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CHEM 311L

Quantitative Analysis Laboratory
Revision 2.0


A Potentiometric Analysis of Fluoride Ion in Toothpaste



In this laboratory exercise, we will analyze a toothpaste sample for its Fluoride Ion (F
-
) content.
This analysis will be performed potentiometrically (ε; think voltage) using a Fluoride Ion
selective membrane electrode (ISE). A Nernst-like relationship is expected to exist between the
Fluoride Ion concentration [F
-
] and the Potential of the ISE. This relationship, which must be
established via calibration, will allow us to determine the desired Fluoride Ion concentration
from the measured Potential of the ISE.














Potentiometry involves the use of two electrodes, a Reference Electrode and an Indicator
Electrode, to measure the Electric Potential (ε
cell
) of an Electrochemical Cell constructed to
include the Analyte Solution. A Cell Diagram for the system is:

Reference Electrode | Salt Bridge | Analyte Solution | Indicator Electrode

Schematically this can be pictured as:










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The Cell Potential ε
cell
is measured using a typical Voltmeter in the limit of zero current flow.

ε
cell
= V in the limit (I ~ 0) (Eq. 1)

This limiting condition is fairly easily realized if a meter with an internal resistance of greater
than 10
11
Ω is used. Modern pH meters are simply high internal resistance voltmeters meeting
this requirement. Therefore, pH meters are capable of making the needed voltage measurements
such that the Cell Potential can be determined.

A simple example of this type of measurement involves the use of a Calomel reference electrode
(Hg(l)|Hg
2
Cl
2
(s)|KCl(aq)) connected via a salt bridge to a cathode consisting of a Cu
2+
analyte
solution and a Cu(s) indicator electrode.


















The oxidation reaction occurring at the Calomel reference electrode is:

2 Hg(l) + 2 Cl
-
(aq) Hg
2
Cl
2
(s) + 2 e
-
(Eq. 2)

whereas the cathodic reduction is:

Cu
2+
(aq) + 2 e
-
Cu(s) (Eq. 3)

The Cu indicator electrode is a metal electrode of the “first kind:” an indicating electrode used to
determine the concentration of an ion derived from the electrode material.

Ideally, the Cell Potential is related to the Cu
2+
concentration via the Nernst Equation:

ε
cell
= ε
Cu2+|Cu
o
+ (0.0592/2) log (1 / a
Cu2+
) - ε
Calomel
(Eq. 4)

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where a
Cu2+
represents the Activity of the Cupric Ion:

a
Cu2+
= γ
Cu2+
[Cu
2+
] (Eq. 5)

Thus, the Nernst equation forms the basis of the relationship between the analyte concentration
and the measured cell potential.

In our laboratory exercise we will be using a Flouride Ion Selective Membrane Double-Junction
Electrode, in which the Indicator and Reference Electrodes are built into a single probe, to
construct the needed electrochemical cell. (See Diagram on Next Page.)

The built-in Reference is a Ag|AgCl electrode which operates according to the following
oxidation half-reaction:

Ag(s) + Cl
-
(aq) AgCl(s) + e
-
(Eq. 6)

The Indicator Electrode is constructed from another AgCl|Ag electrode and a Flouride Ion
Selective Membrane which is inserted into the analyte solution.

The Flouride Ion (F
-
) Membrane selectively binds Fluoride Ion to both its surfaces; the exterior
surface being in contact with the Analyte Solution and the interior surface in contact with a
reference Electrode Solution. Both the Analyte and Electrode solutions contain Fluoride Ion.














However, because the Activity of the F
-
in the analyte solution (a
a
) on the outside of the
membrane is distinctly different than that in the membrane’s interior solution (a
e
), different
concentrations of F
-
bind to the membrane’s two surfaces. This gives rise to a Potential
Difference across the membrane. In our Fluoride Ion Selective Electrode, the active membrane
is a single crystal of LaF
3
doped with Europium (II) Ions to lower its electrical resistance and to
facilitate ionic charge transport. F
-
ions bind to this crystalline surface according to:

LaF
3
(s) + F
-
(aq) LaF
4
-
(s)

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The LaF
3
crystal, sealed into the end of a plastic tube, is in contact with the external F
-
analyte
solution. Internal to the electrode is a solution that is 0.1M in both NaCl and NaF. The internal
F
-
activity controls the Potential on the inner surface of the crystal.

To complete the Indicator, the internal Cl
-
activity controls the Potential of the AgCl|Ag
electrode, operating reductively; in the reverse of that at the Reference.

AgCl(s) + e
-
Ag(s) + Cl
-
(aq) (Eq. 7)

Diagrammatically, the entire Cell (Reference, Analyte, Indicator) can be represented as:



The Potential of the Cell can be written as a composite of the Potentials of the Reference and
Indicator:

ε
cell
= ε
ind
- ε
ref
+ ε
jnc
(Eq. 8)

where ε
jnc
is the Potential which builds at the junctions between the Cell’s chambers and is the
single largest source of error in most Potentiometric measurements. (Note the sign used for each
contribution. This is done by convention.)

The response of the Indicator Electrode to the Fluoride Ion in the analyte soltion is described by
a Nernst Like equation:

ε
ind
= L - 0.0592 log a
F-
(Eq. 9)

where L is a constant specific to the cell in question. Inserting (Eq. 9) into (Eq. 8) and
rearranging, we obtain:

pF = - log a
F-


= (ε
cell
- ε
jnc
- ε
ref
– L) / 0.0592

= (ε
cell
– K) / 0.0592 (Eq. 10)

where K is a Cell constant that must be determined by calibration.

If interfering ions, like Hydroxide Ion (OH
-
), can bind to the Indicator’s membrane surface, these
must also be included in the relevant activity:

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ε
ind
== L - 0.0592 log (a
F-
+ k
F-,OH-
a
PH-
) (Eq. 11)

where k
F-,OH-
is the Selectivity Coefficient for the electrode toward interference by OH
-
.

Our ISE is somewhat sensitive to Hydroxide Ion (OH
-
) and this must therefore be controlled with
a buffer. The recommended buffer is TISAB (Total Ionic Strength Buffer) which not only
controls the OH
-
levels, it provides a constant Ionic Strength environment and a complexing
ligand.

For the LaF
3
crystal, OH
-
becomes a problem when its concentration becomes greater than 10%
of the F
-
present. TISAB helps control the pH of the analyte solution so this does not occur.

Additionally, the buffering action of TISAB also prevents the pH of the solution from dropping
below pH = 5, where F
-
can protonate to form the weak acid HF (pK
a
= 3.17):

F
-
(aq) + H
+
(aq) HF(aq)

Secondly, TISAB controls the Ionic Strength of the Analyte solution. This is important because
(Eq. 10) relates the cell potential ε
cell
to the Fluoride Ion activity a
F-
. However, we are most
interested in the Flouride Ion concentration [F
-
]. Because the activity coefficient γ
F-
is typically
not determinable, the electrode must instead be calibrated against solutions of known
concentration and not known activity. This only works if the ionic strength of the calibration
standards and the analyte solution are the same. The TISAB buffer controls the ionic strengths
of these solutions such that this is the case.

Finally, TISAB provides Complexing Agents for possible contaminants. Aluminium Ion (Al
3+
)
and Ferric Ion (Fe
3+
) contaminants can complex with Fluoride Ions and therefore interfere with
the potentiometric measurement:

Al
3+
(aq) + 4 F
-
(aq) AlF
4
-
(aq) (Eq. 12)

TISAB contains the complexing agent CDTA (trans-1,2-cyclohexanedinitrilotetraacetic acid)
which combines with Al
3+
and Fe
3+
up to concentrations of 5 ppm and renders them inert.











Thus, we will use a series of Standard Fluoride Ion solutions prepared using TISAB so as to
generate a Calibration Curve of:
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ε
cell
vs. log [F
-
] (Eq. 13)

which according to (Eq. 13) should be linear. The Cell Potential will be measured using a
Fluoride Ion Selective Electrode attached to a pH meter. The resulting calibration curve can then
be used to determine the F
-
concentration in a solution prepared from a commercial toothpaste
preparation.







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Pre-Lab Calculations

1. TISAB buffers at pH = 5.25. What is the OH
-
concentration in this buffer?

2. If 10 mL of the NaF Stock solution is to be diluted to prepare 100 mL a 0.01M Standard
solution, what must be the concentration of the Stock solution?

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Procedure

1. Fluoride Ione (F
-
) can adsorb onto the surface of glassware, reducing its solution
concentration. This is especially problematic at low concentrations. Since we will need to
work at low concentrations to determine the Fluoride Ion in our toothpaste sample, make
sure all handling of the Fluoride Ion solutions is conducted using plastic labware.

2. You are provided with a 0.1M NaF stock solution in 10% TISAB. Dilute the stock solution
to make standards with the following concentrations:

0.01M
0.001M
0.0001M
0.00001M

All these solutions are prepared in 10% TISAB buffer.

(You may want to collaborate with your neighbors on preparing these calibration
solutions.)

3. You should prepare a solution of Toothpaste by dissolving 5.00g of Toothpaste in 50.00
mL of 10% TISAB buffer. Record the concentration of Fluoride Ion in the Toothpaste as
reported by the manufacturer.

4. All the standards and the toothpaste sample should be at the same temperature for precise
measurements. A 1
o
C difference in the temperature will result in a 2% measurement error.

5. Caution: The electrode is rather expensive and fragile. Please do not drop it or knock the
tip against the countertop, or with the stir bar. Also, do not rub the tip with anything, such
as with a Kimwipe during drying. Scratches can damage the LaF
3
crystal.

Attach the BNC connector of the Electrode to the input on the pH Meter.

6. Measure the Electrochemical Potential of each of the Sodium Fluoride standards and
solutions. Try to work from the lowest to highest concentration and analyze the Toothpaste
sample last. To make a measurement, place the electrode in a beaker containing the
solution. Use a stir plate and stir bar to gently stir the solution. (Magnetic stirrers can
generate sufficient heat to change the solution temperature. To counteract this effect, place a
piece of insulating material, such as a styrofoam sheet, between the stirrer and the beaker. )
Wait for the Potential to stabilize (~1-3 minutes) and record the reading in millivolts (mV).
Rinse the electrode between each measurement.

7. Using a software package such as Excel, plot ε
cell
vs. pF for the Standard Solutions. Here,
pF is defined as:

pF = - log [F
-
]
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Add a Linear Least Squares trendline and determine the slope and intercept as well as their
associated uncertainties.

8. Use your calibration curve to determine the Fluoride Ion concentration in the Toothpaste.
Report this as the wt% NaF in the Toothpaste. Be sure to determine the associated
uncertainty in this measurement. Compare your result with that reported by the
manufacturer. Be careful here.