Note: to run the OpenOffice
(.ods) spreadsheets, you have to first download the OpenOffice
installer (download
from OpenOffice), then install it (by double-clicking on the
installer file that you just downloaded), and then download my
spreadsheets from this page. Once OpenOffice is installed,
you can run my spreadsheets just by double-clicking on them.
Note 1:Don't use version 3.1. There
is a bug in OpenOffice 3.1 that causes bad x-axis scaling on some
of my graphs. The problems does not occur in version 3.0 or
in the most recent version 3.2. Note 2: Downloading these files with Internet Explorer will change
the file types from ".ods" to ".zip"; you will have to edit the
file names and change the extensions back to ".ods" for them to
work properly. This problem does not occur in Firefox or in Chrome.
Operating instructions:
Type in values for the sample concentration Cx, sample volume Vx,
standard concentration Cs, standard volume added Vs, concentration
of ionic strength buffer Cse, ion charge n, Nernst factor
(usually 0.0591) and potential of reference electrode Eo, into the
table on the left. Measured voltages are shown below in the column
labeled "voltages", both before (cell F17) and after (cell F18) the
addition. The change in voltage deltaE is shown in cell G18, and the
concentration calculated from the standard addition equation is
shown in cell A22 (Click on this cell to display the equation in the
entry bar at the top of the window). Compare the calculated value in
cell A22 to the "correct" value Cx in cell B11. Note that the
reference potential (Eo) has an effect on the measured voltages but
no effect on deltaE nor on the calculated concentration. This
calculated concentration won't be perfect, however, because adding
the standard solution to the sample causes a slight increase in its
ionic strength and thus a slight decrease in the activity
coefficient of calcium. The percent difference between the
calculated and true values of Cx is given in cell C22. You can
reduce this error by using a smaller addition of standard (reduce Cs
or Vx or both) or by using a greater concentration of NaCl ionic
strength buffer (Cse, in cell B13). Using too much NaCl, however,
will increase the interference of Na ions (c.f. the table of
interference factors in rows 39-49). On the other hand, reducing the
amount of standard added reduces deltaE and makes it harder to
measure precisely. This effect can be simulated by specifying a
voltage reading error in cell B14. The resulting % error in
concentration is shown in cell E22, and the total error is shown in
cell G22.
Cell definitions and equations:
Inputs:
Reference potential (volts) Eo (cell B5)
Actual Nernst factor (volts) nf (cell B6)
Assumed Nernst factor (volts) nfa (cell B7)
ion charge (n) (unitless) n (cell B8)
[Ca] in standard (Moles/Liter) Cs (cell B9)
vol. standard added (mL) Vs (cell B10)
[Ca] in unknown (Moles/Liter) Cx (cell B11)
Sample volume (mL) Vx (cell B12)
NaCl TISB conc (Moles/Liter) Cse (cell B13)
voltage reading error (volts) ve (cell B14)
Debye-Hückel factors:
A = 0.5085 (cell A26)
B = 3.28E+07 (cell A27)
bm = 6.00E-08 (cell A28)
Calculated quantities:
Before addition
mmoles Ca volume total [Ca] Activity of Ca measured voltage
mm1=Cx*Vx V1=Vx Ca1=mm1/V1 aCa1=f1*Ca1 V1=Eo+(nf/n)*log(aCa1+totalAE)
After addition of Vs ml of standard solution
mmoles Ca volume total [Ca] Activity of Ca measured voltage
mm2=Cx*Vx+Cs*Vs V2=Vx+Vs Ca2=mm2/V2 aCa2=f2*Ca2 V2=Eo+(nf/n)*log(aCa2+totalAE)
Change in voltage before/after addition
deltaE = V2-V1
[Ca] by standard addition
Casa = Cs*Vs/((Vx+Vs)*10^(-n*deltaE/nfa)-Vx)
ionic strength error (%)
ise = 100*(Casa-Cx)/Cx
measurement error (%)
ma = 100*((Cs*Vs/((Vx+Vs)*10^(-n*(deltaE+ve)/nfa)-Vx))-Casa)/Casa
% total error
=sqrt(ise*ise+ma*ma)
Debye-Hückel calculation of activity coefficient of Ca+2, in water at 25 C:
Ionic strength log activity coefficient activity coefficient
Before addition: I1=Cse+3*Ca1 lf1=(-A*n*n*sqrt(I1))/(1+B*bm*sqrt(I1)) f1=10^lf1
After addition: I2=Cse+3*Ca2 lf2=(-A*n*n*sqrt(I2))/(1+B*bm*sqrt(I2)) f2=10^lf2
Effect of interferences from ions in commercial NaCl ionic strength buffer solution Ion Atomic selectivity ion µg/mL in M in activity activity weight constant* charge solution** solution in solution equivalence --------------------------------------------------------------------------------------- H+ 1.008 10000000 1 (assume pH=7) 1.0E-07 5.1E-08 2.6E-08 Cu++ 63.55 0.3 2 0.02 9.7E-08 4.9E-08 1.5E-08 Mg++ 24.30 0.01 2 20 2.3E-04 1.2E-04 1.2E-06 Na+ 22.99 0.0016 1 100 =Cse =f1*Cse 6.9E-07 ------- * from the electrode's spec sheet totalAE = 1.9E-06 ** from the reagent label
Student Activity Handout:
CaElectrode.wkz is a spreadsheet simulation of
the
standard addition method for calcium determination by
ion-selective electrode. The simulation demonstrates the ability of
the standard
addition method to correct for an unknown reference potential
and ionic
strength (and thus activity coefficient). It includes two
sources of
error: (1) the effect of the addition of standard on the ionic
strength and
(2) effect of voltage reading error. Looking at the screen
display, on the top right is a scrolling text field that contains a
summary of these instructions. On the top left is a table of all of the model
parameters that you can control. These include the potential of
reference electrode Eo, the Nernst factor (with separate values for the
"actual" Nernst factor used to calculate the voltages and the "assumed"
Nernst factor used in the standard addition equation), ion charge n,
concentration of calcium in the standard Cs, standard volume added Vs,
concentration of calcium in the "unknown" sample Cx, sample volume
Vx, concentration of the NaCl ionic strength buffer Cse, and the voltage
reading error, i.e. the precision with which voltages can be read. The
current values of these parameters are shown in boldface type in column
B; you can change any of these parameters simply by clicking on the
number, typing a new value, and pressing the enter key.
The bottom half of the
screen shows all the calculated "outputs" of the simulation. Rows 17 and 18
show the status of the sample solution before and after the addition of
standard, respectively. Measured voltages are shown below in the column
labeled "voltages", both before the addition of standard (cell F17) and
after the addition (cell F18). The change in voltage delta-E is shown in
cell G18, and the concentration calculated from the standard addition
equation is shown in cell A22. (Click on this cell to display the equation in
the entry bar at the top of the window; compare to the equation on
page 48 of the lab manual).
1. Compare the
calculated value in cell A22 to the "correct" value Cx in cell B11. Change the
reference potential (Eo) and note the effect it has on the measured voltages
and on delta-E. Does the reference have an effect on the calculated
calcium concentration?
2. Change the actual and
assumed Nernst factors, keeping them equal. Does this effect the measured
voltages? Does this effect the delta-E? Does this effect the
calculated calcium concentration? What if you make the actual and assumed
Nernst factors
unequal? Will the standard addition method give accurate results
if the Nernst
factor of the electrode is not known?
3. Note that adding
standard solution to the sample causes a slight increase in its ionic
strength and thus a slight difference in the activity coefficient of
calcium. Compare cells D27 and D28, which show the ionic strength of the
sample before and after the addition, respectively. The resulting
effect on the activity coefficient for calcium can be calculated
from the Debye-Huckel equation (Wikipedia;
lab manual, p.
47) and the results are shown in cells F27 and F28. The change
in activity
coefficient gives rise to an error in the determination, because the electrode potential
responds to activity, not concentration. The percent difference between
the calculated and true values of Cx is given in cell C22. You can reduce
this error by using a smaller addition of standard (reduce Cs or Vx
or both) or by using a greater concentration of ionic strength buffer (Cse,
in cell B13). Try it.
4. Reducing the
concentration and/or volume of the added standard reduces the error due to
ionic strength changes, but it also reduces deltaE and makes it harder to
measure precisely. This effect can be simulated by specifying a voltage
reading error ( i.e. the precision with which voltages can be read) in
cell B14. The resulting % error in concentration is shown in
cell E22, and the total error (quadratic sum of voltage error and ionic
strength error) is shown in cell G22. Set the voltage reading error to
0.0001 volts (the least significant digit of the pH meters we use) and
determine if there is a value of Vs that gives a minimum overall error. In
practice, a more realistic value for the voltage reading error is
0.0005 volts. With that value, what dominates the total error? (c) 1991, 2015. This page is part of Interactive
Computer Models for Analytical Chemistry Instruction, created
and maintained by Prof.
Tom O'Haver , Professor Emeritus, The University of Maryland
at College Park. Comments, suggestions and questions should be
directed to Prof. O'Haver at toh@umd.edu.
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