ELECTROCHEMICAL METHODS OF ANALYSIS
Classification of Electrochemical Methods
Although there are only three principal sources for the analytical signal – potential, current, and charge – wide variety of experimental designs are possible; too many, in fact, to cover adequately in an introductory textbook. The simplest division is between bulk methods, which measure properties of the whole solution, and interfacial methods, in which the signal is a function of phenomena occurring at the interface between an electrode and the solution in contact with the electrode. The measurement of a solution’s conductivity, which is proportional to the total concentration of dissolved ions, is one example of a bulk electrochemical method. A determination of pH using a pH electrode is one example of an interfacial electrochemical method. Only interfacial electrochemical methods receive further consideration in this text.
Electrochemical methods of analysis:
§ Methods without potential imposing from the outside (potentiometry).
§ Methods with potential imposing from the outside which are based on measurement different electric parameter (all another methods)
Methods with potential imposing from the outside which are based on measurement of:
§ electric conductivity of solutions – conductometry;
§ quantities of electricians which has passed through a solution – coulometry;
§ dependences of current value from the imposed potential – voltammetry;
§ Time which is necessary for passage of electrochemical reaction – chronoelectric methods (chronovolammetry, chronoconductometry);
§ Weights of substance which was allocated owing to passage of certain current force through a solution – electrogravimetry.
Electrochemical methods on usage can be classified on:
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Direct methods in which substance concentration measure by instrument reading |
Electrochemical titration – in which for indication of equivalence point use of electrochemical measurements |
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Potentiometry |
potentiometric titration |
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Conductometry |
conductometric titration |
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Voltammetry |
amperometric titration |
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Coulometry |
coulometric titration |
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Electrogravimetry |
– |
Interfacial Electrochemical Methods
The diversity of interfacial electrochemical methods is evident from the partial family tree shown in Figure. At the first level, interfacial electrochemical methods are divided into static methods and dynamic methods. In static methods no current passes between the electrodes, and the concentrations of species in the electrochemical cell remain unchanged, or static. Potentiometry, in which the potential of an electrochemical cell is measured under static conditions, is one of the most important quantitative electrochemical methods.
The largest division of interfacial electrochemical methods is the group of dynamic methods, in which current flows and concentrations change as the result of a redox reaction. Dynamic methods are further subdivided by whether we choose to control the current or the potential. In controlled-current coulometry, we completely oxidize or reduce the analyte by passing a fixed current through the analytical solution. Controlled-potential methods are subdivided further into controlled-potential coulometry and amperometry, in which a constant potential is applied during the analysis, and voltammetry, in which the potential is systematically varied. Controlled-potential coulometry and amperometry and voltammetry.
Controlling and Measuring Current and Potential
Electrochemical measurements are made in an electrochemical cell, consisting of two or more electrodes and associated electronics for controlling and measuring the current and potential. In this section the basic components of electrochemical instrumentation are introduced. Specific experimental designs are considered in greater detail in the sections that follow.
The simplest electrochemical cell uses two electrodes. The potential of one of the electrodes is sensitive to the analyte’s concentration and is called the working, or indicator electrode. The second electrode, which is called the counter electrode, serves to complete the electric circuit and provides a reference potential against which the working electrode’s potential is measured. Ideally the counter electrode’s potential remains constant so that any change in the overall cell potential is attributed to the working electrode. In a dynamic method, where the passage of current changes the concentration of species in the electrochemical cell, the potential of the counter electrode may change over time. This problem is eliminated by replacing the counter electrode with two electrodes: a reference electrode, through which no current flows and whose potential remains constant; and an auxiliary electrode that completes the electric circuit and through which current is allowed to flow.
Although many different electrochemical methods of analysis are possible there are only three basic experimental designs: (1) measuring the potential under static conditions of no current flow; (2) measuring the potential while controlling the current; and (3) measuring the current while controlling the potential.
Each of these experimental designs, however, is based on Ohm’s law that a current, i, passing through an electric circuit of resistance, R, generates a potential, E; thus
E = iR
Each of these experimental designs also uses a different type of instrument. To aid in understanding how they control and measure current and potential, these instruments are described as if they were operated manually. To do so the analyst observes a change in current or potential and manually adjusts the instrument’s settings to maintain the desired experimental conditions. It is important to understand that modern electrochemical instruments provide an automated, electronic means of controlling and measuring current and potential. They do so by using very different electronic circuitry than that shown here. Further details about such instruments can be found in the suggested readings listed at the end of the chapter.
Electrochemical cell is vessel with investigated solution in which dipped electrode.
Schematic diagram of a manual potentiostat: C = counter electrode; W = working electrode; SW = slide-wire resistor; T = tap key; i = galvanometer.
Potentiometers
Measuring the potential of an electrochemical cell under conditions of zero current is accomplished using a potentiometer. A schematic diagram of a manual potentiometer is shown in Figure. The current in the upper half of the circuit is
where EPS is the power supply’s potential, and Rab is the resistance between points a
and b of the slide-wire resistor. In a similar manner, the current in the lower half of the circuit is
where Ecell is the potential difference between the working electrode and the counter
electrode, and Rcb is the resistance between the points c and b of the slide-wire resistor.
When
no current flows through the galvanometer and the cell potential is given by
To make a measurement the tap key is pressed momentarily, and the current is noted at the galvanometer. If a non zero current is registered, then the slide wire is adjusted and the current remeasured. This process is continued until the galvanometer registers a current of zero. Using the tap key minimizes the total amount of current allowed to flow through the cell. Provided that the total current is negligible, the change in the analyte’s concentration is insignificant. For example, a current of 10–9 A drawn for 1 s consumes only about 10–14 mol of analyte. Modern potentiometers use operational amplifiers to create a highimpedance voltmeter capable of measuring potentials while drawing currents of less than 10–9 A.
Galvanostats
A galvanostat is used for dynamic methods, such as constant-current coulometry, in which it is necessary to control the current flowing through an electrochemical cell. A schematic diagram of a manual constant-current galvanostat is shown in Figure.
Schematic diagram of a galvanostat: R = resistor; i = galvanometer; A = auxiliary electrode; W = working electrode; R = reference electrode; V = voltmeter or potentiometer (optional).
If the resistance, R, of the galvanostat is significantly larger than the resistance of the electrochemical cell, and the applied voltage from the power supply is much greater than the cell potential, then the current between the auxiliary and working electrodes is equal to
The potential of the working electrode, which changes as the composition of the electrochemical cell changes, is monitored by including a reference electrode and a high-impedance potentiometer.
Potentiostats
A potentiostat is used for dynamic methods when it is necessary to control the potential of the working electrode. Figure shows a schematic diagram for a manual potentiostat that can be used to maintain a constant cell potential.
Schematic diagram of a manual potentiostat: SW = slide-wire resistor; A = auxiliary electrode; R = reference electrode; W = working electrode;V = voltmeter or potentiometer; i = galvanometer.
The potential of the working electrode is monitored by a reference electrode connected to the working electrode through a high-impedance potentiometer. The desired potential is achieved by adjusting the slide-wire resistor connected to the auxiliary electrode. If the working electrode’s potential begins to drift from the desired value, then the slide-wire resistor is manually readjusted, returning the potential to its initial value. The current flowing between the auxiliary and working electrodes is measured with a galvanostat. Modern potentiostats include waveform generators allowing a time-dependent potential profile, such as a series of potential pulses, to be applied to the working electrode.
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Electrochemical cell |
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Methods without potential imposing |
Methods with potential imposing |
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– galvanic cell |
– electrolytic cell – conductometric cell |
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with two different metals connected by a salt bridge or a porous disk between the individual half-cells |
decomposes chemical compounds by means of electrical energy, in a process called electrolysis (except for conductometric cell) |
An electrochemical cell is a device capable of either deriving electrical energy from chemical reactions, or facilitating chemical reactions through the introduction of electrical energy. A common example of an electrochemical cell is a standard 1.5-volt “battery”. (Actually a single “Galvanic cell”; a battery properly consists of multiple cells, connected in either parallel or series pattern.)
A demonstration electrochemical cell setup resembling the Daniell cell. The two half-cells are linked by a salt bridge carrying ions between them. Electrons flow in the external circuit.
As we explained at the end of the preceding section, it is physically impossible to measure the potential difference between a piece of metal and the solution in which it is immersed. We can, however, measure the difference between the potentials of two electrodes that dip into the same solution, or more usefully, are in two different solutions. In the latter case, each electrode-solution pair constitutes an oxidation-reduction half cell, and we are measuring the sum of the two half-cell potentials.
This arrangement is called a galvanic cell. A typical cell might consist of two pieces of metal, one zinc and the other copper, each immersed each in a solution containing a dissolved salt of the corresponding metal. The two solutions are separated by a porous barrier that prevents them from rapidly mixing but allows ions to diffuse through.
If we connect the zinc and copper by means of a metallic conductor, the excess electrons that remain when Zn2+ ions emerge from the zinc in the left cell would be able to flow through the external circuit and into the right electrode, where they could be delivered to the Cu2+ ions which become “discharged”, that is, converted into Cu atoms at the surface of the copper electrode. The net reaction is the oxidation of zinc by copper(II) ions:
Zn(s) + Cu2+ → Zn2+ + Cu(s)
but this time, the oxidation and reduction steps (half reactions) take place in separate locations:
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left electrode: |
Zn(s) → Zn2+ + 2e– |
oxidation |
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right electrode: |
Cu2+ + 2e–→ Cu(s) |
reduction |
Electrochemical cells allow measurement and control of a redox reaction
The reaction can be started and stopped by connecting or disconnecting the two electrodes. If we place a variable resistance in the circuit, we can even control the rate of the net cell reaction by simply turning a knob. By connecting a battery or other source of current to the two electrodes, we can force the reaction to proceed in its non-spontaneous, or reverse direction. By placing an ammeter in the external circuit, we can measure the amount of electric charge that passes through the electrodes, and thus the number of moles of reactants that get transformed into products in the cell reaction.
Electric charge q is measured in coulombs. The amount of charge carried by one mole of electrons is known as the faraday, which we denote by F. Careful experiments have determined that 1 F = 96467 c. For most purposes, you can simply use 96,500 coulombs as the value of the faraday. When we measure electric current, we are measuring the rate at which electric charge is transported through the circuit. A current of one ampere corresponds to the flow of one coulomb per second.
Transport of charge within the cell
For the cell to operate, not only must there be an external electrical circuit between the two electrodes, but the two electrolytes (the solutions) must be in contact. The need for this can be understood by considering what would happen if the two solutions were physically separated. Positive charge (in the form of Zn2+) is added to the electrolyte in the left compartment, and removed (as Cu2+) from the right side, causing the solution in contact with the zinc to acquire a net positive charge, while a net negative charge would build up in the solution on the copper side of the cell. These violations of electroneutrality would make it more difficult (require more work) to introduce additional Zn2+ ions into the positively-charged electrolyte or for electrons to flow into right compartment where they are needed to reduce the Cu2+ ions, thus effectively stopping the reaction after only a chemically insignificant amount has taken place.
In order to sustain the cell reaction, the charge carried by the electrons through the external circuit must be accompanied by a compensating transport of ions between the two cells. This means that we must provide a path for ions to move directly from one cell to the other. This ionic transport involves not only the electroactive species Cu2+ and Zn2+, but also the counterions, which in this example are nitrate, NO3–. Thus an excess of Cu2+ in the left compartment could be alleviated by the drift of these ions into the right side, or equally well by diffusion of nitrate ions to the left. More detailed studies reveal that both processes occur, and that the relative amounts of charge carried through the solution by positive and negative ions depends on their relative mobilities, which express the velocity with which the ions are able to make their way through the solution. Since negative ions tend to be larger than positive ions, the latter tend to have higher mobilities and carry the larger fraction of charge.
In the simplest cells, the barrier between the two solutions can be a porous membrane, but for precise measurements, a more complicated arrangement, known as a salt bridge, is used. The salt bridge consists of an intermediate compartment filled with a concentrated solution of KCl and fitted with porous barriers at each end. The purpose of the salt bridge is to minimize the natural potential difference, known as the junction potential, that develops (as mentioned in the previous section) when any two phases (such as the two solutions) are in contact. This potential difference would combine with the two half-cell potentials so as introduce a degree of uncertainty into any measurement of the cell potential. With the salt bridge, we have two liquid junction potentials instead of one, but they tend to cancel each other out.
Half-cells
An electrochemical cell consists of two half-cells. Each half-cell consists of an electrode, and an electrolyte. The two half-cells may use the same electrolyte, or they may use different electrolytes. The chemical reactions in the cell may involve the electrolyte, the electrodes or an external substance (as in fuel cells which may use hydrogen gas as a reactant). In a full electrochemical cell, species from one half-cell lose electrons (oxidation) to their electrode while species from the other half-cell gain electrons (reduction) from their electrode. A salt bridge (e.g. filter paper soaked in KNO3) is often employed to provide ionic contact between two half-cells with different electrolytes, to prevent the solutions from mixing and causing unwanted side reactions. As electrons flow from one half-cell to the other, a difference in charge is established. If no salt bridge was used, this charge difference would prevent further flow of electrons. A salt bridge allows the flow of ions to maintain a balance in charge between the oxidation and reduction vessels while keeping the contents of each separate. Other devices for achieving separation of solutions are porous pots and gelled solutions. A porous pot is used in the Bunsen cell (right).
The Bunsen cell, invented by Robert Bunsen.
Equilibrium reaction
Each half-cell has a characteristic voltage. Different choices of substances for each half-cell give different potential differences. Each reaction is undergoing an equilibrium reaction between different oxidation states of the ions: when equilibrium is reached, the cell cannot provide further voltage. In the half-cell which is undergoing oxidation, the closer the equilibrium lies to the ion/atom with the more positive oxidation state the more potential this reaction will provide. Similarly, in the reduction reaction, the closer the equilibrium lies to the ion/atom with the more negative oxidation state the higher the potential.
Cell potential
The cell potential can be predicted through the use of electrode potentials (the voltages of each half-cell). These half-cell potentials are derived from the assignment of 0 volts to the standard hydrogen electrode (SHE). (See table of standard electrode potentials). The difference in voltage between electrode potentials gives a prediction for the potential measured. When calculating the difference in voltage, one must first manipulate the half-cell reactions to obtain a balanced oxidation-reduction equation.
Reverse the reduction reaction with the smallest potential (to create an oxidation reaction/ overall positive cell potential)
Half-reactions must be multiplied by integers to achieve electron balance.
An important note with this is that the cell potential does not change when the reaction is multiplied.
Cell potentials have a possible range of about zero to 6 volts. Cells using water-based electrolytes are usually limited to cell potentials less than about 2.5 volts, because the very powerful oxidizing and reducing agents which would be required to produce a higher cell potential tend to react with the water.
ELECTROGRAVIMETRY
§ Electrogravimetric method of analysis is method of quantitative allocation of defined substance on preliminary weighed electrode and an establishment of the contain of substance in sample on increase of electrode weight
Electrogravimetry is a method used to separate and quantify ions of a substance, usually a metal. In this process, the analyte solution is electrolyzed. Electrochemical reduction causes the analyte to be deposited on the cathode. The cathode is weighed before and after the experiment, and weighing by difference is used to calculate the amount of analyte in the original solution. Controlling the potential of the electrode is important to ensure that only the metal being analyzed will be deposited on the electrode.
The process is similar to electroplating.
It is known that in the phenomenon of polarization the products of electrolysis exerts a back emf, which reduces the actual emf of the cell. Thus electrolysis of an electrolyte is possible only when this back emf is overcome. Let us consider a case in which two more platinum electrodes are placed in a dilute solution of copper sulfate. If a source of potential is applied, no appreciable current will flow through the system, until some minimum potential is applied after which the current will increase as the applied potential increases. The applied voltage which is just sufficient to overcome the back emf due to polarization and also to bring about the electrolysis of an electrolyte without any hindrance is known as decomposition potential. The decomposition potential Ed is composed of various potentials and is given by:
Ea(min)= Ed= Eb+ Es+ Ev
where:
Ea = applied potential
Ed = decomposition potential
Eb = theoretical counter or back potential
Ev = overvoltage.
Faraday’s 1st Law of Electrolysis:
The mass of a substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity transferred at that electrode. Quantity of electricity refers to electrical charge, typically measured in coulombs, and not to electrical current.
m = k × Q
Q = i × t
Faraday’s 2nd Law of Electrolysis
For a given quantity of electricity (electric charge), the mass of an elemental material altered at an electrode is directly proportional to the element’s equivalent weight. The equivalent weight of a substance is its molar mass divided by an integer that depends on the reaction undergone by the material.
§ Electrolysis must be with ensuring 100% current efficiency (CE)
Scheme of electrolysis of sodium chloride melt
Factors Affecting Electrolysis Reactions
1. Overpotential- The generated voltage is significantly higher than expected. An overpotential may be necessary to overcome interactions taking place on the electrode itself (especially for gasses).
2. Electrode type- An inert electrode acts as a surface for a reaction to occur on and is not involved in the chemical reaction whereas an active electrode becomes a part of the half reaction.
3. Simultaneous electrode reactions- If two different pairs of half-reactions take place at once. Some half reactions should be eliminated in order to determine a single pair of half reactions best suited for the electrolysis to occur.
4. The state of reactants- If reactants are ionstandard states, the voltage of half cells may differ from that of the standard amount. In this case, the solution for the anode half cell may have a pH that is either higher or lower than the standard pH of 4 which may lead to a nonstandard voltage as well.
Application
Several processes of electrolysis are used in today’s industry:
1. Electrorefining
the anode is the impure metal and any impurities are removed during the process of electrolysis when the metal travels from anode to cathode. During the electrorefining of metals, the cathode has a decomposition of pure metals from a solution containing the metal ion. For example copper is purified through electrolysis in order to be used for applications that require high electrical conductivity. During this process, the cathode is a pure piece of copper, while the anode is an impure piece of copper. The Cu2+ from the anode moves through a sulfuric acid-copper(II) sulfate solution into the cathode where it becomes solid copper. While this is occurring, the impurities are left at the bottom of the tank. This leftover residue is called anode mud. The electrolysis is carried out at 0.15 – 0.30V (low voltage) in order to make sure that Ag, Au, and Pt impurities are not oxidized while in the anode and become anode mud. Whereas most of the other components become oxides or hydroxides and form water-soluble species.
2. Electrosynthesis
a method which uses electrolysis reactions to produce certain products. For example MnO2 needs to undergo electrolysis in order to be used for alkaline batteries. The solution for the electrosynthesis of MnO2 is MnSO4 in H2SO4. The anode is graphite, where Mn2+ is oxidized. While at the cathode, hydrogen is reduced from H+ to H2.
Overall Reaction: Mn2+(aq) + 2H2O(l)–> MnO2(s) + 2H+(aq) + H2(g)
3. Chloro-Alkali Process
Electrolysis of seawater which leads to the production of chlorine and the alkali, sodium hydroxide. There are 3 different methods in which these two components are produced: membrane cell, diaphragm cell, and mercury cell process.
3. Mercury Cell Process
Electrolysis of seawater in a mercury cell leads to the production of chlorine and sodium hydroxide at the same time. This method involves using mercury as the cathode and graphite as the anode.The mercury attracts either sodium or potassium cations and the mercury forms an amalgam with it. However when the amalgam is introduced to water it forms sodium hydroxide and hydrogen leaving the mercury to be reused later. The chlorine gas is left to form at the anode.
4. Diaphragm Cell Process
The diaphragm cell has Cl2 being released from the anode section, while there is H2 being released from the cathode section. If Cl2 manages to mix with NaOH, the Cl turns into other products. Therefore the diaphragm cell has a bigger amount of NaCl,and a smaller amount of solution in the cathode in order for the NaCl to come in contact with the other solution gradually, while simultaneously preventing backflow of NaOH.
5. Membrane Cell Process
This process is more efficient than others as it does not use mercury and does not require a significant amount of energy. Contains a cation-exchange membrane which is usually made from flourocarbon polymer. This membrane allows hydrated cations to pass in between the anode and cathode compartments, but does not allow the backflow of the ions, Cl– and
Physical characteristics of metal deposits
It is important that the deposits produced by electrolysis is pure, strongly adherent, dense and smooth so that it can be washed, dried and weighed without any mechanical loss. Spongy, powdery or flaky deposits are likely to be less pure and less adherent.
As mentioned earlier the principal factors that influence the physical characteristics of deposits are current density, temperature and the presence of complexing agents.
Ordinarily the best deposits are formed at current densities that are less than 0.lA /cm2.
Stirring generally improves the quality of a deposit. The time of deposition is reduced when the solution is stirred vigorously or if the electrode is rotated at a uniform speed.
This type of stirring lowers the concentration overpotential and enables a higher current density without any adverse effect.
Simultaneous evolution of gas at an electrode, during deposition is not a desirable factor, since continuous evolution of bubbles on the electrode surface disturbs the orderly growth of the crystal structure of a metal deposit. Porous and spongy deposits are obtained if there is continuous evolution of gases.
The chemical nature of the ion in solution has an important influence on the physical form of the deposit. For example, a pure bright and adherent deposit of copper can be obtained by electrolysing a nitric acid solution of cupric ions. In contrast, a coarse tree-like deposit of silver is got under similar conditions. The electrolysis from a solution of Ag[CN]− 2 complex produces a suitable deposit. Complex ions exhibit a property known as ‘throwing power’ – the property of a solution by virtue of which a relatively uniform deposit of metal is obtained on irregular surfaces – cyanide and ammonia complexes often provide the best deposits.
Increase in temperature favours diffusion. But the hydrogen overpotential is decreased and the stability of many complex ions is decreased.
In practice, constant current elecctrolysis is limited to the separation of an easily reduced cation from cations that are more difficult to be reduced than hydrogen. Thus, Cu (II) ion can be deposited from an acid solution.
Requirements to precipitates
§ The precipitate should be the certain crystal form.
§ The precipitate should be practically insoluble.
§ Cleanliness of a precipitate should be maintained strictly.
§ The precipitate should have the chemical formula (structure).
Conditions of electrolysis
The physical:
§ Pressure,
§ Current force,
§ Resistance of solution,
§ Current density (than more density, the there passes sedimentation faster, but if it very big so may be formation of too big or small crystals, leaky precipitates). Optimum value of current density 0,01-0,1 А/сm2.
The chemical:
§ The sedimentation medium (in the presence of sulphatic acid is optimal)
§ Competitive complexing for “masking” with formation solutions with low concentration (precipitates must be crystal and clean)
Scheme for electrogravimetry
Usage electrogravimetry
§ For separate metal definitions. It is possible if:
– For singly charged cations if difference in potential of allocation is equal 0.4 V
– For two charged cations if difference in potential of allocation is equal 0.2 V
COULOMETRY
Coulometry is the name given to a group of techniques in analytical chemistry that determine the amount of matter transformed during an electrolysis reaction by measuring the amount of electricity (in coulombs) consumed or produced.
In potentiometry, the potential of an electrochemical cell under static conditions is used to determine an analyte’s concentration. As seen in the preceding section, potentiometry is an important and frequently used quantitative method of analysis.
Dynamic electrochemical methods, such as coulometry, voltammetry, and amperometry, in which current passes through the electrochemical cell, also are important analytical techniques. In this section we consider coulometric methods of analysis.
Coulometric methods of analysis are based on an exhaustive electrolysis of the analyte. By exhaustive we mean that the analyte is quantitatively oxidized or reduced at the working electrode or reacts quantitatively with a reagent generated at
the working electrode. There are two forms of coulometry: controlled-potential coulometry, in which a constant potential is applied to the electrochemical cell, and controlled-current coulometry, in which a constant current is passed through the electrochemical cell.
The total charge, Q, in coulombs, passed during an electrolysis is related to the absolute amount of analyte by Faraday’s law
Q = nFN
where n is the number of electrons transferred per mole of analyte, F is Faraday’s constant (
Q = ite
where te is the electrolysis time.
To obtain an accurate value for N, therefore, all the current must result in the analyte’s oxidation or reduction. In other words, coulometry requires 100% current efficiency (or an accurately measured current efficiency established using a standard), a factor that must be considered in designing a coulometric method of analysis.
There are two basic categories of coulometric techniques. Potentiostatic coulometry involves holding the electric potential constant during the reaction using a potentiostat. The other, called coulometric titration or amperostatic coulometry, keeps the current (measured in amperes) constant using an amperostat.
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Coulometry |
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at constant potential |
at direct current |
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potentiostatic coulometry |
amperostatic coulometry |
Schematic of a coulometric cell
Potentiostatic coulometry
Potentiostatic coulometry is a technique most commonly referred to as “bulk electrolysis”. The working electrode is kept at a constant potential and the current that flows through the circuit is measured. This constant potential is applied long enough to fully reduce or oxidize all of the substrate in a given solution.
Electrolysis cells for poentionstatic coulometry: Working electrode:
a) Platinum gauze (b) Mercury pool
As the substrate is consumed, the current also decreases, approaching zero when the conversion is complete. The sample mass, molecular mass, number of electrons in the electrode reaction, and number of electrons passed during the experiment are all related by Faraday’s laws. It follows that, if three of the values are known, then the fourth can be calculated.
Bulk electrolysis is often used to unambiguously assign the number of electrons consumed in a reaction observed through voltammetry. It also has the added benefit of producing a solution of a species (oxidation state) which may not be accessible through chemical routes. This species can then be isolated or further characterized while in solution.
The rate of such reactions is not determined by the concentration of the solution, but rather the mass transfer of the substrate in the solution to the electrode surface. Rates will increase when the volume of the solution is decreased, the solution is stirred more rapidly, or the area of the working electrode is increased. Since mass transfer is so important the solution is stirred during a bulk electrolysis. However, this technique is generally not considered a hydrodynamic technique, since a laminar flow of solution against the electrode is neither the objective nor outcome of the stirring.
Schematic of a system for potentiostatic coulometry (a) Equivalent circuit (b) resistance within the cell (c) Practical circuit
The extent to which a reaction goes to completion is also related to how much greater the applied potential is than the reduction potential of interest. In the case where multiple reduction potentials are of interest, it is often difficult to set an electrolysis potential a “safe” distance (such as 200 mV) past a redox event. The result is incomplete conversion of the substrate, or else conversion of some of the substrate to the more reduced form. This factor must be considered when analyzing the current passed and when attempting to do further analysis/isolation/experiments with the substrate solution.
An advantage to this kind of analysis over electrogravimetry is that it does not require that the product of the reaction be weighed. This is useful for reactions where the product does not deposit as a solid, such as the determination of the amount of arsenic in a sample from the electrolysis of arsenous acid (H3AsO3) to arsenic acid (H3AsO4).
Controlled-Potential Coulometry
The easiest method for ensuring 100% current efficiency is to maintain the working electrode at a constant potential that allows for the analyte’s quantitative oxidation or reduction, without simultaneously oxidizing or reducing an interfering species.
The current flowing through an electrochemical cell under a constant potential is proportional to the analyte’s concentration. As electrolysis progresses the analyte’s concentration decreases, as does the current. The resulting current-versus-time profile for controlled-potential coulometry, which also is known as potentiostatic coulometry, is shown in Figure. Integrating the area under the curve, from t = 0 until t = te, gives the total charge. In this section we consider the experimental parameters and instrumentatioeeded to develop a controlledpotential coulometric method of analysis.
Gasometric coulometers (Hydrogen-oxygen coulometers)
Hydrogen-oxygen coulometer consists of a glass tube of about
Hydrogen oxygen coulometer
On electrolysis the following reactions occur at anode and cathode
Anode : 4OH− → 2H2O + O2 + 4e
Cathode : 4H+ + 4e → 2H2
Overall reaction: 2H2O → 2H2 + O2
Three moles of gases (2 moles of hydrogen and one mole of oxygen) are produced by consumption of 4 Faradays which is equivalent to 0.l74l cm3 at N.T.P. of mixed gas per coulomb. Lingane and Lehfildt found the actual volume evolved to be 0.l739 cm3.
Such coulometers show an accuracy of about –0.l % at a current density of 0.l A cm-2, falling to – 4 % at 0.0l A cm-2 and the loss of efficiency increases as the current density decreases. At low current strengths below 50 milliamperes, they cause negative errors. The relationship between gas production and current density has been examined.
Silver coulometer
A silver coulometer is an example of a gravimetric coulometer in which the amount of metal deposited at cathode or the amount of metal stripped from an anode is determined
A silver coulometer is shown in Fig. is the most satisfactory either in the cathodic deposition mode or better still, in the anodic stripping mode in perchloric acid media.
A convenient and simple form of silver coulometer consists of a platinum disk or silver disk which acts as a cathode and contains a solution of
The current density at the anode should not exceed
Iodine coulometer
Iodine coulometer is an example of a titration coulometer in which anodically generated iodine is titrated with thiosulphate or arsenic (III) solution. This has been used in the determination of the Faraday constant.
Colorimetric coulometers
They are based on the principle of developing a colored species with a reagent with a metal ion which may be anodically stripped. For example, the formation of a colored species for a cobalt ion with nitroso-R-salt and measurement of absorbance with a spectrophotometer. A metal ion may be cathodically reduced and subsequent absorbance may be measured. For example, Reduction of iron (III) at the cathode and subsequent measurement of absorbance with l,10-phenanthroline reagent.
Radioactivity coulometers
A microcoulometer based on counting deposits of 110Ag has been described. The unknown silver solution is spiked with a known amount of radioactive silver 110Ag and then deposition is made on a platinum wire in a cell in series with one containing only radioactive silver. Equal amounts of silver are plated on each cathode. The ratio of the radioactivities gives the amounts of silver in the unknown solution. The cell containing the radioactive silver is the radioactivity coulometer.
The method is useful for small quantities and plating need not be taken to quantitative completion, as it involves the measurement of the ratio of the radioactivities in the two cells.
Special Features of coulometric methods
1. Coulometric methods give more accurate and precise results than classical methods since the electrical currents can be controlled and measured with utmost precision.
2. These methods are suited for both routine as well as rare analyses which involve electrolytic method of determination.
3. Coulometric titrations are more popular and have the special advantage in the sense that the tedious steps of preparation, storage and handling of standard titrants are avoided.
4. Titrations which cannot be performed by conventional methods can be easily performed coulometrically. Titrations of high hazardous materials, titrations involving unstable or difficulty prepared titrants such as bromine, tin(II), titanium(III), chromium(II), silver(II) etc. and titrations in molten salts can be performed.
6. Constant current coulometry has widely been used than the controlled potential coulometry since the former is faster and requires simpler instrumentation and less expensive.
7. Controlled potential coulometry is a quite sensitive method and has selectivity.
Coulometric titration
Coulometric titrations use a constant current system to accurately quantify the concentration of a species. In this experiment, the applied current is equivalent to a titrant. Current is applied to the unknown solution until all of the unknown species is either oxidized or reduced to a new state, at which point the potential of the working electrode shifts dramatically. This potential shift indicates the endpoint. The magnitude of the current (in amperes) and the duration of the current (seconds) can be used to determine the moles of the unknown species in solution. When the volume of the solution is known, then the molarity of the unknown species can be determined.
Applications
Karl Fischer reaction
The Karl Fischer reaction uses a coulometric titration to determine the amount of water in a sample. It can determine concentrations of water on the order of milligrams per liter. It is used to find the amount of water in substances such as butter, sugar, cheese, paper, and petroleum.
The reaction involves converting solid iodine into hydrogen iodide in the presence of sulfur dioxide and water. Methanol is most often used as the solvent, but ethylene glycol and diethylene glycol also work. Pyridine is often used to prevent the build up of sulfuric acid, although the use of imidazole and diethanolamine for this role are becoming more common. All reagents must be anhydrous for the analysis to be quantitative. The balanced chemical equation, using methanol and pyridine, is:
In this reaction, a single molecule of water reacts with a molecule of iodine. Since this technique is used to determine the water content of samples, atmospheric humidity could alter the results. Therefore, the system is usually isolated with drying tubes or placed in an inert gas container. In addition, the solvent will undoubtedly have some water in it so the solvent’s water content must be measured to compensate for this inaccuracy.
To determine the amount of water in the sample, analysis must first be performed using either back or direct titration. In the direct method, just enough of the reagents will be added to completely use up all of the water. At this point in the titration, the current approaches zero. It is then possible to relate the amount of reagents used to the amount of water in the system via stoichiometry. The back-titration method is similar, but involves the addition of an excess of the reagent. This excess is then consumed by adding a known amount of a standard solution with known water content. The result reflects the water content of the sample and the standard solution. Since the amount of water in the standard solution is known, the difference reflects the water content of the sample.
CONDUCTOMETRY
§ Electrical conductance is a measure of how easily electricity flows along a certain path through an electrical element
§ Unit of electrical conductivity is conductivity of a conductor resistance 1 Ohm. The SI derived unit of conductance is the Siemens.
Conductivity (electrolytic)
The conductivity (or specific conductance) of an proton solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter (S/m).
Conductivity measurements are used routinely in many industrial and environmental applications as a fast, inexpensive and reliable way of measuring the ionic content in a solution. For example, the measurement of product conductivity is a typical way to monitor and continuously trend the performance of the water purification systems.
In many cases, conductivity is linked directly to the total dissolved solids (T.D.S.). High quality deionized water has a conductivity of about 5.5 μS/m, typical drinking water in the range of 5-50 mS/m, while sea water about 5 S/m (i.e., sea water’s conductivity is one million times higher than deionized water).
Conductivity is traditionally determined by measuring the AC resistance of the solution between two electrodes. Dilute solutions follow Kohlrausch’s Laws of concentration dependence and additivity of ionic contributions. Lars Onsager gave a theoretical explanation of Kohlrausch’s law by extending Debye–Hückel theory.
Units
The SI unit of conductivity is S/m and, unless otherwise qualified, it refers to
The commonly used standard cell has a width of
Molar conductivity has the SI unit S m2 mol−1. Older publications use the unit Ω−1 cm2 mol−1.
Electrical conductivity or specific conductance is a measure of a material’s ability to conduct an electric current. Conductivity (c) is the reciprocal (inverse) of electrical resistivity, ρ, and has the SI units of siemens per metre (S·m-1):
Specific conductance corresponds electric conductivity of 1 cm3 solution which are placed between electrodes with area 1 cm2 which are on distances of
c = 1/r.
§ Equivalent conductivity l is equal electric conductivity such volume of a solution which is placed between two parallel electrodes on distance
§ Value of equivalent conductivity l depends on concentration and ions charge, and also speed of their mobility:
§ At infinitely big dilution a = 1 and equivalent conductivity aspires to the greatest value
§ Limiting equivalent conductivity °l is equal sum of limiting equivalent conductivities of ions or sum mobilities of ions at infinitely big dilution.
°l °l
H+ 349,8 OH- 198,3
NH4+ 73,6 1/2SO42- 80,0
Ag+ 61,9 I- 78,8
Li+ 38,7 NO3- 71,5
F- 55,4
C6H5COO- 32,4
Measurement
The electrical conductivity of a solution of an electrolyte is measured by determining the resistance of the solution between two flat or cylindrical electrodes separated by a fixed distance. An alternating voltage is used in order to avoid electrolysis. The resistance is measured by a conductivity meter. Typical frequencies used are in the range 1–3 kHz. The dependence on the frequency is usually small, but may become appreciable at very high frequencies, an effect known as the Debye–Falkenhagen effect.
A wide variety of instrumentation is commercially available. There are two types of cell, the classical type with flat or cylindrical electrodes and a second type based on induction. Many commercial systems offer automatic temperature correction.
Principle of the measurement
Definitions
Resistance, R, is proportional to the distance, l, between the electrodes and is inversely proportional to the cross-sectional area of the sample, A (noted S on the Figure above). Writing ρ (rho) for the specific resistance (or resistivity),
In practice the conductivity cell is calibrated by using solutions of known specific resistance, ρ*, so the quantities l and A need not be known precisely. If the resistance of the calibration solution is R*, a cell-constant, C, is derived.
The specific conductance, κ (kappa) is the reciprocal of the specific resistance.
Conductivity is also temperature-dependent. Sometimes the ratio of l and A is called as the cell constant, denoted as G*, and conductance is denoted as G. Then the specific conductance κ (kappa), can be more conveniently written as
A conductivity meter and probe
Factors which influence on equivalent conductivity of electrolytes:
§ Nature of solvent (viscosity and inductivity of solvent)
§ Nature of electrolyte
§ Concentration of electrolyte
§ equivalent conductivity an electrolyte solution depends on concentration: than more concentration, the low conductivity (because of strengthening interionic interactions due to cathophoretic and relaxation effects)
§ Dependence of equivalent conductivity strong electrolytes which dissociates only on two kinds of ions, from concentration is expressed by Onsager equation:
where В is the function depending from: a ions charge, dynamic viscosity of solvent, temperature, dielectric permeability of solvent.
§ Conductivity (c) of solution in the diluted solutions of strong and weak electrolits can be calculated, if concentration of ions and their equivalent conductivity are known
Scheme of conductometric definitions
Applications
Not with standing the difficulty of theoretical interpretation, conductivity measurements are used extensively in many industries. For example, conductivity measurements are used to monitor quality in public water supplies, in hospitals, in boiler water and industries which depend on water quality such as brewing. This type of measurement is not ion-specific; it can sometimes be used to determine the amount of total dissolved solids (T.D.S.) if the composition of the solution and its conductivity behavior are known.
Sometimes, conductivity measurements are linked with other methods to increase the sensitivity of detection of specific types of ions. For example, in the boiler water technology, the boiler blow down is continuously monitored for “cation conductivity”, which is the conductivity of the water after it has been passed through a cation exchange resin. This is a sensitive method of monitoring anion impurities in the boiler water in the presence of excess cations (those of the alkalizing agent usually used for water treatment). The sensitivity of this method relies on the high mobility of H+ in comparison with the mobility of other cations or anions.
Conductivity detectors are commonly used with ion chromatography.
Direct conductometry
§ Qualitative analysis is used for definition any ions
§ Quantitative analysis is used for definition of electrolytes concentration
Usage of direct conductometry:
§ For definition of individual electrolytes in solution
§ For definition of electrolytes in mix when impurities concentration don’t change
§ For continuous control of manufactures
§ For control of water treatment process
§ For sewage pollution assessment
§ For definition of general content of salts in mineral, ocean and fluvial water
§ For control of operations filter washing and ion-exchange material regeneration
§ For definition of cleanliness slightly soluble precipitate or organic drugs
§ For definition of dampness of organic solvent, gases, crystal salts, paper
§ For detecting in chromatography
Installation for reception of the cleared water with conductometric gauge for water quality assurance
conductometric titration
§ Requirement to reaction: as in classic titrimetric analysis.
Types of reaction:
§ Acid-base
§ Precipitation
§ Complexing
!!! ox-red reaction practical don’t use
conductometric titration curves
Schema for conductometric titration
