# Lesson 1 1) Electrochemical Cells 311 UNIT 2 ¢â‚¬â€œ...

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311 UNIT 2 – ELECTROANALYTICAL TECHNIQUES

Lesson 1

1) Electrochemical Cells

• There are two types of electrochemical cell:

- Galvanic cells convert chemical energy into electrical energy; a spontaneous (ΔG = -ve) reaction is allowed to take place, with the reacting solutions connected electrically but not chemically; the

solutions form a positive electrode (cathode) at which reduction takes place and a negative electrode

(anode) at which oxidation takes place; as a result an electromotive force is set up and current can

flow; the difference between the electrode potentials (E) at each electrode is the emf of the cell

- Electrolytic cells convert electrical energy into chemical energy; a non-spontaneous (ΔG = +ve) reaction is forced to take place by driving electrons around a circuit, which includes an aqueous

solution, in the opposite direction to that in which they would move if a spontaneous reaction was

taking place; this process is known as electrolysis

• A Galvanic cell can be converted into an electrolytic cell if an external voltage is applied which is

greater than the emf which the cell would generate if the cell were operating Galvanically (known as the

back emf); this forces the non-spontaneous reaction to take place and this is how cells are re-charged

2) General principles of electrolysis at low voltages

• A minimum external voltage, known as the decomposition potential or back emf, is required to

electrolyse a solution; below this voltage, very little current can flow; the minimum voltage required

depends on the ECELL of the reaction taking place

• Once the minimum voltage required for electrolysis is reached, the current will start to increase rapidly,

due to the reduction of cations at the cathode (negative) or the oxidation of anions at the electrode

(positive) which allows current to flow

• Once the electrolysis has started, the concentration of electroactive ions at the electrode starts to

decrease; this creates a concentration gradient which causes the electroactive ions to migrate faster to the

electrode, which in turn increases the current

• Once the concentration of cations around the electrode has fallen to zero, the concentration gradient has

reached a maximum (which is the concentration of the solution); the ability of ions to move to the

electrode then becomes a limiting factor and the current stops increasing rapidly, the maximum increase

in current due is called the diffusion current (iD); it is proportional to the concentration of the solution

and can therefore be used as the basis for quantitative analysis

• The potential at which the current rises sharply is characteristic of the ion being reduced; it is taken to be

the voltage at which the current has risen to half of the diffusion current ( iD

2 ) and is known as the half-

wave potential (E1/2); it is an intrinsic property of an ion at a particular temperature and can be used to

identify the ion

311 UNIT 2 – ELECTROANALYTICAL TECHNIQUES

• The resulting graph of current against applied voltage looks as follows:

• If there is more than one cation in solution, other sharp increases in current will be observed at slightly

different voltages

311 UNIT 2 – ELECTROANALYTICAL TECHNIQUES

Lesson 2

3) Principles of polarography

• Polarography is an analytical technique which in which voltage-current graphs obtained during

electrolysis at low voltage are used for the quantitative and qualitative analysis of ions in solution, using

an instrument known as a polarograph.

• A polarograph consists of an electrolytic cell; the cathode is a dropping mercury electrode, which is a

fine capillary through which mercury drops slowly onto the anode; the anode is usually a calomel

electrode, which provides a stable potential: Hg2Cl2(s) + 2e - 2Hg(l) + 2Cl- (electrode potential

of saturated solution of KCl at 25 0C = 0.251 V); the electrolytic cell is connected to a potentiometer

which allows the voltage to be changed gradually; the circuit also includes a galvanometer which can

record small changes in current:

1 – battery, 2 potentiometer, 3 – dropping mercury electrode; 4 – calomel electrode; 5 solution to be

analysed; 6 - galvanometer

• The resulting graph of current against voltage is a polarogram.

311 UNIT 2 – ELECTROANALYTICAL TECHNIQUES

• Important features of a polarograph:

- The anode is non-polarisable, which means that behaves as a good conductor and its potential remains constant; the large surface area of the anode decreases its polarizability further

- The cathode is polarisable, which means it is difficult for current to actually flow between solution and electrode and the electrode behaves as a capacitor; the small surface area of the cathode

increases its polarizability

- The dropping of the mercury continually exposes fresh electrode to the electrolyte and prevents the products of electrolysis from accumulating

• Mercury is a suitable choice of cathode because

- the small droplets can be reproduced exactly

- hydrogen has a high over-voltage on mercury so the technique can be used in acid solutions

- mercury forms stable alloys (amalgams) with many metals which can be analysed if the amalgam is used as the material at the electrode and it is made the anode

• The electrolysis should take place adding an excess of salt with an inert cation; this salt carries most of

the current and thus means that the cation under investigation makes little contribution to the electrical

gradient; the concentration of base electrolyte should be at least 50 times larger than reducible ion

• Oxygen must be removed from the solution as its reduction half-reactions significantly affect the

current-voltage relationship

• The limits of operation of the dropping mercury electrode are -2.4 V (at potentials more negative than

this even the most inert cation - tetramethylammonium - can be reduced) and +0.6 V (at potentials more

positive than this the mercury can be oxidised)

• Polarography can be used to identify and estimate trace metallic impurities in commercial chemicals,

particularly foods and fuels; it can also be used for the estimation of gases, especially oxygen

• Polarography works best as concentrations between 0.01 moldm-3 and 1 x 10-6 moldm-3

311 UNIT 2 – ELECTROANALYTICAL TECHNIQUES

Lesson 3

4) Diffusion current

• The rate of flow of a cation A through a solution is given by vA = kA dμA

dx , where

dμA

dx is the

electrochemical gradient, and kA is a constant linked to the diffusion coefficient DA; dμA

dx in turn depends

on the concentration gradient dC

dx and the potential gradient

dψ

dx as follows:

dμA

dx = zAF

dψ

dx + RT

d(lnCA)

dx

• The flux fA of cation through a solution is the product of the velocity of each ion and the concentration

of A (CA) fA = vACA = Therefore fA = CAkAzAF dψ

dx + CAkART

d(lnCA)

dx

but CA d(lnCA)

dx =

dCA

dx so fA = CAkAzAF

dψ

dx + kART

dCA

dx (Equation 1)

• The total current flowing I = AFΣ(fz), so I

AF = Σ(fz) = F

dψ

dx Σ(Ckz2) + RTΣ(kz

dC

dx )

This expression can be rearranged to get an expression for dψ

dx :

F dψ

dx Σ(Ckz2) =

I

AF – RTΣ(kz

dC

dx )so

dψ

dx =

1

FΣ(ckz2) (

I

AF - RTΣ(kz

dC

dx ))

This can be substituted into equation 1 to give: fA = 𝐂𝐀𝐤𝐀𝐳𝐀

𝚺(𝐜𝐤𝐳𝟐) (

𝐈

𝐀𝐅 - RTΣ(𝐤𝐳

𝐝𝐂

𝐝𝐱 )) + kART

𝐝𝐂𝐀

𝐝𝐱 (Equation 2)

• The contribution made by A to the current based on the electrical gradient iA = CAkAzAF dψ

dx

- but the total current due to the electrical gradient = F dψ

dx Σ(Ckz2)

- therefore the transport number tA of A in the solution be expressed as: tA = CAkAzA

2

Σ(Ckz2) (Equation 3)

• Equation 3 can be rearranged to give tA

zA =

𝐂𝐀𝐤𝐀𝐳𝐀

𝚺(𝐜𝐤𝐳𝟐) and this can be substituted into Equation 2 to give:

fA = 𝐭𝐀

𝐳𝐀 (

𝐈

𝐀𝐅 - RTΣ(𝐤𝐳

𝐝𝐂

𝐝𝐱 )) + kART

𝐝𝐂𝐀

𝐝𝐱 (Equation 4)

The first part of this expression tA

zA (

I

AF - RTΣ(kz

dC

dx )) gives the flux of A due to the potential gradient.

The second part of this expression kART 𝐝𝐂𝐀

𝐝𝐱 gives the flux of A due to the concentration gradient.

If CA is very small compared to the total concentration of ions, then the value of tA is very small. Under

these conditions, the equation can be simplified to:

fA = kART 𝐝𝐂𝐀

𝐝𝐱 = DA

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