Electrical equivalence point

Stoichiometrically, the total quantity of electricity passed is exactly the same as it would have been if the Fe(II) ions had been directly oxidised at the anode and the oxidation of Fe(II) proceeds with 100 percent efficiency. The equivalence point is marked by the first persistence of excess Ce(IV) in the solution, and may be detected by any of the methods described above. The Ce3+ ions added to the Fe(II) solution undergo no net change and are said to act as a mediator. 

A number of commercial titrators are available in which the electrical measuring unit is coupled to a chart recorder to produce directly a titration curve, and by linking the delivery of titrant from the burette to the movement of the recorder chart, an auto-titrator is produced. It is possible to stop the delivery of the titrant when the indicator electrode attains the potential corresponding to the equivalence point of the particular titration this is a feature of some importance when a number of repetitive titrations have to be performed. Many such instruments are controlled by a microprocessor so that the whole titration procedure is, to a large extent, automated. In addition to the normal titration curve, such instruments will also plot the first-derivative curve (AE/AV), the second-derivative curve (A2 E/AV2), and will provide a Gran s plot (Section 15.18). 

Let us introduce into the titrant one Pt indicator electrode vs. an SCE and maintain in the electric circuit a low constant current + /, as indicated by the broken horizontal line in Fig. 3.71. For this line we shall consider the successive points of its intersection with the voltammetric curves during titration and observe the following phenomena as expressed in the corresponding electrode potentials. Immediately from the beginning of the titration E remains high (nearly 1.44 V), but falls sharply just before the equivalence point (E = 1.107 V), and soon approaches a low E value (below 0.77 V) (see Fig. 3.72, cathodic curve +1). 

If a solution forms part of an electrochemical cell, the potential of the cell, the current flowing through it and its resistance are all determined by the chemical composition of the solution. Quantitative and qualitative information can thus be obtained by measuring one or more of these electrical properties under controlled conditions. Direct measurements can be made in which sample solutions are compared with standards alternatively, the changes in an electrical property during the course of a titration can be followed to enable the equivalence point to be detected. Before considering the individual electrochemical techniques, some fundamental aspects of electrochemistry will be summarized in this section. 

Amperometric titrations have an even wider range of application than polarography. Although the titrant may be added from a burette, in many applications it is electrically generated in a coulometric cell (p. 261). Such an arrangement lends itself to complete automation and is particularly valuable for the titration of very small quantities. For examples of coulometric titrations with amperometric equivalence point detection see Table 6.5. 

The electrical conductance of a solution is a measure of its current-carrying capacity and is therefore determined by the total ionic strength. It is a nonspecific property and for this reason direct conductance measurements are of little use unless the solution contains only the electrolyte to be determined or the concentrations of other ionic species in the solution are known. Conductometric titrations, in which the species of interest are converted to non-ionic forms by neutralization, precipitation, etc. are of more value. The equivalence point may be located graphically by plotting the change in conductance as a function of the volume of titrant added. 

From Eq. (a) it is evident that each molecule of FeS04, upon oxidation, happens to lose one electron. Hence, one mole of FeS04 loses 6.02 x 1023 electrons which is equivalent to 1 Faraday or 96,500 C. Thus, in electrochemical determination of equivalence point the quantity of electricity is almost identical with that required to reduce 1 mole of Ce(S04)2. It follows from here that 1 mole of FeS04 and 1 mole of Ce(S04)2 are chemical equivalents. In other words, 1 g of H, acting as a reducing agent, loses electrons equivalent to 96,500 C. 

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... 

Because atmospheric humidity must be avoided, the reaction flask is isolated from the atmosphere with drying tubes. Moreover, since the solvent is rarely perfectly anhydrous and will contain traces of water due to its hygroscopic nature, its water content must be measured prior to the determination. The equivalence point of the titration reaction is detected by an electrical method instead of a visual method. The current intensity that passes between two platinum electrodes inserted in the reaction medium is measured (see Fig. 19.10). The reagent, which is a mixture of sulphur dioxide, iodine and a base, is characterised by the number of mg of water that can be neutralised by 1 cm3 of this reagent. This is referred to as the equivalent mass concentration of water, or the titre T of the reagent. 

Another specialized form of potentiometric endpoint detection is the use of dual-polarized electrodes, which consists of two metal pieces of electrode material, usually platinum, through which is imposed a small constant current, usually 2-10 /xA. The scheme of the electric circuit for this kind of titration is presented in Figure 4.1b. The differential potential created by the imposition of the ament is a function of the redox couples present in the titration solution. Examples of the resultant titration curve for three different systems are illustrated in Figure 4.3. In the case of two reversible couples, such as the titration of iron(II) with cerium(IV), curve a results in which there is little potential difference after initiation of the titration up to the equivalence point. Hie titration of arsenic(III) with iodine is representative of an irreversible couple that is titrated with a reversible system. Hence, prior to the equivalence point a large potential difference exists because the passage of current requires decomposition of the solvent for the cathode reaction (Figure 4.3b). Past the equivalence point the potential difference drops to zero because of the presence of both iodine and iodide ion. In contrast, when a reversible couple is titrated with an irreversible couple, the initial potential difference is equal to zero and the large potential difference appears after the equivalence point is reached. 

The electrical circuit consists of two electrodes a redox indicator electrode and a reference electrode that also passes current. A fixed potential difference is applied and the equivalence point is calculated from the intersection of the two straight lines that show the variation of current before and after the endpoint in a plot of current as a function of added titrant volume. The plots can have various forms, depending on whether the titrated species or titrant are or are not electroactive. Figure 14.1 shows the four possible cases. Sometimes the potential difference applied is less than that necessary to reach the mass-transport-limited current, but sufficient to give good results. 

The thermoelectric power, or thermopower, of the thermocouple is of the order of 2 to 50 iV/°C, depending on the metals and the temperature. In general, the thermopower decreases with decreasing temperature. Typically, in a thermocouple, the first junction is at Th, and the second, or reference junction, is held at the ice point of water (Tc = 0°C) (Fig. 10.21), or its electrical equivalent ("cold junction compensation"). 

Fig. 97. (a) Electrical equivalent circuit of an illuminated semiconductor electrolyte interface, (b), (c) Experimental impedance plots for n-GaAs/selenide under 22mWcnT2 illumination at different potentials, (b) V = -0.60V/SCE (in the photocurrent saturation region) (c) V = - 1.575 V/SCE (in the onset region). The circles are experimental points and the dotted curve is the best fit to (a). 

Another method uses a preset equivalence point potential applied across the electrodes by means of a calibrated potentiometer. A difference between this potential and that of the electrodes causes an error signal, which is amplified. This causes the electronic switch to close, permitting a flow of electricity through the solenoid-operated valve of the burette. As the signal approaches zero, the flow of titrant ceases as the current to the solenoid is switched off. 

A coulometric titration uses an electrolytically generated titrant for reaction with the analyte. In some analyses, the active electrode process involves only generation of the reagent. In other titrations, the analyte may also be directly involved at the generator electrode. The current in a coulometric titration is carefully maintained at a constant and accurately known level. The product of this current and the time required to reach the equivalence point for the reaction yield the number of coulombs and thus the number of equivalents involved in the electrolysis. The coulomb (C) is the quantity of electricity that is transported in 1 by a constant current of 1 ampere. The Faraday constant (F) is the quantity of electricity that produces one equivalent of chemical change at an electrode. ... 

Neutralization reactions can also be looked at through conductivity tests. If a conductivity titration is performed with diluted hydrochloric acid and diluted sodium hydroxide solution (see E7.14), one would attain a certain minimum of electrical conductivity at the equivalence point, but it is not zero (see left diagram of Fig. 7.15) Na + (aq) ions and CF(aq) ions are left behind in the solution and are responsible for the minimal conductivity. The decrease in conductivity is often explained by the misconception that the absolute number of ions decreases and that by the usual ionic equation from an initial number of four ions, only two remain ... 

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