characterized by a horizontal region of an i-E curve

i

E

An electrode at which no chargetransfer across the metal-solutioninterface occurs regardless of thepotential imposed by an outsidesource of voltage.

All charging current.

Electrode Solution


: Charge Transfer Resistance = =


Faradaic Current

Ideal nonpolarizable electrode

Ideal nonpolarizable electrode is an electrode whose potential does not change upon passage of current.Nonpolarizability is characterized by a vertical region on an i-E curve.

i

E

Ag(s) | AgCl(s) | Cl (aq.)

Ag(s) + Cl AgCl(s) + 1e

No charging current.

Electrode Solution


: Charge Transfer Resistance = 0


Faradaic Current

Ideal polarizable electrode vs. ideal nonpolarizable electrode


‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50








Definition of Electrode PotentialElectrode potentials are defined as cell potentials for a cell consisting of the electrode acting as a cathode and the standard hydrogen electrode acting as an anode.

The electrode potential for the half-reaction M2+ + 2e- M(s)

Here, the half-cell on the right (the cathode) consists of a strip of the metal M in contact with a solution of M2+. The half-cell on the left (the anode) is standard hydrogen electrode. By definition, the potential E observed on the voltage-measuring device is the electrode potential for the M/M2+ couple.

Pt l H2 (1 atm), l H+(a=1) ll M2+ (a=1) l M

Schematic Representation of Cells

Zn ZnSO4(aZn 2+ = 0.0100) CuSO4(aCu 2+ = 0.0100) Cu

By convention, the anode and information about the solution with which it is in contact is always listed on the left. Single vertical lines represent phase boundaries across which potential differences may develop.

Schematic Representation of CellsTo simplify the description of cells, chemists often employ a shorthand notation, can be described byZn ZnSO4(aZn 2+ = 0.0100) CuSO4(aCu 2+ = 0.0100) Cu

- Single vertical line indicates change in state or phase. - Activities of aqueous solutionn are written in parentheses afterthe symbol for the ion or molecule.

- A double vertical line indicates a junction between half-cells. - The line notation for the anode (oxidation) is written before

the line notation for the cathode (reduction).

Anode Solution in contact with anode Solution in contact with anode Cathode

If we assume that the activity of M2+ in the solution is exactly 1.00, the potential is called the standard electrode potential for the system and is given the symbol E0. That is, the standard electrode potential for a half-reaction is the electrode potential when the reactants and products are all at unit activity.

Sign Conventions for electrode PotentialsAccording to the IUPAC convention, the term electrode potential is reserved exclusively for half-reaction written as reductions. An oxidation potential should never be called an electrode potential.

The sign of the electrode potential is determined by the actual sign of the electrode of interest when it is coupled with a standard hydrogen electrode in a galvanic cell. Thus, a zinc or a cadmium electrode will behave as the anode from which electrons flow through the external circuit to the standard hydrogen electrode. These metal electrodes are thus the negative terminal of such galvanic cells, and their electrode potentials are assigned negative values.

Thus, Zn2+ + 2e- Zn(s) E0 = -0.763 V

Cd2+ + 2e- Cd(s) E0 = -0.403 V

Pt l H2 (1 atm), l H+(a=1) ll Zn2+ (a=1) l Zn

Pt l H2 (1 atm), l H+(a=1) ll Cd2+ (a=1) l Cd

The potential for the copper electrode is given a positive sign because the copper behaves as a cathode in a galvanic cell constructed from this electrode and the hydrogen electrode; electrons flow toward the copper electrode through the external circuit.

It is thus the positive terminal of the galvanic cell and for copper, we may write

Cu2+ + 2e- Cu(s) E0 = +0.337 V

The sign of the electrode potential indicates whether or not the reduction is spontaneous with respect to the standard hydrogen electrode.

Pt l H2 (1 atm), l H+(a=1) ll Cu2+ (a=1) l Cu


‐3.03

‐2.92

‐2.87

‐2.71

‐2.37

‐1.66

‐0.76

‐0.44

‐0.13

0

+0.34

+0.77

+0.80

+1.33

+1.36

+1.50








CALCULATION OF CELL POTENTIALS FROM ELECTRODE POTENTIALS

An important use of standard electrode potentials is the calculation of the potential obtainable from a galvanic cell or the potential required to operate an electrolytic cell.The electromotive force of a cell is obtained by combining half-cell potentials as follows: Ecell = Ecathode – Eanode

where, Eanode and Ecathode are the electrode potentials for the two half-reactions constituting the cell.

Consider the hypothetical cellZn | ZnSO4(aZn2+ = 1.00) || CuSO4 (aCu2+ = 1.00) | Cuusing E0 data, Ecell = +0.337 –(-0.763) = +1.100 V

The positive sign for the cell potential indicates that the reactionZn(s) + Cu2+ 　 Zn2+ + Cu(s)

occurs spontaneously and that this is a galvanic cell.

Combining a zinc with a copper half cellSo far, we have looked at combinations of a hydrogen electrode with the half cell we have been interested in. What happens if you combine a zinc half cell with a copper half cell?

In the presence of a high resistance voltmeter

The two equilibria which are set up in the half cells are:

The negative sign of the zinc E° value shows that it releases electrons more readily than hydrogen does. The positive sign of the copper E° shows that it releases electrons less readily than hydrogen.

That means that you can compare any two equilibria directly. For example, in this case you can see that the zinc releases electrons more readily than the copper does ‐ the position of the zinc equilibrium lies further to the left than the copper equilibrium.

Combining a zinc with a copper half cellStripping everything else out of the diagram, and looking only at the build up of electrons on the two pieces of metal:

Removing the voltmeter

The high resistance of the voltmeter is deliberately designed to stop any current flow in the circuit. What happens if you remove the voltmeter and replace it with a bit of wire?

Electrons will flow from where there are a lot of them (on the zinc) to where there are fewer (on the copper). The movement of the electrons is an electrical current. Zn Cu

Combining a zinc with a copper half cellElectrons are flowing away from the zinc equilibrium. According to Le Chatelier's Principle, the position of equilibrium will move to replace the lost electrons.

Electrons are being dumped onto the piece of copper in the copper equilibrium. According to Le Chatelier'sPrinciple, the position of equilibrium will move to remove these extra electrons.

If electrons continue to flow, the positions of equilibrium keep on shifting. The two equilibria essentially turn into two one‐way reactions. The zinc continues to ionise, and the copper(II) ions keep on picking up electrons.

Zn Cu

Combining a zinc with a copper half cellWhat occurs when you drop a piece of zinc into some copper(II) sulphate solution?

The blue color of the copper sulphate solution fades as the copper(II) ions are converted into brown copper metal. The final solution contains zinc sulphate. (The sulphate ions are spectator ions.)

You can add the two electron‐half‐equations above to give the overall ionic equation for the reaction

The only difference in this case is that the zinc gives the electrons directly to the copper(II) ions rather than the electrons having to travel along an external circuit.

Galvanic CellsThe net cell reaction that occurs in the cell composed of Zn and Cu is the sum of the two half-cell reactions

Zn(s) + Cu2+ Zn2+ + Cu(s)Cells, that are operated in a way that produces electrical energy, are called galvanic cells.

Electrolytic cells It consume electrical energy, e.g. the cell under discussion could be made electrolytic by connecting the negative terminal of a dc power supply to the zinc electrode and the positive terminal to the copper electrode.

Electrolytic cells If the output of this supply was made somewhat greater than 1.1 V, the two electrode reactions would be reversed and the net cell reaction would become

Cu(s) + Zn2+ Cu2+ + Zn(s)

A cell in which reversing the direction of the current simply reverses the reactions at the two electrodes is termed a chemically reversible cell.

Combining a zinc with a copper half cellElectrons are flowing away from the zinc equilibrium. According to Le Chatelier's Principle, the position of equilibrium will move to replace the lost electrons.

Electrons are being dumped onto the piece of copper in the copper equilibrium. According to Le Chatelier'sPrinciple, the position of equilibrium will move to remove these extra electrons.

If electrons continue to flow, the positions of equilibrium keep on shifting. The two equilibria essentially turn into two one‐way reactions. The zinc continues to ionise, and the copper(II) ions keep on picking up electrons.

Zn Cu

Anode : oxidation rxn

Cathode : reduction rxn


Anion : -ve ion

Cation : +ve ion

Anode : electrode for oxidation reaction

Cathode : electrode for reduction reaction

Galvanic or Electrolytic (Voltaic) cells

Chemical reaction : material transformation

Electrochemical reaction : material transformation and electron flow

Galvanic cell : electron as a product

Use a chemical reaction (material transformation) to generate electrical energy

Ex) discharging of a secondary battery

Electrolytic cell: electron as a reactant

Use electrical energy to drive a chemical reaction (material transformation)

Ex) Charging of a secondary battery

Galvanic cellElectric load

Zn Zn2+ + 2e

Electron generation

Anodic oxidation

Cu2+ + 2e Cu

Electron consumption

Cathodic reduction

Electron flow Electron flow

+ve‐ve

Current flow

Electrolytic cellDC power supply

Zn2+ + 2e Zn


Cathodic reduction

Cu Cu2+ + 2e

Electron generation

Anodic oxidation


+ve‐ve

Current flow

Galvanic cell vs. Electrolytic cell

Electric load

Zn Zn2+ + 2e

Electron generation

Anodic oxidation

Cu2+ + 2e Cu


Cathodic reduction


+ve‐ve

Current flow

DC power supply

Zn2+ + 2e Zn


Cathodic reduction

Cu Cu2+ + 2e

Electron generation

Anodic oxidation


+ve‐ve

Current flow

Galvanic cell Electrolytic cell

Electrochemical cell determines the polarity of electrodes.

DC power supply determines the polarity of electrodes.

REDOX POTENTIALS

E° values are positive. Neither copper nor silver produce ions and release electrons as easily as hydrogen does.

However, of the two, copper releases electrons more readily. In a cell, the copper would have the greater build up of electrons, and be the negative electrode. If the copper and silver were connected by a bit of wire, electrons would flow from the copper to the silver.

Whenever you link two of these equilibria together:The equilibrium with the more negative (or less positive) E° value will move to the left.The equilibrium with the more positive (or less negative) E° value will move to the right.

REDOX POTENTIALS Magnesium reacts with dilute sulphuric acid to give hydrogen and a colourless solution containing magnesium sulphate.

Is this what you would expect from the E° values?

REDOX POTENTIALS Potassium dichromate(VI) acidified with dilute sulphuric acid oxidises iron(II) ions to iron(III) ions. The orange solution containing the dichromate(VI) ions turns green as chromium(III) ions are formed.

Electrons are flowing from the Fe3+/Fe2+ equilibrium to potassium dichromate equilibrium.

Documents

Electrochemical methods : Fundamentals and Applications ... · PDF file10.03.2014 · Kwang Kim Yonsei University [email protected] Electrochemical methods : Fundamentals and Applications