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Automated calibration and Standard Addition

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altFluoride plays an important role in dental health, with its presence in small quantities promoting the re-mineralization and strengthening of tooth enamel [1]. This occurs when hydroxyl ligands in the hydroxyapatite rod structure of the enamel are replaced by Fluoride. As a result of this and the deposition of calcium Fluoride on the enamel surface, the tooth surface can become stronger and more resistant to the destructive effects of plaque acid.

As a result of studies showing these beneficial effects of Fluoride, many countries have added Fluoride – in the form of hexafluosilicic acid (H2SiF6) - to their drinking water supplies. Fluoride is also present in many of the commercially available toothpastes, tooth-gel and mouth-wash products that are used around the world, as well as certain food-stuffs (tea for example).

However, the jury is still out on the benefits of fluoride, and further studies have indicated that long term exposure to high levels of Fluoride in water can prove to be counterproductive. Dental fluorosis (a weakening of the surface tooth enamel leading to a pitted surface with discoloured or mottled appearance) is observed in young children exposed to high fluoride levels. Other research has even suggested links between high levels of Fluoride exposure and an increased risk of hip bone fracture amongst the elderly [2] and even to the crippling disorder skeletal fluoridosis [3] - a condition similar to arthritis in its effects. In response to concerns, the World Health Organization now suggests that a daily intake of less than 3mg Fluoride is acceptable for adults.

As ingestion through drinking water consumption is the most common source of dietary fluoride, the Fluoride level in drinking water is controlled strictly in most countries. In many countries and regions the addition of Fluoride to drinking water supplies is now illegal and/or has ceased altogether. Fluoride limits for some different countries (source from WHO) are in the table below.


In groundwater, the natural concentration of fluoride depends on the geological, chemical and physical characteristics of the aquifer, the porosity and acidity of the soil and rocks, the temperature, the action of other chemical elements, and the depth of wells. Due to the large number of variables, the fluoride concentrations in groundwater can range from well under 1 mg/L to more than 35 mg/L. From this we can see that even when no additional Fluoride is added, there could still be a risk of ingestion above the recommended maximum.

Consequently, monitoring of the Fluoride content in ground and drinking waters is a critical quality parameter, and Fluoride removal techniques, such as flocculation and filtration, are often used in areas with high natural Fluoride in order to reduce the risk of over exposure.

Several analytical methods are available to analyse for Fluoride:

  • Gravimetric methods – precipitation of Fluoride as Lead chlorofluoride or triphenyl Tin Fluoride [4]
  • Titrimetric methods – titration with Lanthanum Nitrate
  • Instrumental methods – ICP-MS or Ion chromatography
  • Direct Potentiometry – measurement with Ion selective electrodes

Of these the first is slow and cumbersome and requires skilled staff, whilst the second is only suitable for high concentrations of Fluoride (>20mg/L). It is also strongly influenced by pH of the test solutions. Below pH 5 the species HF and HF2- are formed, neither of which is sensed by the electrode. Above pH 8, La(OH)3 is formed and the electrode responds to OH- ions in preference to F-. Despite these limitations, titration for fluoride does have some analytical application in the chemical industry, but its use is less relevant to the analysis of tap water.

The instrumental methods (IC and ICP-MS) are very suitable for measuring a range of different ionic species in a single run, but set-up and running costs are high (typically many thousands of pounds). Much sample preparation and calibration is needed, and the tests can be slow (typically 10-15 minutes or more). Highly trained and skilled operators are essential for these techniques and for all these reasons they are not available in every laboratory situation.

For these reasons, the method of choice for measuring Fluoride concentration is to use Ion selective electrodes. The remainder of this paper will examine their application in some detail. METTLER TOLEDO has long been a supplier of electrodes and ion meters for the purpose of measuring Fluoride.

The Fluoride electrode is constructed with a solid state membrane (comprising a crystal of the highly insoluble Lanthanum Fluoride in contact with the measuring solution. The chemical equilibrium below is established at the interface between the crystal and the measurement solution:


The potential difference arising at the interface this is measured by conductance through an inner electrolyte (held in the centre of the electrode) and a silver wire. The magnitude of this potential difference is given by the Nernst equation:


We see from this that the potential difference depends on the temperature (T) but also on the activity of the Fluoride ions in the solution (a).

To make use of this in an analytical application we need to calibrate the electrode so that we can relate the mV potential generated to a known activity of Fluoride ions. In general we find it more convenient to think in terms of concentration rather than ionic activity. For all but very dilute solutions, the two terms are interchangeable, but to ensure this maintain the total ionic strength at a constant level by adding a buffer (TISAB).

When using TISAB to adjust the pH and ionic strength of the solutions, and keeping the temperature of the solutions constant, linear calibrations of the fluoride electrode are possible in the concentration range 0.1 – 10-6 mol/L. Calibration is traditionally performed using prepared standards of known concentration to cover the measuring range and measuring the potential in each. From these measured potentials a calibration graph is plotted, with the slope and zero points determined. The theoretical value of the slope is 59.16mv/decade.

Calibration in this way is time consuming and prone to error. The analyst must ensure that the standard solutions are fresh and correctly prepared, and every dilution step will introduce more error. The electrode assembly requires equilibration in the standard to ensure a stable reading, and thoroughly rinsed between one standard and the next. As the electrode slope and zero point will vary considerably over time, the need for frequent calibration can be a source of much delay.

Unlike bench pH/ion meters in general, the METTLER TOLEDO T50M Excellence™ titrator can automate the entire sequence. The sequence is shown in the flow chart.


 A sample beaker filled with 100mL of pure water is placed on the measuring stand, and 10mL of TISAB is added. The high resolution DV1010 burette of the T50M dispenses aliquots of a stock 0.1mol/L Fluoride standard. These aliquots are in quantities sufficient to make (in-situ) standard solutions of 0.001mol/L, 0.001mol/L and 0.01mol/L respectively. The required addition volumes are calculated by the T50 for each of the three standards using the formula:


Where n is the sample number in the series. The volume added and concentrations of the resulting solutions are as shown in table 2.


Using the T50M, the only operator involvement is to place the beaker on the titration stand and press a single short-cut icon on the touch screen. One-click™ titration does the rest, and much time is saved. All common errors on calibration are eliminated when using this method.

Having performed a sensor calibration, T50M system is to measure the concentration of Fluoride in sample materials using one of two distinct techniques.

  • Direct measurement
  • Single standard addition

Readers should note that a third technique using multiple standard additions and direct Gran evaluation [5] to linearize the response curve is possible using the higher specification T70 titrator in place of the T50M. This technique has wider applicative scope in environmental analysis, but it is not considered in detail here.

Direct potentiometric measurement, where the mV potential converted to a concentration through the Nernst equation and stored electrode data, is quick and easy with the T50M. For most sample types little preparation is necessary and automation of the process using sample changers such as the Rondo 20 is possible. High sample throughput and maximum productivity result, whilst the PowerShower™ rinsing head provides optimal cleaning of the electrode assembly between samples and so prevents errors.

Direct measurement suffers from some drawbacks in practice, most notably the need for frequent calibration and the long equilibration times necessary for correct measurement results to be obtained. As we have seen the calibration issues are mitigated against by using the automated calibration procedure described above. However, the standard addition method offers further advantages over direct addition in that:

  • Less frequent calibration is required
  • For many samples no ISA solution is required
  • Temperature effects are compensated for
  • Solid sample types may be tested with limited sample preparation.
  • Samples containing complexed or bound ions may be tested

The mV potential of the sample is measured as for the direct measurement, but after this a known volume spike of a standard solution is added, after which the potential is measured again. Both potentials are expressed in terms of the Nernst equation:

Before the addition:

E1 = E0 – SLOPE .log (Cx. fx.kx) +ΔED

After addition the concentration of the measured ion increases by an amount ΔC and the potential is:

E2 = E0 – SLOPE .log((Cx+ΔC). f’x.k’x) +ΔED

If the amount of solution added is small enough, - or if TISAB is used - the total ionic strength in the solution, and the fraction of complexed ions remains constant. The terms fx, kx ,E0 and ΔE will therefore cancel out when subtracting these two equations. This leaves us with:

ΔE = E2 – E1  = SLOPE . log (Cx + ΔC)


This rearranges to give:

Cx =        ΔC­­_____                  where ΔC = Cs . Vs/Vp

        10ΔE/SLOPE - 1

From this the calculation formula for the standard addition with consideration of dilution effects can be arrived at [6]:


            Cx =     Cs .                  Vp -Vs_______

                              10ΔE/SLOPE – (Vp +Vs)

                                                   (    Vp     )


E1 = Electrode potential

E0  = zero point of electrode

Cx  = measurement ion concentration in sample

  fx  = activity coefficient of ion

  kx = fraction of non-complexed ions in sample

 ΔED = diffusion potential at phase transition of electrode

 Vp = Volume of sample solution

 Vs = Volume of standard solution added

 Cs = Concentration of standard solution

  ΔE = Potential difference due to addition of standard


Dilution effects should be ignored if the concentration of ions in the standard is 100 times greater than that in the sample solution. However, in most cases it should still be considered in order to arrive at reliable results.

The T50M performs the addition of standard using the DV1010 burette, and copes easily with the calculations quoted above. A system that offers fully automated calibration and measurement by standard addition is therefore a reality. As with direct measurement, the Rondo sample changer will increase throughput and further reduce operator involvement.

Data logging and evaluation, long term, traceable, audit trailed, secure storage of data is guaranteed through the use of LabX software. This software package supports trend analysis and SQC chart generation, and it enhances the possibilities for data sharing, LIMS connection and other system integration tasks. The LabX software is therefore the final part of the 'added value' offered by the One-Click™ Fluoride analysis system over the traditional bench meter approach.


The method was used to measure replicate samples from 2 different UK tap water sources as well as a commercially available mineral water (Drench). The results were as shown in table 3.


The linearity of the method was tested with standard solutions at 20, 2 and 0.5 mg/L. The results of this test showing the correlation coefficient are as shown.


The results in the previous section show the reliability of the test method for real world samples, with repeatability, precision and linearity all within normally accepted guidelines for this type of measurement [6]

We have seen how the level of Fluoride in our drinking water and diet can affect dental and skeletal health. Whilst the debate continues over the actual effects (both harmful and beneficial) of fluoride exposure, analysts will continue to test for Fluoride content. They increasingly desire a fast, accurate and trouble free technique that is fully automated yet not expensive when compared to other instrumental techniques. The T50M Excellence titrator can tick all of these boxes making One-Click™ Fluoride determination an invaluable tool for Environmental Ion analysis.


[1] Staines, M., Robinson, W. H. and Hood, J.A.A. (1981). ‘Spherical indentation of tooth enamel’. Journal of Materials Science.

[2] Jacobsen, S..J, Goldberg, J., Miles, T..P, Brody, J.A., Stiers, W., Rimm, A.A.,(1990), 'Regional variation in the incidence of hip fracture. US white women aged 65 years and older'. Journal of the American Medical Association, Jul 25;264(4):500-2.

[3] Hileman, B. (1988). ‘Fluoridation of water. Questions about health risks and benefits remain after more than 40 years’. Chemical and Engineering News. August, pp 26-42

[4] Vogel, A.I., (1989) Textbook of Quantitative Chemical Analysis, 5th edn. Jeffrey, G.H., Bassett, J., Mendham, J., and Denney, R.C. (eds), Longman Scientific and Technical, Harlow

[5] Liberti, A., Mascini, M., (1969) ‘Anion determination with ion selective electrodes using Gran’s plot’, Analytical Chemistry, 41 (4), pp 676-9

[6] Mettler-Toledo ,Applications Brochure 7: Incremental Techniques with Ion Selective Electrodes

Last Updated on Thursday, 18 July 2013 10:27