Calcium Ion Selective Electrode Simulation
[Operating instructions] [Cell definitions and equations] [Student assignment handout]
[Operating instructions] [Cell definitions and equations] [Student assignment handout]
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: the effect of the addition of standard on the ionic strength and activity of calcium, and effect of voltage reading error.
Download links:
CaElectrode.wkz;
CaElectrode.hqx
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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:
The file 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? The delta-E? 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 (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?