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Physical Chemistry (CHM3101)Equilibrium Electrochemistry

Reference: Atkins, 9th Edition, Chapter 6

Equilibrium Electrochemistry

IntroductionHalf-reactions and electrodesVarieties of CellsLiquid Junction PotentialsThe Cell PotentialThe Nernst EquationCells at EquilibriumStandard Electrode PotentialApplications of Standard PotentialThe Electrochemical SeriesThe determination of activity coefficientsThe determination of equilibrium ConstantsThe determination of thermodynamic functions

2Introduction An electrochemical cell is consisted of two electrodes or metallic conductors in contact with an electrolyte, an ionic conductor.An electrode and its electrolyte compromise an electrode compartment.

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3The two electrode may share the same compartment.If the electrolytes are different, the two compartments may be joined by a salt bridge.A salt bridge is a tube containing a concentrated electrolyte solution such as potassium chloride that completes the electrical circuit and enables the cell to function.

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A galvanic cell is an electrochemical cell that produces electricity as a result of the spontaneous reaction occurring inside it.

An electrolytic cell is an electrochemical cell in which a non-spontaneous reaction (redox reaction) is driven by an external source of current.

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A Galvanic cell, or Voltaic cell, is an electrochemical cell that derives electrical energy from spontaneous redox reaction taking place within the cell. It generally consists of two different metals connected by a salt bridge, or individual half-cells separated by a porous membrane.

In electrochemical reaction, a more active metal atom will give up one or more of its electrons to the ions of less active metal.

An electrolytic cell is an electrochemical cell that undergoes a redox reaction when electrical energy is applied. It is most often used to decompose chemical compounds, in a process called electrolysis. When electrical energy is added to the system, the chemical energy is increased. Similarly to a galvanic cell, electrolytic cells usually consist of two half cells.Important examples of electrolysis are the decomposition of water into hydrogen and oxygen, and bauxite into aluminium and other chemicals.An electrolytic cell has three component parts: an electrolyte and two electrodes (a cathode and an anode). The electrolyte is usually a solution of water or other solvents in which ions are dissolved. Molten salts such as sodium chloride are also electrolytes. When driven by an external voltage applied to the electrodes, the electrolyte provides ions that flow to and from the electrodes, where charge-transferring (also called faradaic or redox) reactions can take place. Only for an external electrical potential (i.e. voltage) of correct polarity and sufficient magnitude can an electrolytic cell decompose a normally stable, or inert chemical compound in the solution. The electrical energy provided undoes the effect of spontaneous chemical reactions.

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6Half Reactions and ElectrodesOxidation is the removal of electrons from the species.Reduction is the addition of electrons to a species.A redox reaction is a reaction in which there is a transfer of electrons from one species to another.The reducing agent (or reductant) is the electron donor.The oxidizing agent (or oxidant) is the electron acceptor.Any redox reaction is expressed as the difference of two reduction half-reactions.The reduced and oxidized species in a half-reaction form a redox couple.Ox + v e- Red7Cu -> Cu2+ + 2e

Cu2+ + 2e -> Cu

7For example, consider this reaction:AgCl (s) Ag+ (s) + Cl- (aq)

This is not a redox reaction but it can be expressed as: AgCl (s) + e- Ag (s) + Cl- (aq) Ag+ (aq) + e- Ag (s)

Thus, the redox couple are AgCl/Ag and Ag+/Ag.

Q. Express the formation of H2O from H2 and O2 in acidic solution (a redox reaction) as the difference of two reduction half-reactions.8For example, consider reaction below:FeSO4 + KMnO4 +H2SO4 Fe2(SO4)3 + K2SO4 + MnSO4 + H2OConcentrate first on the net ionic reaction:Fe2+ + MnO4- + H+ Fe3+ + Mn2+ + H2OAt first glance you can see: Fe2+ Fe3+ (+2 to +3 = +1)MnO4- Mn2+ (+7 to +2 = -5)Balance these half reactions using electrons to balance charge:Fe2+ Fe3+ + e-Using simple balancing by inspection we will add two coefficients to balance atoms:MnO4- + 8H+ Mn2+ + 4H2OThen:MnO4- + 8H+ + 5e- Mn2+ + 4H2ONow:5Fe2+ 5Fe3+ + 5e-Add both reactions: MnO4- + 8H+ + 5Fe2+ + 5e- Mn2+ + 4H2O + 5Fe3+ + 5e-After cancelling electrons:MnO4- + 8H+ + 5Fe2+ Mn2+ + 4H2O + 5Fe3+2KMnO4 + 10FeSO4 + 8H2SO4 5Fe2(SO4)3 + K2SO4 + 2MnSO4 + 8H2O

9K did not change the charge (+1) 9Therefore, in a cell we have;Red1 Ox1 + v e- Ox2 + v e- Red2

The electrode at which oxidation occurs is called the anode.

The electrode at which reduction occurs is called the cathode.

In galvanic cell the cathode has a higher potential than the anode.

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Anode electrode lose electron, ion near to anode will lose electron as well and will experience oxidation.

Cathode electrode receive electron, ion near to cathode will receive electron as well, and will experience rduction10Varieties of CellsGalvanic cell is the simplest type of a cell. There is a single electrolyte common to both electrodes.

Daniell cell is a cell with different electrolytes in which the redox couple at one electrode is Cu2+/Cu and at the other is Zn2+/Zn.

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Concentrations Cells

Electrolyte concentration cell has identical electrode compartments except for the concentrations of the electrolytes

For example:(Zn|Zn2+ (C1))/Anode || (Zn2+ (C2 )|Zn)/Cathode

In an electrode concentration cell, the electrodes themselves have different concentrations.

They are gas electrodes operating at different pressures. For example:(Pt,H2 (Pressure p1))/Anode |H+ | (H2 (Pressure p2)Pt)/Cathode

They are amalgams (solutions in mercury) with different concentrations.Cd(s), Hg(s) | CdCl2(aq) || AgCl(s) | Ag(s)12A concentration cell is a limited form of a galvanic cell that has two equivalent half-cells of the same material differing only in concentrations.(everything is the same except electrolyte concentration)12Two solutions of different concentrations are in contact with each other. The more concentrated solution will have a tendency to diffuse into the comparatively less concentrated one. The rate of diffusion of each ion will be roughly proportional to its speed in an electric field. If anion diffuses more rapidly than the cation, it will diffuse ahead into the dilute solution leaving the later negatively charged and the concentrated solution positively charged. So an electrical double layer of positive and negative charges will be produced at the junction of the two solutions & as a result, a difference of potential will develop because of the ionic transfer. This potential is called liquid junction potential or diffusion potential. The magnitude of the potential depends on the relative speeds of the ions.

13Liquid Junction PotentialSimilar concept of osmisis, higher concentration diffuse to lower concentration of solution.

Liquid junction potential occurs when two solutions of different concentrations are in contact with each other. The more concentrated solution will have a tendency to diffuse into the comparatively less concentrated one. The rate of diffusion of each ion will be roughly proportional to its speed in an electric field. If the anion diffuses more rapidly than the cation, it will diffuse ahead into the dilute solution, leaving the latter negatively charged and the concentrated solution positively charged. So an electrical double layer of positive and negative charges will be produced at the junction of the two solutions. So at the point of junction, a potential difference will develop because of the ionic transfer. This potential is called liquid junction potential or diffusion potential. The magnitude of the potential depends on the relative speeds of the ions.13Consider a Daniall cell. Here, there is an additional source of potential difference across the interface of two electrolytes. This potential is called liquid junction potential, Elj.

The contribution of Elj can be reduced (to about 1 to 2 mV) by joining the electrolyte compartments through a salt bridge.14

Or another example can be different concentrations of hydrochloric acid. At the junction the mobile H+ ions diffuse into the more dilute solution. The bulkier Cl- ions follow, but initially do so more slowly which results in a potential difference at the junction.NotationPhase boundaries are denoted by a vertical bar, For example:Pt (s) | H2(g) | HCl(aq) | AgCl (s) | Ag (s)

A double vertical line means there is no liquid junction potential, such as:Zn (s) | ZnSO4 (aq) || CuSO4 (aq) | Cu (s)

Some gas electrodesPt | Cl2, HCl (aq, 0.1 mol L-1) Pt | H2, H3O+ (aq, 1 mol L-1)

15The Cell PotentialConsider a galvanic cell. The current produced by this cell comes from the spontaneous reaction taking place inside it.

The cell reaction is the reaction in the cell written on the assumption that;The right-hand electrode is the cathodeThus, the spontaneous reaction is the reduction at the right-hand compartment.

For example, In a cell such as;Zn (s) | ZnSO4 (aq) || CuSO4 (aq) | Cu (s)

Right-hand electrode: Cu2+ (aq) + 2 e- Cu (s)Left-hand electrode: Zn2+ (aq) + 2 e- Zn (s)

Therefore;Cu2+ (aq) + Zn (s) Cu (s) + Zn2+ (aq)16Question

Write the cell reaction and electrode half-reactions for following cells:

Pt|Cl2 (g)| HCl (aq) || Ag2CrO4 (aq)|Ag (s)Pt|Fe3+ (aq), Fe2+ (aq) || Sn4+ (aq), Sn2+ (aq) | PtCu|Cu2+ (aq) || Mn2+ (aq), H+ (aq) | MnO2(s) | Pt17Do as homework17Standard Electrode Potential (E0)The potential difference across an electrochemical cell is the potential difference measured between two electronic conductors connected to the electrodes.

In the external circuit, the electrons will flow from the most negative point to the most positive one and, by convention, the current will flow in the opposite direction.

Since the electrode potential can be either positive or negative, the electrons in the external circuit can also be said to flow from the least positive electrode to the most positive electrode.

A voltmeter may be used to measure the potential differences across electrochemical cells but cannot measure directly the actual potential of any single electrode.

Nevertheless, it is convenient to assign part of the cell potential to one electrode and part of that to the other.

The standard electrode potential, E is the measure of individual potential of a reversible electrode at standard state, which is with solutes at an effective concentration of 1 mol dm3, and gases at a pressure of 1 atm. The reduction potential is an intensive property. The values are most often tabulated at 25 C. 18In electrochemistry, the standard electrode potential, abbreviated E or E (with a superscript plimsoll character, pronounced "standard" or "nought"), is the measure of individual potential of a reversible electrode at standard state, which is with solutes at an effective concentration of 1 mol dm3, and gases at a pressure of 1 atm. The reduction potential is an intensive property. The values are most often tabulated at 25 C. The basis for an electrochemical cell such as the galvanic cell is always a redox reaction which can be broken down into two half-reactions: oxidation at anode (loss of electron) and reduction at cathode (gain of electron). Electricity is generated due to electric potential difference between two electrodes. This potential difference is created as a result of the difference between individual potentials of the two metal electrodes with respect to the electrolyte.Although the overall potential of a cell can be measured, there is no simple way to accurately measure the electrode/electrolyte potentials in isolation. The electric potential also varies with temperature, concentration and pressure. Since the oxidation potential of a half-reaction is the negative of the reduction potential in a redox reaction, it is sufficient to calculate either one of the potentials. Therefore, standard electrode potential is commonly written as standard reduction potential.

18The potential bench mark is the half-cell in which hydrogen gas is bubbled over a platinum electrode immersed in a solution having a known concentration of hydrogen ions.

The specially selected electrode is the standard hydrogen electrode (SHE) at all temperatures:Pt (s) | H2 (g) | H+ (aq)E0=0

The SHE is also called "normal hydrogen electrode" (NHE) in reference to a solution containing one equivalent of protons.

It is better to use activity rather than concentration of hydrogen ions and fugacity (=f/p) rather than pressure. To achieve the standard condition, we should have pH=0. 19the electrode potentials, E0 are conventionally defined as reduction potentials19SHEPlatinized platinum electrode

Hydrogen blow

Solution of the acid with activity of H+ = 1 mol.dm-3

Hydroseal for prevention of the oxygen interference

Reservoir through which the second half-element of the galvanic cell should be attached.

The connection can be direct, through a narrow tube to reduce mixing, or through a salt bridge, depending on the other electrode and solution. This creates an ionic conductive path to the working electrode of interest.

Note: Hydrogen's standard electrode potential (E0) is declared to be zero at all temperatures.

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The Electrochemical SeriesRemember the cell convention: For two redox couples;Red1,Ox1 || Red2, Ox2

Cell reaction is;Red1 + Ox2 Ox1 + Red2This reaction has a K > 1 if E0cell > 0, so E02 > E01Since Red1 reduces to Ox1,Red1 has a thermodynamic tendency to reduce Ox2 if E01 > E02 Thus, low reduces high.21

E02 = cathode and E02 = anodeE0 is standard electrode potential

Building the electrochemical series

Arranging redox equilibria in order of their E values

The electrochemical series is built up by arranging various redox equilibria in order of their standard electrode potentials (redox potentials). The most negative E values are placed at the top of the electrochemical series, and the most positive at the bottom.

Remember that each E value shows whether the position of the equilibrium lies to the left or right of the hydrogen equilibrium.That difference in the positions of equilibrium causes the number of electrons which build up on the metal electrode and the platinum of the hydrogen electrode to be different. That produces a potential difference which is measured as a voltage.Obviously if you connect one standard hydrogen electrode to another one, there will be no difference whatsoever between the positions of the two equilibria. The number of electrons built up on each electrode will be identical and so there will be a potential difference of zero between them.

21Table below lists the standard potential at 298 K:

They are unchanged even after multiplying by a numerical factor.By this, a cell potential is independent of the physical size of the cell.22

The values are based on their ability to be reduced, thus, the bigger the standard reduction potentials, the easier they are to be reduced or they are better oxidizing agents.

For example, Zn2+ whose standard reduction potential is 0.76V :

can be oxidized by any other electrode whose standard reduction potential is greater than 0.76V (e.g. H+, Cu2+, F2).

can be reduced by any electrode with standard reduction potential less than 0.76V (e.g. H2, Na+, Li+).23Reduction potential (also known as redox potential, oxidation / reduction potential, ORP or ) is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced23For example consider a galvanic cell:Here, a spontaneous redox reaction drives the cell to produce an electric potential. So, the Gibbs free energy, G must be negative according to this equation: Gcell = nFEcell

where n is number of moles of electrons per mole of products and F is the Faraday constant (F=eNA), ~96485 C/mol.

As such, the following rules apply:

If Ecell > 0, then the process is spontaneous (galvanic cell) If Ecell < 0, then the process is nonspontaneous (electrolytic cell) By this, in order to have a spontaneous reaction (G < 0), Ecell must be positive. Ecell = Ecathode Eanode

where Eanode is the standard potential at the anode and Ecathode is the standard potential at the cathode as given in the table of standard electrode potential.

24Consider this redox reaction:

Electrochemical cell for this reaction is:

The cell potential (emf) of this electrochemical cell under standard conditions is 1.10 V (volt) which is come from of Ecell = Ecathode Eanode = (+0.34 V)-(-0.76 V)=1.10 V

It means that the electrons flow in the external circuit from the anode (Zn), where oxidation takes place, to the cathode (Cu), where reduction happens.

Now, consider the two half-reactions:

Since the cell causes electrons to flow in the external circuit from Zn to Cu, it means that reaction (2) takes place rather than reaction (1). Reaction (2) takes place because the REVERSE of reaction (1) supplies the 2 electrons required.

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What is the potential for the cell; Ag | Ag+(1.0 M) || Li+(1.0 M) | Li

If E0Li+/Li= -3.05 V and E0 Ag+/Ag= +0.80 V

Exercises6.20(a), 6.20(b), 6.21(a), 6.21(b)

26The Nernst EquationThe Nernst equation is an equation to determine the equilibrium reduction potential of a half-cell in an electrochemical cell.

It can also be used to determine the cell potential (electromotive force or emf) for a full electrochemical cell.

A cell is at equilibrium when the potential difference for the overall reaction is zero (no work).

A cell is not at equilibrium when it can do electrical work. The amount of work can be small or large depends on the potential difference of the overall reaction.

You know that the maximum non-expansion work (in electrochemistry=electrical work) for a cell) is; Wadd,exp= G = rG .

Assignment. Derive the equation above using thermodynamic rules.

Maximum work is produced when a change occurs reversibly.

27A cell in which the overall cell reaction has not reached chemical equilibrium can do electrical work as the reaction driveselectrons through an external circuit. This work depends on the potential difference between the two electrodes and iscalled the cell potential [15]. When the cell is operating reversibly at specific, constant composition the cell potentialequals the electromotive force (emf) of the cell [16-18]. This force could be expressed in term of the reaction Gibbs freeenergy because maximum non-expansion work (electrical work) that a cell can do under mentioned conditions equalsthe Gibbs free energy of the cell reaction [16]. Therefore this expression is the key connection between electricalmeasurements on the one hand and thermodynamic properties on the other. The electromotive force of each cell could becalculated using Nernst equation which takes advantage of the standard electromotive force and the quotient of thereaction (or the equilibrium constant when the reaction is in equilibrium) [19-23].27Thus, we suppose that the cell is operating reversibly at a specific, constant composition.

This is achieved by measuring cell potential when it is balanced by an exactly opposing source of potential.

The resulting potential difference is called the cell potential, Ecell, of the cell.-vFEcell= rG

F is Faraday `s constant; F= eNA.v is stoichiometric coefficient of the electrons in the half-reactions

This equation shows the key connection between electrical measurements and thermodynamic properties.

28E is related to the Gibbs energy change only by a constant: dG=-vFE , where n is the number of electrons transferred and is the Faraday constant. There is a negative sign because a spontaneous reaction has a negative free energy and a positive potential E.

The Gibbs energy is related to the entropy by , G=H-TS, where H is the enthalpy and T is the temperature of the system. Using these relations, we can now write the change in Gibbs energy,dG=dH-TdS,

and the cell potential,E=Eo-(kT/ne)lnQ28From equation, a negative Gibbs energy, corresponding to a spontaneous cell reaction, corresponds to a positive cell potential.

Or, the cell potential is proportional to the slope of the Gibbs energy with respect to the extent of the reaction.

For example, when the slope is close to zero (close to equilibrium condition), the cell potential is small.29

The change in G can be considered by an infinitesimal amount called extent of the reaction when the cell reaction proceeds.

Infinitesimal = extremely small

In physical chemistry, the extent of reaction is a quantity that measures the extent in which the reaction proceeds. It is usually denoted by the Greek letter . The extent of a reaction has units of amount (moles).

29Now, we can relate the cell potential to the activities of the participants in the cell reaction.

You know that;

After dividing both sides by vF, we have;

The standard potential (in volts) is;

By this, the Nernst equation (which is the equation for cell potential in terms of the composition) will be;

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The standard reaction Gibbs energy, rGo, is defined (like the standard reaction enthalpy) as thedifference in the standard molar Gibbs energies of the reactants and products.

The ratio Q is an example of a reaction quotienta reaction quotient: Qr is a function of the activities or concentrations of the chemical species involved in a chemical reaction. In the special case that the reaction is at equilibrium the reaction quotient is equal to the equilibrium constant.3031

cell potential at standard conditions E03132

For example, consider the Harned cell;Pt (s) | H2 (g) | HCl (aq) | AgCl (s) | Ag (s)

The overall reaction is: H2 (g) + AgCl (s) HCl (aq) + Ag (s)

We have;

The Nernst equation is;

The activity of H2 equals to 1. Therefore;

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Now, we express the activity in terms of molality, b, of HCl (aq);

After rearranging this equation with b/b0=b for simplicity:

Or;

From Debye-Huckel law for 1,1-electrolyte (meaning you have a solution of singly charged M+ & X- ions) we know that;

If F/2RT=C, the expression will be ;

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b is its molality

mean activity coefficient

Berkadar terus = proportional to34Example. Given that the standard potential of the Cu2+/Cu and Cu+/Cu couples are +0.340 V and +0.522 V, respectively, calculate E0(Cu2+, Cu+ ).

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Cells at EquilibriumThe most important application of the Nernst equation is pH determination of a solution. This can done using a suitable choice of electrodes, of the concentration of the other ions.

A special case is when the reaction has reached equilibrium (Q=K). K is equilibrium constant.

There is no work when a chemical reaction is at equilibrium, so the potential difference is zero (for a galvanic cell)(Ecell=0). Therefore; 36

36The Determination of Activity CoefficientsIf you know the standard potential of an electrode in a cell:

Mean activity coefficient can be determined.This can be done by measuring the cell potential with the ions at any concentration.

For example, in HCl of molality b, the mean activity coefficient of ions is equals to;

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The Determination of Equilibrium ConstantsStandard potential are used to calculate the standard potential of a cell formed from any two electrodes.

Thus, we subtract the standard potential of the left-hand electrode from the right-hand one;

You already know that;

Therefore, if we have E0cell> 0, then the cell reaction has K > 1.

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E0 (right) = cathodeE0 (left)= anode38For example;2Cu+(aq) Cu (s) + Cu2+(aq)

For right-hand electrode (cathode):Cu (s) | Cu+(aq)Cu+(aq) + e- Cu(aq)E0=+0.52 V

For left-hand electrode (anode):Pt (s) | Cu2+(aq), Cu+(aq)Cu2+(aq) + e- Cu+(s)E0=+0.16 V

At 298 K, we have:E0cell= + 0.52 V - 0.16 V = + 0.36 V

Now, we can calculate K for the cell reaction. ln K = vFE0cell /RTK=1.2 106

39The Determination of Thermodynamic FunctionsWe know that; -vFE0cell= rG0

For example;Pt (s) | H2 | H+(aq) || Ag+(aq) | Ag (s) E0cell= +0.7996 V

The cell reaction is: Ag+(aq) + H2(g) H+(aq) + Ag (s) rG0= -fG0 (Ag+,aq) fG0(Ag+,aq) = - (- vFE0cell) = ( FE0cell) = +77.15 kJ/mol

Using the temperature coefficient of the standard cell potential, dE0cell/dT, we can get the standard entropy of the cell reaction.

40Because;

We know that;

If we combine these equations;

If we combined all the results we obtained until now, the standard enthalpy of a reaction will be;

By this, we have a non-calorimetric method for measuring the enthalpy.

From the convention, rH0(H+,aq)=0, therefore, all standard enthalpies of formation of ions in solutions can be calculated.

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Example; consider this cell;Pt (s) | H2 (g) | HBr (aq) | AgBr (s) | Ag (s)

The standard potential measured over a range of temperatures is:E0cell / V= 0.07131- 4.9910-4 (T/K-298) - 3.4510-6 (T/K-298)2

The cell reaction is: AgBr (s) + H2 (g) Ag (s) + HBr (aq)

Evaluate the standard reaction Gibbs energy, enthalpy, and entropy at 298 K.

42At, T= 298 K, E0cell= +0.07131 V, so; rG0 = - vFE0cell= - (1) (9.6485 104C mol-1) (+ 0.07131 V) = - 6.880 103 V C mol-1 = - 6.880 kJ mol-1

Now, for the temperature coefficient of the cell potential we have,dE0cell/dT = - 4.99 10-4 V K-1 2 (3.45 10-6) (T/K-298)V K-1

At, T= 298 K; dE0cell/dT = - 4.99 10-4 V K-1

Therefore; rS0 = 1 (9.6485 104 C mol-1) (- 4.99 10-4 V K-1)= - 48.1 J K-1mol-1 rH0 = rG0 + TrS0 = - 6.880 kJ mol-1 + (298 K) (- 0.0481 J K-1mol-1)= - 21.2 kJ mol-1

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