CH 429 Fluoride

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CH 429 Fluoride Powered By Docstoc
					Jarrett Long

Determination of Fluoride Ion Potentiometrically



INTRODUCTION

       Fluoride happens to be a good candidate for ion electrode potentiometric measurements

due to certain characteristics of the fluoride ion. Namely, it is a small ion which is capable of

traveling through certain membranes. These membranes allow for the migration of the small,

negatively charged fluorine ions between the calibration solution and the solution in question

until a charge equilibrium is reached due to the difference in potential of the solutions. When

there are concentration of fluoride anions in solution is greater then more ions will flow through

the membrane, leading to a larger potential difference. This laboratory experiment will

demonstrate this relation by determining the concentration of fluoride ions in an unknown

sample by mathematical extrapolation.



METHOD

       Since the relationship between the concentration and the voltage is generally logarithmic,

it is possible to graph the correlation in such a way that allows for the determination of the

original concentration. Due to fluoride etching, all containers except for weighing containers are

plastic. The first step is making up 100 ml “Known Add” solution of 10mg/l of F by mixing 221

mg NaF to 1 liter of water. Then pour 10 ml of this solution and 10 ml of a pH buffer (TISAB in

this case) to a 100 ml volumetric flask with water. Transfer from flask to plastic. This will be

added in 1 ml aliquots to three various solutions. A 100 ml blank solution, with no original

fluoride concentrations, a test solution (quality control) of 0.2 mg/l fluoride concentration in 100
ml (stored in plastic), and 100 ml of unknown in it’s own flask. 10 additions of the “Known

Add” is added to each solution one solution at a time with measurements of voltage after each of

the additions.

       The data is then plotted in two different fashions. Using a computer, a variation of the

Nernst function (Vs+Va)exp(-nEF/RT) can be plotted against the concentration of fluoride

added, which we know to be 0.01 mg of F per mL aliquot. Using a linear fit of this relationship,

the slope and the y-intercept of this graph can be determined for each of the three solutions. The

original concentration is found by taking the absolute value of the quotient (|fluoride intercept| =

|fi|) of the y-intercept (b) by the slope (m) and dividing this by the solution volume. This is:

                                                | fi | | b / m |
                                         co          
                                                 Vo       Vo

where |m/b| is the least fit line of the corresponding linear fit. (See: FIGURES AND GRAPHS)

       The other form of the data is by using Gran’s paper. This is special logarithmic paper that

allows the concentration-potential relationship to easily be hand-graphed and then through

graphical analysis the same information can be gathered. The graphs are attached in the DATA

section and will be the results will be discussed briefly in the next section.



CALIBRATION

       The blank solution was analyzed so that through this relatively-analog process can have a

zero calibration. The ten aliquots were added and graphed onto the attached Graph 1. With a

|fi|/Vo of 1.15 x 10-3  4.37 x 10-3 mg/l then this can be assumed as determinate error of the

experiment, and therefore subtracted from the masses of the other two trials. For instance,

through the same procedure the original fluoride mass in the quality control was calculated to be

0.207  0.017 mg/l when the original known amount was to be 0.200  0.001 mg/l. That shows a
relative error of 3.5%, a seemingly respectful mark of accuracy with 8.5% total uncertainty.

       When discussing the Gran’s Paper method, it must be noted that it uses no fancy

least-squared fit systems, or even an automated linear fit process! It simply boils down to

graphing the voltage vs. concentration and from there using a ruler to determine the fluoride

intercept. This is done for all three on the attached Gran’s Paper, however, the results for the

quality control were about 0.23mg/L (0.26-0.03 for the blank determinate error) and the results

were 0.51 mg/l for the unknown. The 0.51is a good estimate, however, as indicated by the

quality control’s 15% error, this method should be used only when electricity and computers

have disappeared from Earth.



ERROR ANALYSIS

       The error budget is presented as Table 1 in TABLES.

A note on the lack of indeterminate error: As understood, any other source of indeterminate error

would involve either the concentration of the “Known Add” or perhaps error on the Voltage

detector. However, it seems that either one of very small error sources would be taken into

account by the standard deviation calculations from the linear fit of the model which would

account for random error from the machine and random error on aliquots. Also, the error for the

linear fit is from the formula:



<(WRITE) ERROR ON LINEAR EXTRAPOLATION FORMULA HERE>

RESULTS

       By looking at Graph 3 and through the same procedure as for the other two solutions, it is

determined that the original concentration of fluoride in the unknown sample is 0.49  0.02 mg/l.
The calculation for this and the error are given in the SAMPLE CALCULATIONS. The 95%

confidence interval lies within (0.45 <  < 0.53).



DISCUSSION

         A relatively simple experiment that just requires patience and time, along with a good

hand at making weighing out compound and making solutions to ensure proper mathematical

models. The Gran’s paper would be an excellent way of avoiding the mean-looking Nernst

function in the days before heavy computational analysis. However, nowadays, it seems to just

increase error likelihood, especially due to the technique of human interpolation. The 3.5% error

on the quality control assures at least adequate reassurance of the final determination, though, as

with most labs, more trials and quality controls would be appreciated - infinitely so would be

ideal.



TABLES

Error Budget

Error Source              Indeterminate              Standard Deviation       Determinate
Blank Solution                                                                -1.15 x 10-3 
Correction                                                                    4.37 x 10-3 mg/l
Machine Error             -                          Random, See: linear      -
                                                     fit error
Aliquot Fluctuations      -                          Random, See: linear      -
                                                     fit error
Linear Fit Error                                     Blank:
                                                     1.15 x 10-2 mg/l
                                                     QC:
                                                     1.71 x 10-2 mg/l
                                                     Unknown:
                                                     1.65 x 10-2 mg/l
FIGURES AND GRAPHS

GRAPH 1

                 0.30              Blank Calibration Curve

                 0.25
(-EnF/RT)




                 0.20
      (Vs+Va)e




                 0.15                                            y = 2.922x + 0.0127

                 0.10                                        |b/m| = |fluoride intercept|
                                                             = |-0.0127/2.922| = 0.0486
                 0.05



                        0   20            40           60              80                   -3
                                                                                  100x10
                                     Total Fluoride Added (mg)


GRAPH 2

                 0.35            Quality Control Calibration Curve

                 0.30
(-EnF/RT)




                 0.25

                 0.20
      (Vs+Va)e




                                                              y = 2.8683x + 0.072085
                 0.15

                 0.10                                     |b/m| = |fluoride intercept|
                                                          = |-0.072085/2.8683| = 0.02513
                 0.05

                 0.00

                        0   20            40           60              80                   -3
                                                                                  100x10
                                     Total Flouride Added (mg)


GRAPH 3
                 0.45            "Unknown" Calibration Curve

                 0.40
(-EnF/RT)




                 0.35
                                                               y = 3.0145x + 0.1598
      (Vs+Va)e




                 0.30
                                                     |b/m| = |fluoride intercept|
                 0.25                                = |-0.1598/3.0145| = |0.05301|

                 0.20



                        0   20          40           60            80                  -3
                                                                              100x10
                                   Total Fluoride Added (mg)


DATA

Raw Uncharted Data

BLANK                          TEST                           UNKNOWN
E (V)      Fluoride Added (mg) E (V)      Fluoride Added (mg) E (V)      Fluoride Added (mg)
     0.213                   0      0.183                   0      0.163                   0
     0.199                0.01      0.176                0.01      0.159                0.01
     0.187                0.02       0.17                0.02      0.156                0.02
     0.177                0.03      0.165                0.03      0.153                0.03
      0.17                0.04       0.16                0.04       0.15                0.04
     0.165                0.05      0.157                0.05      0.148                0.05
      0.16                0.06      0.154                0.06      0.146                0.06
     0.157                0.07      0.151                0.07      0.144                0.07
     0.155                0.08      0.149                0.08      0.142                0.08
     0.152                0.09      0.147                0.09       0.14                0.09
     0.149                 0.1      0.146                 0.1      0.139                 0.1




SAMPLE CALCULATIONS

<(WRITE) DO CALCULATION FOR Unknown Mass AND Error HERE>
QUESTIONS

7.1|

a) E = c - 59log[F] where c is a constant

b) c = 159, so 0.92ppm after converting from M.

c) Yes



7.2| a) Should be low b) high c) 4.7 d) 9.4



7.3| a) 1.9 mM b) 0.044 mM c) 0.057 mM

7.4|




7.5| 11ppm
2.7| About 4%



Question 1 from Lab: 3.17

Question 2 from Lab:

				
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