Potentiometric Methods Instrumentation: Electrodes, Automatic Titrator

INSTRUMENTATION

Figure 16.2 illustrates a typical assembly for carrying out a potentiometric titration. Broadly speak-ing, the titration essentially comprises of measuring and subsequently recording a cell potential in terms of either mV or pH, after each sequentially known addition of reagents.

In usual practice, the titrant (e.g., Lanthanum Nitrate) is added in large amounts at the initial stage ; as the end-point is approached, which is marked by distinct larger potential changes per addition, the subse-quent increments are made smaller to the tune of 0.1 ml for each addition.

It is always advisable to allow sufficient time lapse after each addition of titrant so as to attain equilibrium. A gentle and uniform stirring by means of a magnetic stirrer also helps in hastening the ultimate achievement of equilibrium :

The various components shown in Figure 16.2, are as follows :

A = Saturated Calomel Electrode (SCE),

B = Indicator Electrode,

C = Burette to discharge titrant in the reacting vessel,

D = pH Meter with a mV scale,

E = Magnetic stirrer with variable speed, and

F = Magnetic Guide.

1.  ELECTRODES

The accurate, precise and effective potentiometric measurements are evidently made with the aid of the following two types of electrodes namely :

(i) Reference Electrodes, such as :

(a) Standard Hydrogen Electrode,

(b) Saturated Calomel Electrode, and

(c) Silver-silver Chloride Electrode.

(ii) Indicator Electrodes, such as :

(a) Metal Indicator Electrode, and

(b) Membrane Indicator Electrode.

These various kinds of electrodes will be discussed briefly, along with a diagrammatic representation wherever possible, in the sections that follow :

1.1. Reference Electrodes

In general, reference electrodes exhibit a potential which is absolutely independent of the solution wherein it is used. Besides, it must not display any significant change even when a small quantum of current is passed through it.

1.1.1. Standard Hydrogen Electrode (SHE)

The standard hydrogen electrode (SHE), as shown       in Figure 16.3, is considered to be the universally accepted reference electrode. The metal electrode comprises of a small piece of platinum foil with a finely divided platinum,usually termed as platinum black because of its dark look.The coated foil is immersed in an acidic medium having a hydrogen ion activity of 0.1, and through which H2 gas is bubbled at a partial pressure of 1.0 atm (unit activity). The Pt-black-foil possesses a relatively large-surface-area thereby enabling it to absorb an appreciable amount of  H2+H (a = 1.0 M) gas, ultimately bringing it into direct contact with the surrounding H+ ions at the electrode surface. Consequently,the Pt-electrode attains a potential which is finally estimated   Figure 16.3 : A Standard Hydrogen by the relative tendencies of H+ ions to undergo reduction Electrode. and H2  (g) to undergo oxidation simultaneously. It is an usual convention to assign the potential of SHE a value exactly equal to zero at all temperatures.

1.1.2. Saturated Calomel Electrode

The schematic diagram of a commercial saturated calomel elec-trode (SCE) is depicted in Figure 16.4. It essentially consists of a plati-num wire immersed in a slurry made up of pure mercury, solid mercurous chloride Hg₂Cl₂ (commonly known as calomel), and aqueous saturated solution of KCl, packed in the inner-tube (c) having a small hole (B). The outer-tube contains a saturated solution of KCl (D) having a porous ce-ramic fiber (A) at its lower end. It serves as a salt-bridge which allows the entire set-up immersed directly into the solution to be measured. The po-rous ceramic fiber permits establishment of electrical contact between one side of the salt-bridge and the solution under the examination and serves as a barrier between the said two solutions. The small opening at the top end of the salt-bridge tube serves as a fill-hole (E) through which either KCl solution may be filled or replaced as and when required. 

The differ-ent parts of the saturated calomel electrode are as follows :

A = Porous ceramic fiber,

B = Small-hole,

C = Slurry of Hg, Hg₂Cl₂ and saturated KCl, D = Saturated KCl solution,

E = Fill-hole, and

F = Electrical lead.

The half-cell of SCE may be expressed as :

According to the Nernst equation, the potential of the electrode is represented by :

assuming the activities of Hg and Hg₂Cl₂ solid are both unity.

Advantages : The two major advantages of SCE are, namely :

(a) Concentration of Cl^– does not alter appreciably even if some of the solvent gets evaporated, and

(b) Generates a comparatively small junction potential (E_j) at the two salt-bridge solution interfaces.

1.1.3. Silver-silver Chloride Electrode

Figure 16.5 shows a silver-silver chloride electrode which com-prises of a silver wire coated with silver chloride (B) and is duly placed in a 1 M KCl solution saturated with AgCl (C).

The half-cell of silver-silver chloride electrode may be represented as :

for which half-reaction would be :

According to the Nernst equation, the potential of the electrode is expressed as :

considering that the potential of the electrode is solely dependent on the concentration of Cl^–.

The various components of a silver-silver chloride electrode are, namely :

A = Porous ceramic fiber,

B = Ag wire coated with AgCl,

C = 1 M KCl saturated with AgCl,

D = Fill-hole, and

E = Electrical lead.

1.2. Indicator Electrodes

An indicator electrode is invariably used exclusively in conjunction with a reference electrode the response of which solely depends upon the concentration of the analyte.

1.2.1. Metal Indicator Electrode

Metal indicator electrodes develop a potential which is usually determined by the equilibrium posi-tion of a redox half-reaction at the electrode surface. These are further classified into the following three types, namely :

(i) First order electrodes,

(ii) Second order electrodes, and

(iii) Inert electrodes.

which shall be discussed briefly below.

1.2.1.1.  First-order electrodes

They are essentially comprised of a metal placed in a solution of its respective ions, for instance : a silver wire immersed into a AgNO₃ solution. Hence, the reversible half reaction may be represented as:

and the corresponding Nernst equation would be as follows :

The metals that display reversible half reactions with their respective ions and are found to be suitable for employing as first-order electrodes are Ag, Hg, Cu, Cd, Zn, Bi, Pb and Sn. However, several other metals like : Fe, Co, Cr and W are not useful due to the following reasons :

(i) Non-reproducible potentials largely influenced by impurities,

(ii) Irregular crystal structures in the solid-state, and

(iii) Formation of oxide layers on their surfaces.

1.2.1.2.  Second-order electrodes

Sometimes a metal electrode may be directly responsible to the concentration of an anion which either gives rise to a complex or a precipitate with the respective cations of the metal. Therefore, they are termed as second-order electrodes as they respond to an ion not directly involved in the electron transfer process. The silver-silver chloride electrode, as already described, is a typical example of a second-order electrode. In this particular instance, the coated Ag wire when dipped in a solution, sufficient AgCl dissolves to saturate the layer of solution just in contact with the respective electrode surface. Thus, the Ag⁺ ion concentration in the said layer of solution may be determined by the status of the solubility product (K_sp) equilibrium :

Disadvantages : The four serious disadvantages are, namely :

(a) May be used effectively over a certain range of anion concentration only so that the solution must remain saturated with the substance coating the metal,

(b) In the case of Ag-AgCl electrode, a very low Cl^– ion concentration would dissolve the AgCl-coating to a great extent,

(c) Likewise, a very high concentration of Cl^– ion would result into the formation of soluble complex ions as shown below :

(d) Ions like Br^–, I^– SCN^–, CN^– and S^2– cause interference while using a Ag-AgCl electrode to esti-mate Cl^– ion concentrations because of the facts that these ions usually form salts with Ag⁺ ion which are significantly less soluble than AgCl.

1.2.1.3. Inert electrodes

Inert electrodes comprise of chemically inert conductors, for instance : Au, Pt and C which do not necessarily take part either directly or indirectly in the various redox processes. However, the potential developed at an inert electrode solely depends upon both the nature as well as the prevailing concentration of the different redox-reagents present in the solution.

Example : A Pt-electrode placed in a solution consisting of both Fe³⁺ and Fe²⁺ ions develops a poten-tial which is duly represented by the Nernst equation for ions as given below :

Advantages : The two main advantages of inert-electrodes are, namely :

(a) Exhibit no chemical selectivity, and

(b) Respond to any reversible redox-system.

1.2.2. Membrane Indicator Electrodes (or Ion-Selective Electrodes)

The underlying principle of this type of electrode is that the potential developed due to an unequal charge generated at the opposing surfaces of a ‘special’ membrane. The resulting charge at each surface of the membrane is exclusively controlled and monitored by the exact position of an equilibrium involving analyte ions, which in turn, solely depends upon the concentration of those ions present in the solution. Ion-selective electrodes occupy a very important place in the analytical chemistry by virtue of the fact that one may use the acquired skill, expertise and wisdom to design and commercially prepare membranes that are practically selective towards a specific ion besides producing potentials according to the Nernst-type equation. These are classified further into the following four kinds, namely :

(i) Glass membrane electrodes,

(ii) Polymer (liquid) membrane electrodes,

(iii) Crystalline membrane electrodes, and

(iv) Gas-sensing electrodes,

which will be described below briefly :

1.2.2.1. Glass Membrane Electrodes

The diagram of a typical glass-membrane electrode is depicted in Figure 16.6. The internal element essentially comprises of a Ag-AgCl electrode (B) dipped in a pH 7 buffer saturated with AgCl (A). The thin, ion-selective glass membrane (I) is carefully fused to the bottom of a high resistance non-responsive glass tube (H) so that the entire membrane may be immersed while taking measurements.

The half-cell of glass-membrane electrode may be expressed as :

Ag (s) | AgCl [saturated], Cl^– (inside), H⁺ (inside) | glass membrane | H⁺ (outside)

According to the Nernst equation, the potential of the electrode is represented by :

              .......................(i)

Now, separating the ratio of H⁺ ion concentrations into two log terms we may have :

As the activities (i.e., concentrations) of H⁺ and Cl^– in the internal electrolyte solution are constant, the first three components on the right hand side of Eq. (ii) may be confined into a single constant, K, and the equation could be rewritten as :

E = K + 0.0592 log [H+]_outside

The various components of Figure 16.6 are as follows :                                                               

A = pH 7.0 buffer solution saturated with AgCl,         

B = Ag-AgCl internal reference electrode,           

C = Mercury connection,                                                                 

D = Connecting wire,                                          

E = Shield,                                                          

F = Cap,                                                              

G = Shielded and insulated connecting wire,                                                                

H = High resistance non-responsive glass, and                                                   

I = H+–selective glass membrane.                                                             

1.2.2.2. Polymer (Liquid) Membrane Electrode

Figure 16.7. illustrates a calcium-ion polymer (liquid) membrane electrode. It has a close similarity to the glass pH electrode, and it essentially comprises of an internal Ag-AgCl electrode (B) and an internal reference solution having a fixed composition e.g., aqueous CaCl₂ saturated with AgCl (C). The liquid calcium di (n-decyl) phosphate, [{CH₃(CH₂)₈CH₂O}₂PO₂]₂ Ca serves as the membrane, positioned at the lower end of the electrode, and strategically immobilized by a thin disk of PVC (polyvinyl chloride) (A) which is not penetrable with water.

Thus, the calcium di (n-decyl) phosphate forms an equilibrium with its ions at every membrane surface :

where, R = CH₃(CH₂)₈ –CH₂– i.e., n-decyl hydrocarbon chain.

Interestingly, the didecylphosphate anion represents a fixed component of the non-aqueous liquid membrane. As the concentration of Ca⁺ ions present in the solutions on either side of the membrane varies ; hence, the concentration of didecylphosphate anion at every membrane surface would also vary accordinly, thereby causing a potential that may be expressed by the following equation :

           ..........................(i)

Again, separating the ratio of Ca²⁺ ion concentration into two log terms we have :

Since the activities of Ca²⁺ and Cl^– in the internal electrolyte solution are more or less constant, the first three terms on the right hand side of Eq. (ii) may be combined to a single constant, K, and the same equation may be rewritten as follows :

      .....................(iii)

The different essential components of Figure 16.7 are as stated below :

A = Calcium di (n-decyl)-phosphate immobilizes in PVC,

B = Silver-silver chloride electrode, and

C = Aqueous CaCl₂ saturated with AgCl.

1.2.2.3.  Crystalline Membrane Electrodes

The crystalline membrane electrodes have a very close similarity to those of glass-membrane electrodes except that glass has been replaced with crystalline membrane. In fact, these electrodes offer a means to devise responsive to anions by making use of a membrane containing specific anionic sites.

Example : Fluoride-ion Electrode : In this particular instance the mem-brane essentially comprises of a single crystal of lanthanum fluoride (LaF₃), usually doped with a slight trace of europium (II), Eu²⁺, so as to initiate the crystal defects required for establishing its electrical conductivity. Therefore, the potential developed at each surface of the membrane is finally determined by the exact status of the equilibrium :

and is represented by the following equation :

Salient features of Fluoride-Ion Electrode are, namely :

(a) At low pH, F^– ion gets readily converted to the weak acid HF (pKa = 3.17) thereby rendering the electrode insensitive,

(b) It is almost 10³ times more specific and selective for F^– ion as compared to other common anions, of course with the exception of OH^– ion, and

(c) This  electrode can tolerate conveniently the maximum concentration of OH^– ion to the extent of 1/10^th as compared to the F^– ion concentration.

Table 16.2 records the characteristics of certain selected crystalline-membrane electrodes.

1.2.2.4.  Gas-Sensing Electrode

The schematic diagram of a gas-sensing electrode is illustrated in Figure 16.8, that comprises of essentially a reference electrode (E), a specific-ion electrode (B), and   internal electrolyte solution (F) contained in a cylindrical plastic tube (G). One end of the plastic tubing is provided with a thin, replaceable, gas-permeable membrane that separates the internal electrolyte solution from the external solution containing gaseous analyte. However, the exact composition and specifications of this gas-permeable membrane is  usually  described by  its respective manufacturers. It is normally made up of a thin microporous film fabricated from a hydrophobic plastic material.

The various components of Figure 16.8 are as follows :

A = Gas permeable membrane,

B = Specific ion electrode (a glass electrode),

C = ‘O’-Ring to hold the membrane,

D = External solution containing dissolved gaseous analyte,

E = Reference electrode (a Ag/AgCl electrode),

F = Internal electrolyte solution, and

G = Plastic tube.

In general, it must fulfil the following requirements, namely :

(a) It should act as a 100% barrier for both water and electrolytes i.e., they must not pass through this membrane,

(b) Pores of the film contain exclusively air or other gases to which it is exposed, and

(c) A solution containing a particular gaseous-analyte, for instance CO₂, when comes in contact with the membrane the former migrates swiftly into the pores of the latter, as expressed by the follow-ing reaction :

        .......................(a)

As the number of pores in the gas-permeable membrane are plenty, therefore, an equilibrium is established. Evidently, the carbon-dioxide present in the pores is in direct contact with the internal-electrolyte solution (F), thereby giving rise to a second equilibrium reaction that may be represented as follows :

              ............................(b)

As a result of the above two reactions, Eq. (a) and Eq. (b), the external solution containing dissolved gaseous analyte (D) immediately attains an equilibrium with the film of internal electrolyte solution (F) present very close to the gas-permeable membrane (A). Thus, another equilibrium gets established that affords the pH of the internal-surface film to alter according to the following expression :

          .........................(c)

The above change in pH is instantly detected by means of a Ag/AgCl reference electrode pair (E) dipped in the film of internal solution as shown in Figure 16.8.

Therefore, the net overall reaction caused by the entire aforesaid process may be achieved by simply summing up the three chemical reactions (a), (b), and (c) to give :

              .............................(d)

The equilibrium constant, K, for Eq. (d) may be represented by :

                ..............................(e)

Assuming that the concentration of HCO₃–present in the internal-electrolyte solution (F) is made comparatively high such that its concentrations do not undergo any appreciable change due to the migrating CO₂, we may have :

                .............................(f)

Thus, Eq. (f) may be rewritten as follows :

   ...........................(g)

where, a₁ = Internal hydrogen ion activity

It is given that :

E_cell = L + 0.0592 log a₁            ...(h)

Consequently, the potential of the electrode system present in the internal-electrolyte solution (F) is solely dependent on a₁ according to Eq. (h). Hence, substituting Eq. (g) into Eq. (h), we may have :

In short, therefore, the potential of the cell comprising of the Ag/AgCI reference electrode (E) i.e., the internal reference and the specific ion electrode (B) i.e., the indicator electrode is normally determined by the CO₂ concentration of the external solution containing dissolved gaseous analyte.

Notes : (i) None of the electrodes (reference & indicator) ever gets in contact directly with the analyte solution, and

(ii) The only substances which may cause interference with the measurement of potential are dissolved gases which may have a free-access through the membrane, and in turn may affect the pH of the internal solution accordingly.

Selectivity of Gas-sensing Electrode : The selectivity of the gas-sensing electrode may be enhanced by making use of such an internal electrode which is particularly sensitive enough to certain species other than the H⁺ ion.

Example : Nitrate-sensing electrode is employed to cater for a cell which will be sensitive exclusively to nitrogen dioxide (NO₂). The equilibrium of such a reaction may be represented as follows :

The nitrate-sensing electrode allows the determination of NO₂ in the presence of certain specific gases only, for instance, NH₃, SO₂ and CO₂, that will also affect the change in pH of the internal electrolyte solution significantly.

2. AUTOMATIC TITRATOR (PRESET END-POINT TITRATOR)

The schematic diagram of an automatic titrator* is shown in Figure 16.9.

The various components of Figure 16.9 are, namely :

A = Magnetic stirrer with a Regulator,

B = Solenoid valve, and

C = Error Signal,

D = Amplifier,

E = Electronic Switch,

F and G = AC-Source,

H = End-point Potential,

I = Calibrated Potentiometer, and

J = Accurately calibrated Burette.

In this case a preset equivalence point potentiometer is applied at the two electrodes with the aid of a calibrated potentiometer (I). It will give rise to an “error” signal (C) provided a difference is caused between this potential and that of the electrodes. The feeble signal thus generated is duly amplified (D) and closes an electronic switch (E) which allows the electricity to flow through the solenoid operated value (B) of the burette (J). As the titration proceeds, the error signal (C) starts approaching a zero value, subsequently the current to the solenoid valve (B) is instantly switched off, and finally the flow of titrant from the burette (J) comes to a halt. The solution of the sample is constantly and uniformly stirred with the help of a magnetic stirrer (A).