1 Determination of Fluoride in Toothpaste 7

Method 11.1 Determination of Fluoride in Toothpaste 7

Description of the Method. The concentration of fluoride in toothpastes containing soluble F – may be determined with a F – ion-selective electrode, using a calibration curve prepared with external standards. Although the F – ISE is very selective (only OH – with K F–/OH– of 0.1 is a significant interferent), Fe 3+ and Al 3+ interfere with the analysis by forming soluble fluoride complexes that do not interact with the ion-selective electrode’s membrane. This interference is minimized by reacting any Fe 3+ and Al 3+ with a suitable complexing agent.

Procedure. Prepare 1 L of a standard solution of 1.00% w/v SnF 2 , and transfer

to a plastic bottle for storage. Using this solution, prepare 100 mL each of

standards containing 0.32%, 0.36%, 0.40%, 0.44%, and 0.48% w/v SnF 2 , adding

Representative Methods —Continued

490 Modern Analytical Chemistry

Continued from page 489 400 mg of malic acid to each solution as a stabilizer. Transfer the standards to

plastic bottles for storage. Prepare a total ionic strength adjustment buffer (TISAB) by mixing 500 mL of water, 57 mL of glacial acetic acid, 58 g of NaCl, and

4 g of the disodium salt of DCTA (trans-1,2-cyclohexanetetraacetic acid) in a 1-L beaker, stirring until dissolved. Cool the beaker in a water bath, and add 5 M NaOH until the pH is between 5 and 5.5. Transfer the contents of the beaker to a 1-L volumetric flask, and dilute to volume. Standards are prepared by placing approximately 1 g of a fluoride-free toothpaste, 30 mL of distilled water, and

1.00 mL of the standard into a 50-mL plastic beaker and stirring vigorously for 2 min with a stir bar. The resulting suspension is quantitatively transferred to a 100-mL volumetric flask along with 50 mL of TISAB and diluted to volume with distilled water. The entire standard solution is then transferred to a 250-mL plastic beaker until its potential is measured. Samples of toothpaste are prepared for analysis by using approximately 1-g portions and treating in the same manner as the standards. The cell potential for the standards and samples are measured using a F – ion-selective electrode and an appropriate reference electrode. The solution is stirred during the measurement, and 2–3 min is allowed for equilibrium to be reached. The concentration of F – in the toothpaste is reported

as %w/w SnF 2 .

Questions

1. The total ionic strength adjustment buffer serves several purposes in this procedure. Identify these purposes.

The composition of the TISAB accomplishes three things: (1) The high concentration of NaCl (approximately 1 M) ensures that the ionic strength of the standards and samples are essentially identical. Since the activity coefficient for fluoride will be the same in all solutions, the Nernst equation can be written using the concentration of F – in place of its activity; (2) Glacial acetic acid and NaOH are used to prepare an acetic acid/acetate buffer of pH 5–5.5. The pH of this buffer is high enough to ensure that the predominant form of fluoride is F – instead of HF; and (3) DCTA is added as a complexing agent for any Fe 3+ or Al 3+

that might be present, preventing the formation of FeF 6 3– or AlF 6 3– .

2. Why is a fluoride-free toothpaste added to the standard solutions?

Fluoride-free toothpaste is added as a precaution against any matrix effects that might influence the ion-selective electrode’s response. This assumes, of course, that the matrices of the two toothpastes are otherwise similar.

3. The procedure specifies that the standard and sample solutions should be stored in plastic containers. Why is it not a good idea to store the solutions in glass containers?

The fluoride ion is capable of reacting with glass to form SiF 4 .

4. The slope of the calibration curve is found to be –57.98 mV per tenfold change in the concentration of F – , compared with the expected slope of –59.16 mV per tenfold change in concentration. What effect does this have on the

quantitative analysis for %w/w SnF 2 in the toothpaste samples?

No effect at all—this is the reason for preparing a calibration curve with multiple standards.

Chapter 11 Electrochemical Methods of Analysis

Measurement of pH With the availability of inexpensive glass pH electrodes and pH meters, the determination of pH has become one of the most frequent quantita- tive analytical measurements. The potentiometric determination of pH, however, is not without complications, several of which are discussed in this section.

One complication is the meaning of pH. 8,9 The conventional definition of pH as presented in most introductory texts is

pH = –log [H + ]

The pH of a solution, however, is defined by the response of an electrode to the H + ion and, therefore, is a measure of its activity.

pH = –log(a H+ )

Calculating the pH of a solution using equation 11.17 only approximates the true pH. Thus, a solution of 0.1 M HCl has a calculated pH of 1.00 using equation 11.17,

but an actual pH of 1.1 as defined by equation 11.18. 8 The difference between the

two values occurs because the activity coefficient for H + is not unity in a matrix of

0.1 M HCl. Obviously the true pH of a solution is affected by the composition of its matrix. As an extreme example, the pH of 0.01 M HCl in 5 m LiCl is 0.8, a value that is more acidic than that of 0.1 M HCl! 8

A second complication in measuring pH results from uncertainties in the rela- tionship between potential and activity. For a glass membrane electrode, the cell po- tential, E X , for a solution of unknown pH is given as

where K includes the potential of the reference electrode, the asymmetry potential of the glass membrane and any liquid junction potentials in the electrochemical cell. All the contributions to K are subject to uncertainty and may change from day to day, as well as between electrodes. For this reason a pH electrode must be calibrated using a standard buffer of known pH. The cell potential for the standard, E S , is

where pH S is the pH of the standard. Subtracting equation 11.20 from equation

11.19 and solving for pH gives

which is the operational definition of pH adopted by the International Union of Pure and Applied Chemistry.*

*Equations 11.19–11.21 are defined for a potentiometric electrochemical cell in which the pH electrode is the cathode. In this case an increase in pH decreases the cell potential. Many pH meters are designed with the pH electrode as the anode so that an increase in pH increases the cell potential. The operational definition of pH then becomes

pH X = pH S − ( E X − EF S ) . 2 303 RT

This difference, however, does not affect the operation of a pH meter.

492 Modern Analytical Chemistry

Table 11.6 pH Values for Selected NIST Primary Standard Buffers a

Saturated

0.025 m (25 °C)

0.025 m

0.008695 m

0.01 m NaHCO 3 , Temperature

Na 4 B 4 O 7 0.025 m (°C)

KHC 4 H 4 O 6 KH 2 C 6 H 5 O 7 KHC 8 H 4 O 4 0.025 m

Na 2 HPO 4 Na 2 HPO 4 (borax) Na 2 CO 3

9.011 9.828 Source: Values taken from Bates, R. G. Determination of pH: Theory and Practice, 2nd ed. Wiley: New York, 1973. 10

a Concentrations are given in molality (moles solute per kilograms solvent).

Calibrating the electrode presents a third complication since a standard with an accurately known activity for H + needs to be used. Unfortunately, it is not possible to calculate rigorously the activity of a single ion. For this reason pH electrodes are calibrated using a standard buffer whose composition is chosen such that the de- fined pH is as close as possible to that given by equation 11.18. Table 11.6 gives pH values for several primary standard buffer solutions accepted by the National Insti- tute of Standards and Technology.

A pH electrode is normally standardized using two buffers: one near a pH of 7 and one that is more acidic or basic depending on the sample’s expected pH. The pH electrode is immersed in the first buffer, and the “standardize” or “calibrate” control is adjusted until the meter reads the correct pH. The electrode is placed in the second buffer, and the “slope” or “temperature” control is adjusted to the- buffer’s pH. Some pH meters are equipped with a temperature compensation fea- ture, allowing the pH meter to correct the measured pH for any change in tempera- ture. In this case a thermistor is placed in the sample and connected to the pH meter. The “temperature” control is set to the solution’s temperature, and the pH meter is calibrated using the “calibrate” and “slope” controls. If a change in the sample’s temperature is indicated by the thermistor, the pH meter adjusts the slope of the calibration based on an assumed Nerstian response of 2.303RT/F.

Clinical Applications Perhaps the area in which ion-selective electrodes receive the widest use is in clinical analysis, where their selectivity for the analyte in a complex matrix provides a significant advantage over many other analytical methods. The most common analytes are electrolytes, such as Na + ,K + , Ca 2+ ,H + , and Cl – , and dis-

solved gases, such as CO 2 . For extracellular fluids, such as blood and urine, the analy- sis can be made in vitro with conventional electrodes, provided that sufficient sample is available. Some clinical analyzers place a series of ion-selective electrodes in a flow

Chapter 11 Electrochemical Methods of Analysis

ed

a Figure 11.18

Schematic diagram for the Kodak Ektachem analyzer for K + : (a) support base; (b) silver; (c) silver chloride; (d) potassium chloride film; (e) ion-selective membrane containing

Potentiometer valinomycin; (f) paper salt bridge; (g) well for sample solution; (h) well for standard solution.

cell, allowing several analytes to be monitored simultaneously. Standards, samples, and rinse solutions are pumped through the flow cell and across the surface of the electrodes. For smaller volumes of sample the analysis can be conducted using dis- posable ion-selective systems, such as the Kodak Ektachem analyzer for K + shown in Figure 11.18. The analyzer consists of separate electrodes for the sample and refer- ence solutions. Each electrode is constructed from several thin films, consisting of a Ag/AgCl reference electrode, a salt bridge and an ion-selective membrane, deposited on a support base. The two electrodes are connected by a paper salt bridge saturated with the sample and reference solutions. The overall dimensions of the analyzer are

2.4 cm with a thickness of 150 µ m and require only 10 µ L each of sample and reference solution. Similar analyzers are available for the determination of Na + , Cl – , and CO 2 . The analysis of intercellular fluids requires an ion-selective electrode that can be inserted directly into the desired cell. Liquid-based membrane microelec- trodes with tip diameters of less than 1 µ m are constructed by heating and draw- ing out a hard-glass capillary tube with an initial diameter of approximately 1–2 mm (Figure 11.19). The tip of the microelectrode is made hydrophobic by dipping in dichlorodimethyl silane. An inner solution appropriate for the desired analyte and a Ag/AgCl wire reference electrode are placed within the microelec- trode. The tip of the microelectrode is then dipped into a solution containing the liquid complexing agent. The small volume of liquid complexing agent entering the microelectrode is retained within the tip by capillary action, eliminating the need for a solid membrane. Potentiometric microelectrodes have been developed for a number of clinically important analytes, including H + ,K + , Na + , Ca 2+ , Cl – , and I – .

2.8 cm ×

494 Modern Analytical Chemistry

To meter

Environmental Applications Although ion-selective electrodes find use in envi- ronmental analysis, their application is not as widespread as in clinical analysis.

Standard methods have been developed for the analysis of CN – ,F – , NH 3 , and NO 3 – in water and wastewater. Except for F – , however, other analytical methods are con- sidered superior. By incorporating the ion-selective electrode into a flow cell, the continuous monitoring of wastewater streams and other flow systems is possible. Such applications are limited, however, by the electrode’s response to the analyte’s activity, rather than its concentration. Considerable interest has been shown in the development of biosensors for the field screening and monitoring of environmental samples for a number of priority pollutants. 11

Ag/AgCl reference electrode

Potentiometric Titrations In Chapter 9 we noted that one method for determining the equivalence point of an acid–base titration is to follow the change in pH with a pH electrode. The potentiometric determination of equivalence points is feasible for

Inner solution

acid–base, complexation, redox, and precipitation titrations, as well as for titrations in aqueous and nonaqueous solvents. Acid–base, complexation, and precipitation potentiometric titrations are usually monitored with an ion-selective electrode that is selective for the analyte, although an electrode that is selective for the titrant or a reaction product also can be used. A redox electrode, such as a Pt wire, and a refer- ence electrode are used for potentiometric redox titrations. More details about po- tentiometric titrations are found in Chapter 9.