2. Outline of lecture Two
Figures of merit
Calibrations
Standardizations
Blank correction
2
Tuesday, February 27, 2024
3. Figures of merit
• A figure of merit is a numerical expression
representing the efficiency of a given instrument or
procedure. Figures of merit are a way for analytical
chemists to characterize a method. The six figures
of merit we use are;
Precision-A measure of the reproducibility(Relative
SD, Absolute SD)
Accuracy-How close a measured value is to the
true value
Sensitivity-A measure of the methods ability to
distinguish between two samples reported as
change in signal per unit change in the amount of
analyte
Tuesday, February 27, 2024 3
4. Figures of merit cont’d
Linear dynamic range-Concentration range-(range
over which measurements can be made)
Detection limit -smallest amount of analyte that
can be determined with confidence or the smallest
amount of analyte that has a signal larger than the
signal from the reagent blank
Selectivity-A measure of a methods freedom from
interferences
Tuesday, February 27, 2024 4
5. Calibrations
• Calibration is defined as the act of making sure that a
scientific process or instrument will produce results
which are accurate. In more complex terms, calibration
is the act which determines the functional relationship
between measured values and analytical quantities.
Tuesday, February 27, 2024 5
6. Calibration cont’d
•The goal of calibration is to minimize any
measurement uncertainty by ensuring the
accuracy of test equipment. Calibration
quantifies and controls errors or uncertainties
within measurement processes to an acceptable
level.
Tuesday, February 27, 2024 6
7. When do you calibrate instruments?
After an event e.g. if there is a knock,
bump anything that can impact accuracy
When measurements don’t seem right
When instructed by manufacturer
Tuesday, February 27, 2024 7
9. Calibration curve method
•In the calibration method, also known as
working curve method, a set of
standards must be prepared. They will each
contain a known amount of the analyte being
measured. These standards are then measured
using the instrument in question, and
a calibration curve will be plotted. This curve
will show the relationship between the
response of the instrument and the
concentration of the analyte. An example of a
calibration curve can be found below.
Tuesday, February 27, 2024 9
11. Calibration cont’d
• When using the working curve method, it is important that each standard is
prepared individually and not all from the same stock solution. Any errors
in the stock solution will carry through the entire calibration process, and
thus the instrument will not be calibrated correctly.
• Also, the calibration curve should be checked for any outliers. An outlier
is a measurement which is significantly different from the other
measurements. Put simply, these results will shift the regression line (line of
best fit) and give inaccurate results, and should, therefore, be removed.
Tuesday, February 27, 2024 11
12. Steps to follow during Calibration
•The calibration standards should cover the range
of interest – this is so, during your actual
experiment, you are sure to get the most accurate
results from your curve
•A ‘blank’ should be included in your calibration –
this is a standard which contains no analyte
•Don’t automatically set your regression line
intercept to zero! Only do this if you have enough
evidence to show that the intercept point is not
actually statistically different from zero.
Tuesday, February 27, 2024 12
13. Example: Pb in Blood by GFAAS
9(Students plot)
[Pb] Signal
(ppb) (mAbs)
0.50 3.76
1.50 9.16
2.50 15.03
3.50 20.42
4.50 25.33
5.50 31.87
Tuesday, February 27, 2024 13
15. .EXAMPLE
A sample containing an unknown amount of
Pb gives a signal of 27.5 mAbs. Calculate
the Pb concentration
Tuesday, February 27, 2024 15
16. Standard addition calibration
The standard-addition method of calibration helps to remove bias that may arise
from a number of factors, including the temperature and composition of the actual
matrix.
For the standard-addition method of calibration, two requirements must be met:
1.The calibration curve has to be linear
2.The regression line must pass through zero
• In this method, the signal intensity of the sample solution is measured. Then, the
analyte is added to this solution at known concentrations – the signal intensity is
measured after each addition of the analyte. This, therefore, gives a calibration
curve which is linear and shows signal intensity vs. added concentration.
The concentration of the analyte is determined from the point where
the regression line crosses the axis at zero.
Tuesday, February 27, 2024 16
18. Standard addition cont’d
•In this method, the matrix itself remains
completely unchanged – it is for this
reason that this method is useful in cases
where the matrix is either very
complicated or hard to reproduce.
Tuesday, February 27, 2024 18
19. Standard Addition Method
1. Most convenient when a small number of
samples are to be analyzed.
2. Useful when the analyte is present in a
complicated matrix and no ideal blank is
available.
Tuesday, February 27, 2024 19
20. Standard Addition Procedure
1. Add one or more increments of a standard
solution to sample aliquots of the same size. Each
mixture is then diluted to the same volume.
2. Prepare a plot of Analytical Signal versus:
a) volume of standard solution added, or
b) concentration of analyte added.
Tuesday, February 27, 2024 20
21. Standard Addition Procedure
3. The x-intercept of the standard addition plot
corresponds to the amount of analyte that must
have been present in the sample (after accounting
for dilution).
4. The standard addition method assumes:
a) the curve is linear over the concentration range
b) the y-intercept of a calibration curve would be 0
Tuesday, February 27, 2024 21
22. Example: Fe in Drinking Water
Sample
Volume
(mL)
Standard
Volume
(mL) Signal (V)
10 0 0.215
10 5 0.424
10 10 0.685
10 15 0.826
10 20 0.967
The concentration of
the Fe standard
solution is 11.1 ppm
All solutions are
diluted to a final
volume of 50 mL
Tuesday, February 27, 2024 22
24. [Fe] = ?
x-intercept = -6.08 mL
Therefore, 10 mL of sample diluted to 50 mL would give a
signal equivalent to 6.08 mL of standard diluted to 50 mL.
Vsam x [Fe]sam = Vstd x [Fe]std
10.0 mL x [Fe] = 6.08 mL x 11.1 ppm
[Fe] = 6.75 ppm
Tuesday, February 27, 2024 24
25. Internal Standard Method
1. Most convenient when variations in
analytical sample size, position, or matrix
limit the precision of a technique.
2. May correct for certain types of noise.
Tuesday, February 27, 2024 25
26. Internal Standard Procedure
1. Prepare a set of standard solutions for
analyte (A) as with the calibration curve
method, but add a constant amount of a
second species (B) to each solution.
2. Prepare a plot of SA/SB versus [A].
Tuesday, February 27, 2024 26
27. Notes
1. The resulting measurement will be
independent of sample size and position.
2. Species A & B must not produce signals that
interfere with each other. Usually they are
separated by wavelength or time.
Tuesday, February 27, 2024 27
28. Example: Pb by ICP Emission
Each Pb solution contains 100
ppm Cu.
[Pb]
(ppm) Pb Cu Pb/Cu
20 112 1347 0.083
40 243 1527 0.159
60 326 1383 0.236
80 355 1135 0.313
100 558 1440 0.388
Signal
Tuesday, February 27, 2024 28
29. Standardization
• Standardization is the process of determining the
exact concentration of a solution. It is the process
of experimentally determining the relationship
between the signal and the amount of analyte
Tuesday, February 27, 2024 29
30. Blank correction
•In blank determination all steps of the analysis are
performed in the absence of a sample. A blank solution
contains the solvent and all the reagents in an analysis
but none of the sample. The results from the blank are
then applied as a correction to the sample
measurements. Blank determinations reveal errors due
to interfering contaminants from the reagents and
vessels employed in analysis.
Tuesday, February 27, 2024 30
32. Calculations
1. Using the data on the Precision and Accuracy tab, calculate the
average, standard deviation, percent relative standard deviation,
and 95% confidence interval.
a. What is the precision of the data?
b. The known value for the data is 0.1500. Is there evidence of
bias? Support your answer.
2. A calibration curve is presented in the Calibration Curve tab, where
the response of a method is plotted versus the analyte
concentration.
a. Estimate the linear region of the data. One way to approach this
problem is to selectively remove data points from the plot until
you maximize the R2 value.
b. What is the sensitivity in the linear region?
Tuesday, February 27, 2024 32
33. Questions continued
3. Data are presented in the Limit of Detection tab for 10
replicate measurements of a 4.00 mM sample ([A] =
4.00 mM) and 10 replicate measurements of a blank
([A] = 0 mM). Perform the following calculations in the
spreadsheet. Use the calibration curve from part (2)
to determine the slope.
a.Calculate the signal detection limit.
b.Calculate the limit of detection.
c. Calculate the signal quantitation limit.
d.Calculate the limit of quantitation.
Tuesday, February 27, 2024 33
Editor's Notes
Answer is m=5.56mAbs/ppb. B= 0.93( Y= Mc +b
Calculate ( Answer, C = 4.78 ppb)
( Answer, C = 4.78 ppb) (3 significant figures)
