Unit 3

Electrochemistry

3.1 Electrochemical Cells

 In Class XI, Unit 8, we had studied the construction and functioning of Daniell cell (Fig. 3.1). This cell converts the chemical energy liberated during the redox reaction

Zn(s) + Cu2+­­­(aq) → Zn2+(aq) + Cu(s)                                                     (3.1)

to electrical energy and has an electrical potential equal to 1.1 V when concentration of Zn2+ and Cu2+ ions is unity (1 mol dm–3)*. Such a device is called a galvanic or a voltaic cell.

Fig. 3.1: Daniell cell having electrodes of zinc and copper dipping in the solutions of their respective salts.

Fig. 3.2 Functioning of Daniell cell when external voltage Eext opposing the cell potential is applied.

If an external opposite potential is applied in the galvanic cell [Fig. 3.2(a)] and increased slowly, we find that the reaction continues to take place till the opposing voltage reaches the value 1.1 V [Fig. 3.2(b)] when, the reaction stops altogether and no current flows through the cell. Any further increase in the external potential again starts the reaction but in the opposite direction [Fig. 3.2(c)]. It now functions as an electrolytic cell, a device for using electrical energy to carry non-spontaneous chemical reactions. Both types of cells are quite important and we shall study some of their salient features in the following pages.

*Strictly speaking activity should be used instead of concentration. It is directly proportional to concentration. In dilute solutions, it is equal to concentration. You will study more about it in higher classes.

3.2 Galvanic Cells 

 As mentioned earlier (Class XI, Unit 8) a galvanic cell is an electrochemical cell that converts the chemical energy of a spontaneous redox reaction into electrical energy. In this device the Gibbs energy of the spontaneous redox reaction is converted into electrical work which may be used for running a motor or other electrical gadgets like heater, fan, geyser, etc.

Daniell cell discussed earlier is one such cell in which the following redox reaction occurs.

Zn(s) + Cu2+(aq) → Zn2+ (aq) + Cu(s)

This reaction is a combination of two half reactions whose addition gives the overall cell reaction:

(i) Cu2+ + 2e– → Cu(s) (reduction half reaction)                                      (3.2)

(ii) Zn(s) → Zn2+ + 2e– (oxidation half reaction)                                      (3.3)

These reactions occur in two different portions of the Daniell cell. The reduction half reaction occurs on the copper electrode while the oxidation half reaction occurs on the zinc electrode. These two portions of the cell are also called half-cells or redox couples. The copper electrode may be called the reduction half cell and the zinc electrode, the oxidation half-cell.

We can construct innumerable number of galvanic cells on the pattern of Daniell cell by taking combinations of different half-cells. Each half-cell consists of a metallic electrode dipped into an electrolyte. The two half-cells are connected by a metallic wire through a voltmeter and a switch externally. The electrolytes of the two half-cells are connected internally through a salt bridge as shown in Fig. 3.1. Sometimes, both the electrodes dip in the same electrolyte solution and in such cases we do not require a salt bridge.

 At each electrode-electrolyte interface there is a tendency of metal ions from the solution to deposit on the metal electrode trying to make it positively charged. At the same time, metal atoms of the electrode have a tendency to go into the solution as ions and leave behind the electrons at the electrode trying to make it negatively charged. At equilibrium, there is a separation of charges and depending on the tendencies of the two opposing reactions, the electrode may be positively or negatively charged with respect to the solution. A potential difference develops between the electrode and the electrolyte which is called electrode potential. When the concentrations of all the species involved in a half-cell is unity then the electrode potential is known as standard electrode potential. According to IUPAC convention, standard reduction potentials are now called standard electrode potentials. In a galvanic cell, the half-cell in which oxidation takes place is called anode and it has a negative potential with respect to the solution. The other half-cell in which reduction takes place is called cathode and it has a positive potential with respect to the solution. Thus, there exists a potential difference between the two electrodes and as soon as the switch is in the on position the electrons flow from negative electrode to positive electrode. The direction of current flow is opposite to that of electron flow.

 The potential difference between the two electrodes of a galvanic cell is called the cell potential and is measured in volts. The cell potential is the difference between the electrode potentials (reduction potentials) of the cathode and anode. It is called the cell electromotive force (emf) of the cell when no current is drawn through the cell. It is now an accepted convention that we keep the anode on the left and the cathode on the right while representing the galvanic cell. A galvanic cell is generally represented by putting a vertical line between metal and electrolyte solution and putting a double vertical line between the two electrolytes connected by a salt bridge. Under this convention the emf of the cell is positive and is given by the potential of the half-cell on the right hand side minus the potential of the half-cell on the left hand side i.e.,

Ecell = Eright – Eleft

This is illustrated by the following example:

Cell reaction:

Cu(s) + 2Ag+(aq) → Cu2+(aq) + 2 Ag(s)                                     (3.4)

Half-cell reactions:

Cathode (reduction): 2Ag+(aq) + 2e– → 2Ag(s)                             (3.5)

Anode (oxidation): Cu(s) → Cu2+(aq) + 2e–                                  (3.6)

It can be seen that the sum of (3.5) and (3.6) leads to overall reaction (3.4) in the cell and that silver electrode acts as a cathode and copper electrode acts as an anode. The cell can be represented as:

Cu(s)|Cu2+(aq) || Ag+(aq)|Ag(s)

and we have Ecell = Eright – Eleft = EAg+Ag – ECu2+Cu                                        (3.7)

3.2.1 Measurement of Electrode Potential

 The potential of individual half-cell cannot be measured. We can measure only the difference between the two half-cell potentials that gives the emf of the cell. If we arbitrarily choose the potential of one electrode (half-cell) then that of the other can be determined with respect to this. According to convention, a half-cell called standard hydrogen electrode (Fig.3.3) represented by Pt(s) H2(g) H+(aq), is assigned a zero potential at all temperatures corresponding to the reaction

H+ (aq) + e– → H2(g)

The standard hydrogen electrode consists of a platinum electrode coated with platinum black. The electrode is dipped in an acidic solution and pure hydrogen gas is bubbled through it. The concentration of both the reduced and oxidised forms of hydrogen is maintained at unity (Fig. 3.3). This implies that the pressure of hydrogen gas is one bar and the concentration of hydrogen ion in the solution is one molar.

 At 298 K the emf of the cell, standard hydrogen electrode second half-cell constructed by taking standard hydrogen electrode as anode (reference half-cell) and the other half-cell as cathode, gives the reduction potential of the other half-cell. If the concentrations of the oxidised and the reduced forms of the species in the right hand half-cell are unity, then the cell potential is equal to standard electrode potential, EƟR of the given half-cell.

EƟ = EƟR – EƟL

As EƟL for standard hydrogen electrode is zero.

EƟ = EƟR – 0 = EƟR

The measured emf of the cell:

Pt(s)  ∣ H2(g, 1 bar)  ∣ H+ (aq, 1 M)  ∣ ∣ Cu2+ (aq, 1 M)   ∣ Cu

is 0.34 V and it is also the value for the standard electrode potential of the half-cell corresponding to the reaction:

Cu2+ (aq, 1M) + 2 e– → Cu(s)

Similarly, the measured emf of the cell:

Pt(s)  ∣ H2(g, 1 bar)  ∣  H+ (aq, 1 M)   ∣ ∣  Zn2+ (aq, 1M)  ∣  Zn

is -0.76 V corresponding to the standard electrode potential of the half-cell reaction:

Zn2+ (aq, 1 M) + 2e– → Zn(s)

The positive value of the standard electrode potential in the first case indicates that Cu2+ ions get reduced more easily than H+ ions. The reverse process cannot occur, that is, hydrogen ions cannot oxidise Cu (or alternatively we can say that hydrogen gas can reduce copper ion) under the standard conditions described above. Thus, Cu does not dissolve in HCl. In nitric acid it is oxidised by nitrate ion and not by hydrogen ion. The negative value of the standard electrode potential in the second case indicates that hydrogen ions can oxidise zinc (or zinc can reduce hydrogen ions).

In view of this convention, the half reaction for the Daniell cell in Fig. 3.1 can be written as:

Left electrode: Zn(s) → Zn2+ (aq, 1 M) + 2 e–

Right electrode: Cu2+ (aq, 1 M) + 2 e– → Cu(s)

The overall reaction of the cell is the sum of above two reactions and we obtain the equation:

Zn(s) + Cu2+ (aq) → Zn2+ (aq) + Cu(s)

emf of the cell = = E0R – E0L

= 0.34V – (– 0.76)V = 1.10 V

 Sometimes metals like platinum or gold are used as inert electrodes. They do not participate in the reaction but provide their surface for oxidation or reduction reactions and for the conduction of electrons. For example, Pt is used in the following half-cells:

Hydrogen electrode: Pt(s) | H2(g) | H+(aq)

With half-cell reaction: H+ (aq)+ e– → ½ H2(g)

Bromine electrode: Pt(s) | Br2(aq) | Br–(aq)

With half-cell reaction: ½ Br2(aq) + e– → Br–(aq)

The standard electrode potentials are very important and we can extract a lot of useful information from them. The values of standard electrode potentials for some selected half-cell reduction reactions are given in Table 3.1. If the standard electrode potential of an electrode is greater than zero then its reduced form is more stable compared to hydrogen gas. Similarly, if the standard electrode potential is negative then hydrogen gas is more stable than the reduced form of the species. It can be seen that the standard electrode potential for fluorine is the highest in the Table indicating that fluorine gas (F2) has the maximum tendency to get reduced to fluoride ions (F–) and therefore fluorine gas is the strongest oxidising agent and fluoride ion is the weakest reducing agent. Lithium has the lowest electrode potential indicating that lithium ion is the weakest oxidising agent while lithium metal is the most powerful reducing agent in an aqueous solution. It may be seen that as we go from top to bottom in Table 3.1 the standard electrode potential decreases and with this, decreases the oxidising power of the species on the left and increases the reducing power of the species on the right hand side of the reaction. Electrochemical cells are extensively used for determining the pH of solutions, solubility product, equilibrium constant and other thermodynamic properties and for potentiometric titrations.

3.3 Nernst Equation

 We have assumed in the previous section that the concentration of all the species involved in the electrode reaction is unity. This need not be always true. Nernst showed that for the electrode reaction:

Mn+(aq) + ne–→ M(s)

the electrode potential at any concentration measured with respect to standard hydrogen electrode can be represented by:

but concentration of solid M is taken as unity and we have

                          (3.8)

${\mathrm{E}}_{\left({\mathrm{Mn}}^{+}/\mathrm{M}\right)}^{⊝}$has already been defined, R is gas constant (8.314 JK–1 mol–1), F is Faraday constant (96487 C mol–1), T is temperature in kelvin and [Mn+] is the concentration of the species, Mn+.

Table 3.1: Standard Electrode Potentials at 298 K

Ions are present as aqueous species and H2O as liquid; gases and solids are shown by g and s.

1. A negative EƟ means that the redox couple is a stronger reducing agent than the H+/H2 couple.

2. A positive EƟ means that the redox couple is a weaker reducing agent than the H+/H2 couple.

In Daniell cell, the electrode potential for any given concentration of Cu2+ and Zn2+ ions, we write

For Cathode:

              (3.9)

For Anode:

                 (3.10)

The cell potential, E(cell) = ${\mathrm{E}}_{\left({\mathrm{Cu}}^{2+}/\mathrm{Cu}\right)}-{\mathrm{E}}_{\left({\mathrm{Zn}}^{2+}/\mathrm{Zn}\right)}$ 

= 

=                                                                             (3.11)

 It can be seen that E(cell) depends on the concentration of both Cu2+ and Zn2+ ions. It increases with increase in the concentration of Cu2+ ions and decrease in the concentration of Zn2+ ions.

By converting the natural logarithm in Eq. (3.11) to the base 10 and substituting the values of R, F and T = 298 K, it reduces to

                                                             (3.12)

 We should use the same number of electrons (n) for both the electrodes and thus for the following cell

Ni(s)| |   Ni2+(aq) ∣ ∣  Ag+(aq) ∣ Ag

The cell reaction is Ni(s) + 2Ag+(aq) → Ni2+(aq) + 2Ag(s)

The Nernst equation can be written as

and for a general electrochemical reaction of the type:

a A + bB cC + dD

Nernst equation can be written as:

                                                                   (3.13)

3.3.1 Equilibrium Constant from Nernst Equation

 If the circuit in Daniell cell (Fig. 3.1) is closed then we note that the reaction

Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)                               (3.1)

takes place and as time passes, the concentration of Zn2+ keeps on increasing while the concentration of Cu2+ keeps on decreasing. At the same time voltage of the cell as read on the voltmeter keeps on decreasing. After some time, we shall note that there is no change in the concentration of Cu2+ and Zn2+ ions and at the same time, voltmeter gives zero reading. This indicates that equilibrium has been attained. In this situation the Nernst equation may be written as:

or  

But at equilibrium,

$\frac{\left[Z{n}^{2+}\right]}{\left[C{u}^{2+}\right]}$ = Kc for the reaction 3.1

and at T = 298K the above equation can be written as

log KC = $\frac{\left(1.1V\times 2\right)}{0.059 V}=37.288$

KC = 2 × 1037 at 298K.

In general,

                                                                          (3.14)

Thus, Eq. (3.14) gives a relationship between equilibrium constant of the reaction and standard potential of the cell in which that reaction takes place. Thus, equilibrium constants of the reaction, difficult to measure otherwise, can be calculated from the corresponding EƟ value of the cell.

3.3.2 Electro-chemical Cell and Gibbs Energy of the Reaction

 Electrical work done in one second is equal to electrical potential multiplied by total charge passed. If we want to obtain maximum work from a galvanic cell then charge has to be passed reversibly. The reversible work done by a galvanic cell is equal to decrease in its Gibbs energy and therefore, if the emf of the cell is E and nF is the amount of charge passed and ∆rG is the Gibbs energy of the reaction, then

∆rG = – nFE(cell)                                                                                                   (3.15)

It may be remembered that E(cell) is an intensive parameter but ∆rG is an extensive thermodynamic property and the value depends on n. Thus, if we write the reaction

Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)                                            (3.1)

∆rG = – 2FE(cell)

but when we write the reaction

2 Zn (s) + 2 Cu2+(aq) →2 Zn2+(aq) + 2Cu(s)

∆rG = – 4FE(cell)

∆rGƟ = – nFEƟ(cell)                                                                            (3.16)

Thus, from the measurement of EƟ(cell) we can obtain an important thermodynamic quantity, ∆rGJ, standard Gibbs energy of the reaction. From the latter we can calculate equilibrium constant by the equation:

∆rGƟ = –RT ln K.

3.4 Conductance of Electrolytic Solutions

 It is necessary to define a few terms before we consider the subject of conductance of electricity through electrolytic solutions. The electrical resistance is represented by the symbol ‘R’ and it is measured in ohm (Ω) which in terms of SI base units is equal to (kg m2)/(S3 A2). It can be measured with the help of a Wheatstone bridge with which you are familiar from your study of physics. The electrical resistance of any object is directly proportional to its length, l, and inversely proportional to its area of cross section, A. That is,

R ∝ $\frac{l}{A}$ or R = ρ $\frac{l}{A}$                                                   (3.17)

1 Ω m = 100 Ω cm or 1 Ω cm = 0.01 Ω m

The inverse of resistance, R, is called conductance, G, and we have the relation:

G = $\frac{1}{R}$=   $\frac{A}{\rho l}=\kappa \frac{A}{l}$                                             (3.18)

It can be seen from Table 3.2 that the magnitude of conductivity varies a great deal and depends on the nature of the material. It also depends on the temperature and pressure at which the measurements are made. Materials are classified into conductors, insulators and semiconductors depending on the magnitude of their conductivity. Metals and their alloys have very large conductivity and are known as conductors. Certain non-metals like carbon-black, graphite and some organic polymers* are also electronically conducting. Substances like glass, ceramics, etc., having very low conductivity are known as insulators. Substances like silicon, doped silicon and gallium arsenide having conductivity between conductors and insulators are called semiconductors and are important electronic materials. Certain materials called superconductors by definition have zero resistivity or infinite conductivity. Earlier, only metals and their alloys at very low temperatures (0 to 15 K) were known to behave as superconductors, but nowadays a number of ceramic materials and mixed oxides are also known to show superconductivity at temperatures as high as 150 K.

Electrical conductance through metals is called metallic or electronic conductance and is due to the movement of electrons. The electronic conductance depends on

(i) the nature and structure of the metal

(ii) the number of valence electrons per atom

(iii) temperature (it decreases with increase of temperature).

* Electronically conducting polymers – In 1977 MacDiarmid, Heeger and Shirakawa discovered that acetylene gas can be polymerised to produce a polymer, polyacetylene when exposed to vapours of iodine acquires metallic lustre and conductivity. Since then several organic conducting polymers have been made such as polyaniline, polypyrrole and polythiophene. These organic polymers which have properties like metals, being composed wholly of elements like carbon, hydrogen and occasionally nitrogen, oxygen or sulphur, are much lighter than normal metals and can be used for making light-weight batteries. Besides, they have the mechanical properties of polymers such as flexibility so that one can make electronic devices such as transistors that can bend like a sheet of plastic. For the discovery of conducting polymers, MacDiarmid, Heeger and Shirakawa were awarded the Nobel Prize in Chemistry for the year 2000.

 As the electrons enter at one end and go out through the other end, the composition of the metallic conductor remains unchanged. The mechanism of conductance through semiconductors is more complex.

We already know (Class XI, Unit 7) that even very pure water has small amounts of hydrogen and hydroxyl ions (~10–7M) which lend it very low conductivity (3.5 × 10–5 S m–1). When electrolytes are dissolved in water, they furnish their own ions in the solution hence its conductivity also increases. The conductance of electricity by ions present in the solutions is called electrolytic or ionic conductance. The conductivity of electrolytic (ionic) solutions depends on:

(i) the nature of the electrolyte added

(ii) size of the ions produced and their solvation

(iii) the nature of the solvent and its viscosity

(iv) concentration of the electrolyte

(v) temperature (it increases with the increase of temperature).

Passage of direct current through ionic solution over a prolonged period can lead to change in its composition due to electrochemical reactions (Section 3.4.1).

3.4.1 Measurement of the Conductivity of Ionic Solutions

 We know that accurate measurement of an unknown resistance can be performed on a Wheatstone bridge. However, for measuring the resistance of an ionic solution we face two problems. Firstly, passing direct current (DC) changes the composition of the solution. Secondly, a solution cannot be connected to the bridge like a metallic wire or other solid conductor. The first difficulty is resolved by using an alternating current (AC) source of power. The second problem is solved by using a specially designed vessel called conductivity cell. It is available in several designs and two simple ones are shown in Fig. 3.4.

Fig. 3.4 Two different types of conductivity cells.

Basically it consists of two platinum electrodes coated with platinum black (finely divided metallic Pt is deposited on the electrodes electrochemically). These have area of cross section equal to ‘A’ and are separated by distance ‘l’. Therefore, solution confined between these electrodes is a column of length l and area of cross section A. The resistance of such a column of solution is then given by the equation:

R = ρ =                                                                                 (3.17)

The quantity l / A is called cell constant denoted by the symbol, G*. It depends on the distance between the electrodes and their area of cross-section and has the dimension of length–1 and can be calculated if we know l and A. Measurement of l and A is not only inconvenient but also unreliable. The cell constant is usually determined by measuring the resistance of the cell containing a solution whose conductivity is already known. For this purpose, we generally use KCl solutions whose conductivity is known accurately at various concentrations (Table 3.3) and at different temperatures. The cell constant, G*, is then given by the equation:

G* = = R κ                                                                                 (3.18)

Table 3.3: Conductivity and Molar conductivity of KCl solutions at 298.15K

 Once the cell constant is determined, we can use it for measuring the resistance or conductivity of any solution. The set up for the measurement of the resistance is shown in Fig. 3.5.

 

Fig. 3.5: Arrangement for measurement of resistance of a solution of an electrolyte.

It consists of two resistances R3 and R4, a variable resistance R1 and the conductivity cell having the unknown resistance R2. The Wheatstone bridge is fed by an oscillator O (a source of a.c. power in the audio frequency range 550 to 5000 cycles per second). P is a suitable detector (a headphone or other electronic device) and the bridge is balanced when no current passes through the detector. Under these conditions:

Unknown resistance R2 =                                                                      (3.19)

These days, inexpensive conductivity meters are available which can directly read the conductance or resistance of the solution in the conductivity cell. Once the cell constant and the resistance of the solution in the cell is determined, the conductivity of the solution is given by the equation:

                                                                           (3.20)

 The conductivity of solutions of different electrolytes in the same solvent and at a given temperature differs due to charge and size of the ions in which they dissociate, the concentration of ions or ease with which the ions move under a potential gradient. It, therefore, becomes necessary to define a physically more meaningful quantity called molar conductivity denoted by the symbol Λm (Greek, lambda). It is related to the conductivity of the solution by the equation:

Molar conductivity = Λm =                                                                  (3.21)

In the above equation, if κ is expressed in S m–1 and the concentration, c in mol m–3 then the units of Λm are in S m2 mol–1. It may be noted that:

1 mol m–3 = 1000(L/m3) × molarity (mol/L), and hence

Λm(S cm2 mol–1) =

If we use S cm–1 as the units for κ and mol cm–3, the units of concentration, then the units for Λm are S cm2 mol–1. It can be calculated by using the equation:

Λm (S cm2 mol–1) =

Both type of units are used in literature and are related to each other by the equations:

1 S m2mol–1 = 104 S cm2mol–1 or

1 S cm2mol–1 = 10–4 S m2mol–1.