iterative method of calculation in excel

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INSA DE ROUEN

Laboratoire de chimie analytique

TP ANALYSE

Study of an ion-selective electrode for the determination of fluoride ions

I - Principle.

We consider two solutions (1) and (2), containing a common ion X, separated by a selective membrane.

As activities in (1) and (2) are different, it appears a membrane potential.

We cannot measure this potential alone; we have to build a complete electrochemical chain : electrode A solution (1)

Electrode A Potential membrane solution (2)

Membrane potential electrode B

Electrode B potential

So that the potential difference measured between the electrodes A and B depends only on the membrane potential, it is necessary that the electrode potentials of A and

B remain constant, this means that A and B are reference electrodes.

The electrochemical chain will be formed as follows:

Internal reference

Electrode

Solution with fixed a x membrane

Commercial electrode

Test solution External reference electrode

It goes without saying that the quality of the electrode is essentially dependent on the quality of the membrane.

In the case of the fluorine selective electrode, the membrane consists of a single crystal of lanthanum fluoride, LaF

3.

Under these conditions, the measured potential difference is related to the activity of

X

in solution by the relation:

E = A (T) + (RT / zF) * ln ( a x

) (1) with z = charge of X with its sign

Cautions to take during measures with the fluoride electrode for reducing its response time:

- Check for bubbles in the electrode (same thing using pH electrode)

- Do not wipe the electrode (modification of the crystal surface)

- Soak 30 s between 2 measurements in a beaker of deionized water

- Start with the more dilute solutions

1

INSA DE ROUEN

Laboratoire de chimie analytique

TP ANALYSE

II - Study of the characteristics of the fluoride sensitive electrode.

II - 1: Slope of the electrode - Calibration.

Refer to the simplified instructions of the potentiometer on the bench to understand the concept of stability criteria and the procedure for the calibration.

Preparation of solutions of constant ionic strength from 0.1 mol.L -1 NaF solution in

NaCl medium by serial dilutions.

Solution pF = 1 solution NaF 0.1 mol.L -1 NaF solution 0.1 mol L -1 pF = 2 5 mL of pF=1 + NaCl 0.1 mol.L -1 qsp 50.mL pF pF

=3

= 4

5 mL of pF=2 + NaCl 0.1 mol.L -1 qsp 50.mL

5 mL of pF=3 + NaCl 0.1 mol.L -1 qsp 50.mL pF=5 pF =6

5 mL of pF=4 + NaCl 0.1 mol.L -1 qsp 50.mL

5 mL of pF=5 + NaCl 0.1 mol.L -1 qsp 50.mL

Verify that these solutions are at constant ionic strength: this allows to fix the value of activity coefficients and to have a solution sufficiently conductive to reduce response time.

Reminder: the ionic strength is defined by

I

1

2

 i cz

2 i i where c i

is the concentration of the ion i and z i

its charge number.

Show that under these conditions the relation (1) can be written E =

(T) + (RT ln(10)/ F) * pF

HANDLING:

 For each solution, starting with the more diluted, measure the potential difference (in mV) between the ion-selective electrode and the external reference.

Use the B method and press if necessary on pH / mV to see the potential difference

E.

Plot the curve



= f (pF) . Search the linear part of the curve.

(Linear regression) and verify that the experimental slope of the linear part is RTln

(10) / F.

 We can now calibrate the instrument. Take two solutions located in the linear part, as for instance the vials pF = 2 and pF = 5.

.

The% slope must be close to 100%.

We will now check that the calibration is correct.

Prepare by appropriate dilution a solution of 5.10 -5 mol.L -1 of F in NaCl 0.1 mol L -1 . Measure the pF of this solution and compare with the expected value of pF.

We will carry out three times the measure so far to check the repeatability of the measurement.

Do not discard solutions.

II-2: pH of the test solution

2

INSA DE ROUEN

Laboratoire de chimie analytique

TP ANALYSE

In acidic medium, free [F ] decreases by the formation of HF.

But the electrode is only sensitive to free F .

In basic medium, the electrode is attacked by OH -.

We will study at a constant concentration of total fluorides, the influence of pH on the fluoride electrode response, this for pH values close to 3, 4, 5, 7 and 9.

Prepare the solutions by adding:

- 2.5 mL of a 0.01 mol L -1 fluoride solution

- 10 mL of the corresponding Britton-Robinson buffer

- 10 mL of NaCl 0.1 mol L -1

- Deionized water, qsp 25 mL.

For each solution, measure :

 Its pH, please refer to the corresponding part in the simplified instructions : proceed to the calibration of the device (use the pH electrode)

 The potential difference



(fluoride selective electrode), refer to the manual.

Plot the response curve



E) = f (pH), conclusion?

III - Fluoride content in mineral water.

One could, for this measure, consider implementing a calibration method as was seen in § II-1.

This could be realized by making all the calibration solutions in the same conditions of ionic strength of the sample water. However it’s difficult to perform given the wide differences in mineral content that may exist between two waters.

On the other hand, if we want to determine the whole of fluoride present, we must take into account those who may be engaged in complexes with trivalent metals such as Fe 3 + and Al 3 +.

Finally the pH conditions should be optimal (see § II-2).

To meet these requirements, it is better to implement a method of standard additions in a TISAB medium (Total Ionic Strength Adjustment Buffer).

Appendix: composition of TISAB: for 1 L of aqueous solution:

57 mL glacial acetic acid

58 g NaCl

4 g DCTA: diamino-1 ,2-cyclohexane tetraacetic acid

- Adjust to pH 5 with NaOH 5 mol L -1

The water to be analyzed, once degassed, will be diluted to half in the medium

WATER / TISAB volume to volume (50% vol TISAB) .

 Measure the pH of the water + TISAB to verify that the pH conditions are optimal.

3

INSA DE ROUEN

Laboratoire de chimie analytique

TP ANALYSE

 Measure the potential difference between the fluoride sensitive electrode and the external reference in the water medium / TISAB volume to volume for the following solutions in a beaker:

.

1) 19 ppm F in the medium WATER / TISAB volume to volume.

2) 1.9 ppm F in the medium WATER / TISAB volume to volume.

Determine the slope of the electrode in the medium WATER / TISAB volume to volume (We can write

E = A + slope *log [F ] ).

 Prepare a 100 mL beaker containing V

0

= 50.0 mL of sample (sample water diluted 50% vol TISAB).

Measure the potential difference (denoted

E

1)

 Add a volume V a

= 1.0 mL of a fluoride solution concentration C a

= 0.01 mol

L -1.

Measure the potential difference (denoted

E

2)

We then have E

1

-

E

2

= slope * log



* (c i

+ c a

V a)

/ (c i

V i)]

(2) with

=(V i

+V

TISAB

)/ (V i

+V

TISAB

+ V a

), V i

is the volume of the analyzed water,

V

TISAB

is the volume of the TISAB solution added.

Determine the fluoride concentration c i

of the water analyzed. For this, demonstrate the relation (2) and use the iterative method of calculation in excel presented below.

The result is expressed as ppm F .

It is desirable to perform at least three (3) times this determination, in order to determine the confidence interval on the result.

ITERATIVE METHOD OF CALCULATION IN EXCEL

In a cell (for instance A1), enter any value for c i.

It is in this cell that c i

will be read after the iterative calculation.

In a second cell (for instance A2) enter the formula "= slope * log



* (c i

V i

+ V a

c a)

/ (c i

V i

)]"

In the menu "tool" ( « outil » ) choose application "target value" ( « valeur cible » ) and fill in:

"Set cell" ( « Cellule à définir » ) put the cell of the mathematical function (A2 in our example)

"Target value" ( « valeur cible ») : value for the desired function (eg 10 mV)

" changing cell" ( « cellule à modifier » ) cell where c i

is displayed (A1 in this example).

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