3. COULOMETRIC TITRATIONS

 

In a coulometric titration the titrant is generated electrochemically by constant current from a proper electrolyte. Coulometric titrations are in many ways similar to volumetric titrations: the concentration of the titrant is equivalent to the generating current, and the volume of the titrant is equivalent to the generating time. The two modes are exemplified with an argentometric titration (Fig.3-1).

Generating electrode:

Counter electrode:


Fig.3-1 Titration of chlorides with Ag+: (a) volumetric, (b) coulometric.

 

Coulometric titrations have numerous advantages:

 

Coulometric vs Volumetric Titrations

 

Coulometric

Volumetric

Preparation of standard solutions

None

Yes

Standardization of titrant

None

Yes

Storage of titrant

None

Yes

Use of labile reagents

Trivial

Difficult

free KOH or NaOH titrants

Trivial

Possible

Dilution effects during titration

None

Yes

Addition of microquantities of analyte

Trivial

Difficult

Determination of microamounts of analyte

Yes

Difficult

Determination of microvolumes

Yes

Difficult

Accuracy of titration

High

O.K.

Economy of reagent

Maximal

Depends

Automation

Perfect

Possible

Remote control

Perfect

Possible

End-point detection

Same for both modes

Price

Similar

 

3.1. Electrogeneration of titrant

The basic requirement of a coulometric titration is 100% current efficiency of titrant generation.

 

In the table below several options for electrogeneration of titrant are presented. The most straightforward options are those in which the titrant is produced as a result of (i) dissolution of electrode material or (ii) decomposition of the solvent at an inert electrode. The reagent precursor in those cases is present at infinitely large amounts.

 

Sources of electrogenerated titrant

Electrode material

Solvent

Reagent precursor

 

In a large number of coulometric titrations, however, the reagent precursor has finite concentration. For example, in order to generate bromine as titrant, bromide is added as precursor.

To ensure 100% current efficiency, the generation of titrant should be the only process, taking place at the generating (working) electrode. The current by which the titrant is generated has to be smaller than the limiting current of the electrode process of interest. If this condition is not maintained, some unwanted electrode process could take place and bring to the reduction of the current efficiency.

This will be exemplified by a current-potential curve (Fig.3-2) obtained in stirred solution containing 10 mM KBr. Due to the stirring of the solution, a constant amount of electroactive material reaches the electrode and the plots are time independent. At potentials around +1.0 V vs SCE the oxidation of Br- takes place; at more positive potentials water is oxidized. The oxidation of Br- can proceed at a maximum current density of 5 mA/cm2. If the current forced through the electrodes corresponds to a current density lower than that value, say 2.5 mA/cm2 (dotted line (1) in Fig.3-2), the only reaction that takes place is the oxidation of bromide. If, however, a larger current density is applied, say 7.5 mA/cm2 (dotted line (2) in Fig.3-2), only 5 mA/cm2 are contributed by the oxidation of Br-. An additional 2.5 mA/cm2 are due to the oxidation of water. The problem is evident - the current efficiency of the generation of Br2 is not 100% any more.

Note: For 100% current efficiency: ig < il

 

 

Fig.3-2 Experimental current-potential curve for oxidation of bromides at a rotating disk electrode.

Composition of solution: 10 mM KBr, 60 mM HClO4 and 0.1 M KNO3.

Area of the electrode: 0.16 cm2. Rotating rate: 400 rpm.

Auxiliary lines (1) and (2) are referred in the text.

 

3.2. Estimation of the maximal generating current when reagent precursor is used

The amount of precursor reaching the electrode is determined by the rate of mass transport, which is controlled by the concentration of the precursor, the intensity of stirring and the cell geometry. Proper choice of those parameters is of paramount importance for ensuring 100% current efficiency. The rigorous mathematical analysis of mass transport in stirred solutions is a complex task. We shall proceed by a simplified approach, introduced by Nernst, using the concept of diffusion layer.

According to Nernst approach, a layer of thickness (the Nernst diffusion layer), adjacent to the electrode, remains stagnant. Away from it the solution is in motion and uniform in concentration. The thickness of the layer remains unchanged with time. The mass transfer in the Nernst layer proceeds by diffusion and the concentration gradient is linear. The model is rather primitive, but adequate for a rough estimation.

The concentration profile of the electroactive species in stirred solutions, according to the Nernst approach, is presented in Fig.3-3.


Fig. 3-3 Nernst model of mass transfer in stirred solutions.

 

The Nernst diffusion layer, , is:

              independent of time

              inversely dependent on square root of stirring rate

 

The flux of the electroactive species at the electrode surface is given by Fick's first law

(1)

 

where C* and C(x=0) are the bulk and surface concentrations of the electroactive species and D is its diffusion coefficient. The corresponding current is

(2)

A limiting value of the current, il, is reached at sufficiently large potentials, where C(x=0) = 0. Then

(3)

 

The thickness of the Nernst diffusion layer, , is inversely proportional to the square root of the intensity of stirring. No exact analytical expression is available for a bar-stirred solutions and can be estimated only experimentally by measuring il at a given bulk concentration, C*, of electroactive species. Furthermore, is dependent on the geometry of the cell, the electrode arrangement and the distance between the bar and the electrode. Thus, we refer in our examples (Fig.3-2 and Fig.3-5) to a rotating disk electrode, the current for which is independent of the above mentioned geometric parameters. Analytical expression for il at a rotating disk electrode has been derived.

(4)

where is the rotating rate in Hz, il in A, C* in mol/cm3, and D in cm2/s.

 


In titrimetric analysis bar-stirred solutions are used. Thus, equivalence in currents compared to rotating electrode is needed. Considering the cell presented in Fig.1-7 (cf., Titrimetric Methods of Analysis), effective stirring is achieved by rotating the magnetic stirrer in the range of 400 - 1200 rpm. (The upper value is limited by the appearance of vortexes, and the lower - ensures that the electrogenerated titrant has the chance to encounter virtually all the analyte within the time of about 100 s needed to reach the equivalence point in a continuous titration). The limiting currents obtained under these conditions are approximately equal to those observed when the electrode itself is rotated at the same rate.

 


 

3.3. Optimal values of generating current, concentration of precursor and area of working electrode

Plots of limiting current density, j = il /A, as function of concentration of precursor, calculated according to eq.4, are displayed in Fig.3-4.

 


Fig.3-4 Limiting current density in stirred solutions as function of concentration of precursor, calculated according to eq.4, for D = 10-5 cm2/s. The right axes corresponds to the recommended current density at the generating electrode for a coulometric titration.

 

Fig.3-4 provides an estimation of the limiting values of the current density at different rotating rates. The generating current, as stated above, should be lower than the limiting current of the precursor in order to ensure 100% current efficiency. A safety factor of 2 is used in estimating the recommended current density at a generating electrode in coulometric titrations (right axes of Fig.3-4). Fig.3-4 can be used to determine the concentration of reagent precursor for a given current density at the generating electrode or vice versa. For example, if a titration is carried out at 20 mA/cm2, for , the lowest concentration of the precursor that can be used is ~60 mM. If the rate of rotation were decreased to 400 rpm, only 10 mA/cm2 could be passed at the same concentration without affecting the current efficiency.

A well-designed experiment should ensure successful results also in less favorable conditions, thus the possibility of the working electrode being located in a region of reasonably low stirring rate (400 rpm) should be considered. The generating current, ig, in these conditions (Fig.3-4) is

(5)

where n is the number of electrons involved in the electrogeneration of the titrant. (A different coefficient for eq.5 is given by Lingane1: 0.5 instead of 0.2. The difference may be related to differences in degree of stirring. Lingane refers to "well stirred solutions" and we refer to moderate stirring. Furthermore, we use a safety factor of 2).

Eq.5 provides a guide for determining the experimental parameters: area of generating electrode and concentration of precursor. The generating current is chosen considering the amount of analyte and a reasonable time for the titration to be accomplished. For example, if the total amount of charge needed to reach the equivalence point is 0.5 Coulomb and it is desired to accomplish the titration in 100 s, a generating current of 5 mA is to be used. The product Cprec (mM)Ag (cm2) should be at least 25 (cf., eq.5, with n = 1). Thus, for a reasonable value of the area ranging from 0.5 to 2 cm2, the respective concentration of precursor should be 50 to 13 mM. Solubility limitations or price of the precursor may dictate the choice for the electrode area.

 

3.4. Counter electrode

In many cases the reaction at the counter electrode is not compatible with the reaction of interest. There are several reasons for incompatibility:

* The product of the reaction between the analyte and titrant is restored at the counter electrode to the initial form of the analyte, e.g., titration of Fe2+ with Ce3+ as precursor. Fe3+, the product of the titration, is reduced to Fe2+ at a non-isolated Pt counter electrode.

* The electrogenerated titrant reacts at the counter electrode, e.g., titration of Cl- with electrogenerated Ag+. Silver ions, which did not have the chance to react with Cl-, are lost by being reduced at the counter electrode.

* The main product at the counter electrode reacts with the analyte or with the electrogenerated titrant, e.g., titration of H+ with electrogenerated OH-. The product of the electrode reaction at a non-isolated platinum counter electrode (H+) counterbalances the product at the working electrode (OH-), nullifying the titration process.

An accepted solution for all these problems is isolation of the counter electrode. This, however, imposes experimental difficulties:

(i)                              the solution of the counter compartment has to be replaced frequently;

(ii)                            incomplete isolation of the counter electrode will affect the accuracy of the titration;

(iii)                           it is unsuitable for automation and miniaturization; (iv) it substantially increases the resistance between the electrodes.

Thus, it is preferable to use a non-isolated counter electrode. Care must, however, be taken to ensure 100% current efficiency.

Note: If the resistance between the generating and the counter electrodes reaches , the passed current is limited to 50 mA, since most coulometers operate under 40 V.

 

3.5. Models for non-isolated counter electrodes

There are several approaches in devising non-isolated counter electrodes.

(a) Creating conditions at which an undesired process is prevented by limiting the potential of the counter electrode.

The Ag/AgBr counter anode2,3 is an elegant solution for the titration of H+, where in a two-platinum electrode cell the OH- formed at the generating electrode is counterbalanced by the H+ formed at the counter electrode. Replacing the platinum electrode with silver, the anodic decomposition of water is prevented (Fig.3-5).

 

 

Fig.3-5 Current-potential relationship at rotating disk electrodes (platinum and silver) at 400 rpm.

At Pt-RDE: 2 mM HCl, 0.1 M KNO3.

At Ag-RDE: 2 mM HCl, 0.1 M KNO3 and 10 mM KBr.

 

The composition of the solution is modified by adding excess of a halide salt, whose role is forming insoluble silver salt, thus preventing reduction of Ag+ at the cathode. (Reduction of Ag+ would reduce the titration efficiency).

The excess of X- has to be controlled due to the formation of soluble complexes AgX2- ,AgX32- ,AgX43-. The total concentration of the dissolved species as function of concentration of halide is given in Fig.3-6. In the concentration range of interest, 5-100 mM, bromides are most suitable, since the solubility of AgBr is the lowest. It is advisable, that the concentration of Br- be not higher than 50 mM. The size of the counter electrode should be not smaller than that of the generating electrode, otherwise the life span of the electrode is shortened more rapidly by the formation of a thick layer of AgX precipitate, which isolates electrically the electrode.

(b) Hampering direct reaction of the titrant at the counter electrode based on geometric and kinetic considerations.

One of the problems resulting from the use of non-isolated counter electrodes is that the electrogenerated titrant can react at it instead of reacting with the analyte. A general solution is presented here4. The basic principle is to render mass transport of the titrant at the counter electrode negligibly small by modifying the factors involved. Consider for this purpose the Nernst approach, which allows us to estimate the mass transport limited current in stirred solutions (eq.3).

 


Fig.3-6 Solubility of silver halides in sodium halide solution at 18oC (K.H.Leiser, Z. Anorg.Allgem. Chem., 292, 97 (1957)).

 

Simple analysis of the equation shows the parameters, which need to be modified:

* Decreasing the area of the counter electrode.

* Using an electrode geometry for which il will be minimal.

* Keeping the Nernst diffusion layer as large as possible.

* Keeping the concentration of the titrant in the solution as low as possible.

Each of the above points is treated below.

Decreasing the area. For the case where the main reaction at the counter electrode is the decomposition of the solvent, a high current density of up to at least 100 mA/cm2 can be used. Thus, if a current of 10 mA is used in the coulometric titration, a counter electrode as small as 0.05 cm2 can be employed.

Geometry of the counter electrode. A small disk is better than a thin wire of identical area, since the flux at the former is smaller.

Keeping as large as possible. The only way to increase the Nernst diffusion layer at the counter electrode is to decrease the stirring rate in the vicinity of the counter electrode. This is somewhat contradictory to the requirement of efficient stirring. However, if a small cell with a volume of 5 - 10 ml is used (Fig.1-7), efficient stirring throughout the solution can be reached at moderate rotation of the magnetic bar (400 - 600 rpm). The optimal place to locate the counter is far away from the working electrode and from the magnetic stirrer.

Low values of the instantaneous concentration of electrogenerated titrant in the solution can be achieved by:

(i) Producing a uniformly distributed titrant by efficient stirring and using a large-area generating electrode.

(ii) Increasing the rate of reaction between the analyte and the electrogenerated titrant. The higher the rate, the smaller the concentration of free reagent, and thus the smaller the chances for its reaction at the counter electrode. For example, the rate of reaction between chloride and Hg(I) can be substantially changed by manipulating the composition of the solution. Acidity and alcohol content are the most important factors. For the completion to 90% of the reaction between Cl- and Hg(I) (mixing 0.2 mM of each in 50% methanol) more than 200 s are required at 5 mM HClO4 and only 5 s at 50 mM HClO4. The increase in the rate of the chemical reaction is of importance not only with respect to the counter electrode, but also for the completion of the titration process in reasonable time.

The above outlined principles will be tested with an example of constant-current titration of Cl- with electrogenerated Hg(I). A 1 mM solution of Cl- is titrated with a generating current of 5 mA. A small-area counter electrode (0.05 cm2) is located in the upper layer of the solution, where the stirring is equivalent to 400 rpm of a rotating disk electrode. It will be shown that only a negligibly small fraction of the titrant, Hg(I), is lost by reduction at the counter electrode:


The current of the electroreduction of Hg(I) can be estimated according to Levich equation (eq.4), provided the instantaneous concentration of Hg(I) is known. It is, however, very difficult to determine the instantaneous concentration. A worst case, in which none of the titrant reacts up to the equivalence point, will be considered. Since the generating current is constant, the instantaneous concentration of Hg(I) increases linearly with time, and its average concentration up to the end point is half the initial concentration of the analyte, i.e., 0.5 mM. Substituting this concentration in the Levich equation, one finds that the average rate of titrant loss corresponds to . This represents 0.2% of the total current passed, leading to a 0.2% error at most. In fact the error is much smaller since the basic requirement for a titration is a fast reaction between titrant and analyte.

Note: (1) Conditions for titration with :

        strong acid (HClO4 or HNO3)

       

(2) Electrode reduction of at the counter electrode decreases the efficiency of the titration.

Reaction of interest:

Competing reaction:

An additional example of successful application of the above principles is the titration of As(III) with electrogenerated iodine. The reaction between iodine and As(III) is very fast. Thus, even with less strict observation of the above mentioned conditions, high accuracy can be achieved with a non-isolated counter electrode.

In conclusion, the approach proposed above is a simple and elegant method for using a non-isolated counter electrodes for cases in which the electrogenerated titrant can react at the counter electrode. The flux of the titrant at the counter electrode is rendered virtually zero on the basis of geometric and kinetic considerations. Another benefit of this approach is that it also largely decreases the possibility that the analyte or its product would react at the counter electrode.

As good analytical practice, however, it is suggested to test whether the functioning of the non-isolated counter electrode meets all expectations. The example given below (titration of Cl-) demonstrates a problem encountered with a non-isolated counter electrode. The titration of Cl- can be performed with electrogenerated Ag+ or with . The difference between the two titrants is that silver, which may be deposited on the non-isolated counter electrode, forms dendrites, while mercury being a liquid metal, does not. After certain incubation period, typically 300 s, at a generating current of 2 mA, the silver dendrites start to protrude toward the solution and form a barely visible web with considerable area. Thus, the central condition of a small-area counter is violated in the case of silver, and from that point spongy black silver deposits start flowing in the solution and large and irreproducible delays of the end point are observed.

Limitations of the proposed counter electrodes. The principles outlined above are suitable for most types of titrations, with few exceptions. For example, titrations at which the products formed at the counter electrode react with the analyte (in the titration of OH- with non-isolated counter electrode, H+ formed at the generating electrode is counterbalanced by OH- formed at the counter electrode).

 

3.6. Isolated counter electrodes. Design and materials

Isolation between the counter and generating electrodes is achieved by several ways:

1. The electrodes are placed in separate vessels joined by an electrolyte bridge, closed at both ends by porous membrane (sintered glass or ion-exchange membrane).

2. The counter electrode may be kept in a single armed bridge with a fine porous membrane, isolating it from the solution being titrated. In this case there may be some diffusion from the counter electrode compartment, and thus it is advisable to complete the titration quickly.

3. In place of a porous membrane, a plugged tube of Vicor brand thirsty glass (Corning 7930) effectively prevents mixing of the two solutions while maintaining electrolyte contact. Thirsty glass is a porous, adsorbent glass with 28% of volume void and 4 m average pore diameter. Thin tubes (inner diameter ~3.5 mm and wall thickness ~1 mm) are recommended for . The bottom end of the tube is sealed with a small soft plug (silicon rubber, viton or others).

 


The electrolytic resistance between the counter and the generating electrode, Rc-g, is considerably increased by the separator. Thirsty glass tubes are the best separators in view of low resistivity and effective separation between generating and counter compartments.

The electrolytic resistance Rc-g is easily measured by a conductometer connected to the counter and working electrodes. The product iRc-g can reach considerably large values. With a sinter separator, Rc-g may be as high as 500 ; at ig =20 mA, the product iRc-g alone reaches 10 V. The overall potential across the cell, Vc-g, is mainly determined by the potential drop iRc-g. It should be noted, that due to safety considerations the galvanostats for coulometric titrations are usually constructed with limitation of the output potential. The output voltage of a galvanostat, Vc-g, for coulometric titrations is limited to ~40 V.

Several electrode materials are suitable as isolated counter electrode: Pt, Au, C, Ag, W (tungsten only as cathode), etc. The area of the counter electrode may be smaller than that of the working electrode (Ac > 0.1 Ag).

 

3.7. Working electrodes. Materials and shapes

The choice of material for the generating electrode is made according to the electrode reaction in which the titrant is generated:

 

Typical Electrogenerated Titrants

 

Electrogenerated

titrant

Generating

electrode

Reagent

precursor

Oxidants

Br2

Pt

Br-

I2

Pt

I-

Cl2

Pt

Cl-

Reductants

Fe(II)

Pt

Fe(III)

Cu(I)

Pt

Cu(II)

Sn(II)

Au

Sn(IV)

U(V), (IV)

Pt

UO2SO4

Precipitation and complexation agents

Ag(I)

Ag

Ag

Hg(I)

Hg(Ag)

Hg

EDTA

Hg(Ag)

Hg-EDTA2-

Acids and bases

OH-

Pt

H2O

H+

Pt

H2O

 

Inert electrodes, mainly Pt or Au, are used in redox reactions involving soluble species.

Active electrode as Ag and Hg are used for the generation of Ag(I) and Hg(I).

Except for mercury, all other electrodes are convenient and safe for use. Mercury pool electrodes are commonly mentioned in the literature, but unless special precautions are taken, they are unsafe. Mercury-coated gold electrodes have been proposed as substitute. The problem is the fast disintegration of the gold. We recommend the use of mercury-coated silver electrodes, which can be used over years.

The shape of the electrode is dictated by the price of the metal. Because of its relatively low price, silver may be used as rods (2 or 3 mm diameter) or foils. Platinum and gold are used as thin-foiled flags or thin-wired spirals. Wide-looped spirals are effective in uniform distribution of the titrant. Dense-looped spirals in the contrary can impede uniformity.

 

3.8. Supporting electrolyte

The prime task of the supporting electrolyte is to reduce the resistance between the generating and counter electrodes so that the voltage between them is within the dynamic range of the galvanostat. Most instruments designed for coulometric titrations operate up to 40 V. If this limit is exceeded, the following measures can be taken: (i) increasing the concentration of the supporting electrolyte, (ii) decreasing the resistance of the diaphragm separating the counter electrode compartment or (iii) decreasing the current.

While in a large group of titrations any inert electrolyte can be used, there are several cases in which both the type and the concentration of electrolyte play a role in the chemistry of the system. Several examples will be given.

 

Electrogenerated Ce(IV). The electrogeneration of strong oxidants (Ce(IV), Cl2) poses a problem due to competing reactions. The stronger the oxidant, the higher the potential of the generating electrode during the electrogeneration of the oxidant. For very strong oxidants the electrode surface of even noble metals becomes covered with oxides:

and at more positive potentials oxygen is evolved due to electrooxidation of water:

High current efficiency is achieved by:

* shifting the water decomposition to more positive potentials by increasing the proton concentration;

* shifting the potential of the reaction of interest to more negative potentials by (i) increasing the concentration of the precursor: for a given current density, the higher the concentration of the precursor, the more negative the potential of its electrooxidation; (ii) addition of complexant that stabilizes the titrant in respect to its precursor.

The electrogeneration of Ce(IV) was thoroughly studied by Lingane1 (see figures below). The current-potential curves for oxidation of Ce(III) in different acid solutions are given in the left figure. The plots for the background due to oxide formation and oxygen evolution are also included. The main difference between the two acids is in the negative shift of the potential for the generation of Ce(IV). In H2SO4 the negative potential shift results from the complexation of Ce(IV) with . The effect of the acids on the background currents is elatively small.

The values of are given in the table below:

 

Acid

vs NHE, V

1 M H2SO4

1.44

1 M HClO4

1.70

 

The respective current efficiencies are shown in the right figure. A current efficiency of 99.8% is achieved under the following conditions: a) sulfuric acid (3 M) rather than perchloric acid is used because of the complexation ability of the former with ceric ion; b) the concentration of the precursor, Ce(III), is high, close to its solubility limit; and c) the current density is limited to 1 - 10 mA/cm2.

 

 

 


Current-potential plots for oxidation of Ce3+ and

the respective plots for the oxidation of water at a Pt electrode.

 

 

 


Current efficiency for electrogeneration of Ce4+

as a function of current density and solution composition.

 

 

 

Optimal conditions for generation of Ce(IV):

        Presence of 2-3 M H2SO4

        Precursor 0.2 M Ce(III)

        Current density 1-10 mA/cm2

A relatively narrow range of optimal current density characterizes the electrogeneration of strong oxidants. Beyond the upper limit there will be a competition from the oxidation of water, and below the lower limit a formation of platinum oxide interferes.

 

Non-isolated Ag anode in a solution of halides (counter electrode in titration of H+). Such an electrode is described in this chapter, section 3.5. The role of the halide is the formation of an insoluble silver salt. However, in excess of halide, soluble complexes are formed. In the concentration range of interest, 5-100 mM, Br- is the most suitable halide (Fig.3 - 5). The least suitable is I-, in spite of the fact that the Ksp of AgI is about four orders of magnitudes lower than that of AgBr. In order to keep the concentration of the soluble silver species lower than 10-6 M, the concentration of Br- should not exceed 50 mM.

 

Titration of Cl- with electrogenerated Hg22+. The presence of strong acid is essential for the precipitation reaction to proceed in reasonable rate. The minimal concentration is 30 mM. Beyond 50 mM no increase in the rate is observed. The role of the acid is not understood. While both HNO3 and HClO4 are effective, the potentiometric indication obtained with dual polarized electrodes is better defined with HClO4.

 

3.9. Cells

A great variety of cells and electrode arrangements are found in the literature. Volumes in the range of 0.1 to 200 ml are used. The cell recommended here with different generating electrodes is shown in Fig.3-7. The working volume in the lower part of the cell is 3 to 10 ml.

 


Fig.3-7 Cells and electrodes in coulometric titrations:

(a) with an isolated counter electrode;

(b) with a non-isolated small-area counter electrode, designed to hamper direct reaction of the titrant at it;

(c) with a non-isolated counter electrode at which only inactive products are formed.

 

3.10. Collecting data

Coulometric titrations take little time and you are advised to repeat each one at least five times and carry out a statistical analysis on the results. For each experiment report mean, standard deviation and reject data according to rules and common sense.

 

SUMMARY OF COULOMETRIC TITRATIONS

 


 

 

 

 

Exp.1. Titration of As(III)

Chemicals 1. 5 mM As2O3 solution

2. 0.5 mM As2O3 solution

3. Combined 0.1 M KI and 0.1 M NaHCO3 solution

4. 1% starch solution (freshly prepared)

5. 0.5 M H2SO4 (for pretreatment of Pt electrodes)

 

Electrodes: generating - Platinum;

counter - Non-isolated platinum, carbon or tungsten (area 0.03 - 0.1 cm2);

indicating - Twin platinum electrodes.

 

Electrode reactions:

anode: (I2 in excess of I- is in the form of I-3 )

cathode: (before the end point)

(after the end point)

 

The titration of As(III) is based on the reaction:

The optimal pH range for performing the reaction is 7 - 9. Complete oxidation of As(III) requires pH above 7, but to avoid disproportionation of iodine the pH must be smaller than 9. The bicarbonate used in this experiment has the ability to restrict the pH in this range (Explain! Hint: cf. Exp. 3 in Potentiometric Titrations).

Note: Disproportionation of I2 at pH > 9:

 

Procedure

a) Visual detection of the end point

Insert the electrodes into the cell and connect them to the coulometer. Note that the auxiliary electrode is not isolated. Why I2 is not reduced at the cathode prior to the end point?

Add to the titration vessel just enough KI-NaHCO3 solution to cover the electrodes and 2 drops of 1% starch solution. Adjust the current to 20 mA. The clock should be zeroed at the beginning of each titration.

Pretitration. Start the stirrer. Turn on the current for a short time (~1 s) and note the darkening of the solution. Add a small amount of the arsenite stock solution dropwise until the color disappears. Then operate the current on-off switch intermittently until a light blue color develops in the entire solution. This color will be taken as the end point of the titration. Set the timer back to zero.

Pipet 0.500 ml of the 5 mM arsenite solution into the vessel and titrate with rapid stirring until the same light blue color develops, then stop the titration and record the time.

As the end point is approached, the titration should be stopped periodically to allow the iodine (seen as blue streaks emanating from the generating electrode) to react before addition of the next portion of the titrant. At this stage the current should be stopped for short periods of time (~0.1 s).

Return the timer to zero, pipet another 0.500 ml of the sample into the vessel and repeat the coulometric titration. Several runs may be made in the same solution. Repeat until at least three consecutive values agree to within 0.2 s.

Dilute your unknown arsenite sample in the volumetric flask to the mark and titrate 0.500 ml portions of it as you did before.

 

b) Potentiometric determination of the end point

In the above experiment you performed your first coulometric titration. You observed the generation of the titrant (I2 formation) and determined the end point with reasonable accuracy and relative ease. In this part of the experiment you will repeat the above titration, but with an arsenite solution ten times more diluted. What accuracy would you expect to obtain in this case using the visual end-point determination?

Try to envisage what effort would be required to perform the same titration in its volumetric version: preparation of titrant solution, its standardization and storage, use of clean glassware, pipettes, burettes, analytical balances, chemical standards and others.

Two improvements are introduced in this section:

(i)      The titration is performed with monotonic generation of titrant, using the repetitive mode of titrations (Titrimetric Methods of Analysis, section 1.5);

(ii)    The end point is determined potentiometrically using two identical platinum electrodes. Since the titration is performed in a continuous mode, well-defined end point is observed without passing current between the twin indicating electrodes (note, that for point-by-point titration a small constant current (~1 A/cm2) should be passed between the indicating electrodes).

Repetitive-monotonic titration. Add to the titration vessel just enough KI - NaHCO3 solution to cover the electrodes. Pipet 0.500 ml of the 0.5 mM arsenite solution. Insert the indicating twin platinum electrodes. Set the current for the generating electrodes at 2 mA, and for the indicating electrodes at 0.5 A. Titrate until the expected potential peak is observed. Stop the titration somewhere after the end point, add to the cell an additional 0.500 ml portion of the sample and continue to titrate. Perform a series of repetitive titrations in the same solution. The time elapsed from peak to peak is the time corresponding to the end point and does not include the time lag of the electrodes.

Perform an additional series of titrations under the above conditions, but without passing current between the indicating electrodes. Compare the two types of titrations and comment.

Measure the distances between the end points and calculate the average time and the standard deviation. Compare the average with the time of the first titration.

Report the concentration of As(III) in mol/l:

a) in the stock solutions (note that the stock solutions are not standardized),

b) in the unknown, as received in the volumetric flask.

 

Exp.2. Acid-base titrations

Chemicals 1. 0.1 M KNO3

2. 0.05 M KBr

3. 5.0 mM HCl

4. 0.1% Bromothymol Blue or Methyl Red solution

 

Procedure (a)

Electrodes: generating - Platinum (~0.3 cm2 area);

counter (isolated) - Platinum, tungsten (only as cathode) or carbon.

Electrode reactions

cathode:

anode:

Pretitration. Add to the coulometric cell few drops of 5.0 mM HCl, 2 drops of the indicator solution and enough of 0.1 M KNO3 to cover the electrodes. Insert the generating electrodes into the solution. Check that the counter-electrode compartment is filled with electrolyte (1 M KNO3). Titrate at a current of 10 mA until a color change is observed. This change of color will be taken as the end point of the titration. Set the timer back to zero.

Pipet 1.00 ml of 5.0 mM HCl into the vessel. Let the titration continue until the same color is reached. Several runs may be made in the same solution. This procedure, however, brings to a progressive dilution of the analyte and the experiment should be started anew after several runs. You should strive to reach a 0.2 seconds agreement between the results.

A sample can also be pretitrated by simply reversing the polarity of the electrodes and passing the same current for the same length of time. The composition of the solution is now the same as it was before the start of the first titration. Now reverse the polarity once again and titrate.

 

Procedure (b)

Electrodes: generating - Platinum;

counter (non-isolated) - Silver (~1.5 mm wire).

Electrode reactions

cathode:

anode: Ag + Br- = AgBr + e

Acids can be titrated with a non-isolated silver counter electrode in presence of KBr as background electrolyte. In this case the anodic reaction is the formation of AgBr, which adheres to the electrode and there is no need to isolate the counter electrode. The bromide deposit should be mechanically removed from time to time.

Replace the isolated platinum electrode with a silver electrode. Add just enough of 0.05 M KBr to cover the electrodes and 2 drops of the indicator solution. Perform a pretitration at a current of 10 mA as explained above in Procedure (a). Add 1.00 ml of 5.0 mM HCl and titrate. Several runs may be carried out in the same solution.

Report the normality of the acid as obtained by the two sets of electrodes.

 

Questions

1. With the help of current-voltage curves, describe the reactions taking place at the working electrodes, at various stages of the titration. What are the reactions at the counter electrode?

2. Why is it necessary to separate the electrode in one case and not in the other?

3. Could the generating and counter electrodes be replaced by graphite instead of platinum? Explain.

4. Is a reagent precursor necessary in acid-base reactions? Explain.

5. Describe an experimental method for a base titration. Is it possible in this case to use platinum and silver as the generating electrode pair?

6. What is the advantage of coulometric generation of OH- over titration with a solution of NaOH?

7. Suggest a coulometric apparatus for the titration of a) dichromate, b) bromide.

8. Why is it not convenient to titrate coulometrically large volumes of more concentrated solutions (e.g., 100 ml of 0.1 M HCl)?

 

Exp. 3. Determination of chlorides in drinking water with coulometrically generated mercurous ion

Chemicals 1. Methanol

2. 5 mM HCl or/and drinking water samples

3. 1.2 M HClO4

 

Electrodes: generating - Mercury-coated silver electrode;

counter - Non-isolated platinum or tungsten electrode (area ~0.05 cm2);

indicating - Twin mercury-coated silver electrodes.

 

Electrode reactions:

Anode:

The mercurous ion () is the main product. However, the possible formation of small amounts of Hg2+ does not affect the accuracy of the titration, since in both cases one electron per one chloride anion is involved.

Cathode:

At low concentration of chlorides (lower than 10 mM), the argentometric titration is not practical because of the relatively high Ksp of AgCl (1.610-10).

The solubility of Hg2Cl2 is several orders of magnitude lower in 70-80% methyl alcohol (Fig.3-8) and mercury ions can be generated at 100% efficiency from a mercury-coated silver anode. The end point is determined potentiometrically with two identical mercury-coated silver electrodes at constant current of 0.5 A (~2 A/cm2).

 


Fig.3-8 Apparent solubility product (left axis) and solubility (right axis) of Hg2X2 as function of percentage of methanol (data taken from E.P.Przybylowicz and L.B. Rogers, Anal.Chem., 28, 799 (1956)).

 

Procedure

The titration is performed in the repetitive-monotonic mode (Titrimetric Methods of Analysis, section 1.5).

1. Set the current for generating Hg(I) to 2 mA and the current for the indicating electrodes to 0.5 A.

2. Add to the coulometric cell a 0.500 ml sample of tap water or chloride solution, about 0.2 ml (5 drops) of 1.2 M HClO4 and just enough methanol to cover the electrodes.

3. Start to titrate. Continue the titration until the expected potential peak is observed. Stop the process at any point after the peak of the end point.

4. Add an additional 0.500 ml portion of the sample to the previously titrated solution. Continue to titrate. Make several more additions of the sample. Observe the titration curve. The time elapsed from peak to peak is the time corresponding to the end point and does not include the time lag of the electrodes.

5. Measure the distances between the peaks and calculate the average time and the standard deviation. Compare the average with the time of the first titration. Report the concentration of Cl- in ppm and in mol/l.

 

Exp. 4. Titration of Br- or I- with generation of Ag+

Chemicals 1. 0.1 M KNO3

2. 5.0 mM KBr or KI

3. 1.2 M HClO4

4. 0.3% PVA (Polyvinyl alcohol)

 

Electrodes: generating - Silver and platinum electrodes;

indicating - Twin silver wires.

Procedure

Add to the coulometric cell 0.500 ml of 5.0 mM KBr or KI solution, ~4 ml 0.1 M KNO3, 0.2 ml (5 drops) of 1.2 M HClO4 and one drop of 0.3% PVA solution.

Note: PVA is a surfactant. It hampers the coating of the generating anode with AgX.

Carry out a titration at a generating current of 2 mA. Use the repetitive-monotonic method as described in Titrimetric Methods of Analysis, section 1.5.

The silver generating electrode gradually acquires a coating of silver halide, which isolates electrically the electrode and should be removed mechanically from time to time. Clean the silver wire with a fine grade emery paper and rinse it with distilled water. At the end of the experiment clean the electrode and store it in the vessel provided.

Report the concentration of the halide in mol/l.

 

Questions

1. With the help of current-voltage diagrams list the reactions, which take place at the silver generating electrode at various stages of the titration.

2. In the titrations carried out in this experiment the electrode itself took part in the reaction. Is the addition of a precursor necessary in such a case?

3. Why the counter electrode may not be isolated?

4. What is the purpose of the KNO3?

5. Is this type of automatic titration possible in the case of an acid-base titration with a glass electrode? Why?

 

Exp. 5. Titration of Fe2+ with coulometrically generated Ce4+.

Amperometric indication of the end point

Principle of the method. The potentiometric indication for the titration of Fe2+ with Ce4+ is not applicable at low concentration levels (< 5 mM), where steady-state potentials are reached extremely slowly. The reason for the failure of potentiometric indication is the formation of oxide on the platinum indicating electrode as the equivalence point is approached. The response of the electrode becomes sluggish at low concentrations and is totally unsuitable for automatic titrations.

In order to avoid the formation of oxides we propose an amperometric type of indication, where the indicating electrode is kept at a constant potential, negative to the potential at which oxides are formed5.

Concentrations of Fe2+ as low as 20 M can be determined in continuous titrations with a precision of 2%.

 


Fig.3-9 (a) Repetitive coulometric titration of 1 mM Fe2+ with electrogenerated Ce4+.

Initial composition: 200 L 1.78 mM Fe2+, 4 ml 0.1 M Ce(NO3)3 in 3 M H2SO4. Generating electrodes: Pt (~0.3cm2) and non-isolated Au counter; ig = 1.0 mA. Amperometric indication: Pt electrode (0.2 cm2 area) vs Ag/AgCl/1 M KCl reference electrode (E = 420 mV).

(b) Voltammograms at different stages of the titration (progress of titration F = 0 1.4) of Fe2+ at a Pt-RDE (0.16 cm2 area).

Rotation rate: 400 rpm. Initial composition: 1 mM Fe2+ in 0.1 M Ce(NO3)3, 3 M H2SO4.

 

Chemicals 1. 0.1 M Ce(NO3)3 in 3 M H2SO4

2. 2 mM Fe(NH4)2(SO4)2 in 3 M H2SO4

 

Electrodes: Generating - Platinum anode (area 0.2 - 1 cm2) and non-isolated cathode (Pt, C, W or Au; ~0.05 cm2);

Indicating - Platinum wire (area ~0.2 cm2) and reference electrode.

 

Electrode reactions

anode:

cathode:

Overall reaction during titration:

 

Procedure

The progress of the titration is followed by amperometric indication. A constant potential of +420 mV vs Ag/AgCl/1 M KCl is applied to the indicating electrodes. The current, flowing in the indicating system, is recorded.

Add to the coulometric cell about 4 ml of 0.1 M Ce3+ solution and 0.500 ml of 2 mM Fe2+ solution. To avoid penetration of oxygen, which affects the electrode processes, keep the cell closed. Titrate with a generating current of 2 mA. (The optimum current density range is from 1 to 10 mA/cm2).

Use the repetitive mode to perform a series of titrations. In order to avoid the oxidation of Fe2+, the time of the interruption between subsequent titrations is to be kept short (not more then few seconds). It is adviced to add the new portion of analyte without interrupting the titration.

 

Treatment of results

1. Calculate the concentration of Fe2+ in the solution.

2. With the help of current-voltage diagrams, list the reactions that take place at the working generating electrode at various stages of the titration.

3. What is the role of Ce3+?

 

Exp. 6. Determination of ascorbic acid in a Vitamin C tablets

The titration is based on the following reaction:

Ascorbic acid + Br2 + H2O = Dehydroascorbic acid + 2Br- + 2H+

 

Chemicals 1. Vitamin C tablets

2. 0.05 M KBr

 

Electrodes: generating - Platinum;

counter - Isolated platinum wire or graphite in 0.05 M KBr compartment solution;

indicating - Twin gold electrodes (area 0.2 - 0.3 cm2).

 

Procedure

The bromine is coulometrically generated at a platinum electrode and the end point of the titration is followed potentiometrically by passing a small current of about 0.5 A between the indicating electrodes.

You are provided with a Vitamin C powder, obtained from about 10 Vitamin C tablets. Dissolve in water 50 mg of the powder in a 250 ml measuring flask, make up to volume. The resulting solution is somewhat cloudy due to the presence of inert substance in the tablets. Transfer 0.500 ml of the Vitamin C solution to the coulometric cell, add about 5 ml of 0.05 M KBr and titrate at a current of 2 mA.

Use the repetitive mode of titration. Report % of ascorbic acid in the tablet.

Note: Keep the Vitamin C solution out of light and perform the titration within two hours after the preparation of the solution.

 

 

References

1. J. J. Lingane, Electroanalytical Chemistry, Interscience Pub., 1958.

2. L. Szebelledy and Z. Somogoi, Z. Anal. Chem., 112, 395(1938).

3. J. J. Lingane, Anal. Chim. Acta, 11, 283(1954).

4. E. Kirowa-Eisner, D. Tzur and V. Dosortzev, Anal. Chim. Acta, 359, 115(1998).

5. D. Tzur, V. Dozortsev and E. Kirowa-Eisner, Anal. Chim. Acta, 392, 307(1999).

 

Recommended Literature

1. D. A. Skoog, Principles of Instrumental Analysis.

2. D. A. Skoog and D. M. West, Principles of Instrumental Analysis.

3. D. A. Skoog and J. J. Leary, Instrumental Analysis.

4. L. Meites and H. C. Thomas, Advanced Analytical Chemistry, ch.7-11.

 

 

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