Introduction & Figures of Merit
Suggested Reading
 Skoog/Holler/Crouch 6th Edition: Chapter 1A, 1B, 1E,
Appendix 1
Chemical Analysis
Classical
"Wet" Chemical
Qualitative Analysis
Instrumental
Quantitative Analysis
Quantitative
Analysis
Qualitative Analysis
Instrumental Methods
Thermal
Mass/Separations
Spectroscopic
Electrochemical
To perform an analysis, the analyte must often first be
separated from a mixture.
1
Analytical Separations
Chromatography
GC, LC, SFC
Mass Spectrometry
Capillary
Electrophoresis
After separation chemical analysis often performed on analyte.
 Preparatory Separations – analysis often performed off-line.
(Synthesis, large scale separations)
 Analytical Separations – analysis often performed on-line
with separation method. This course is concerned with
analytical, or very small scale separations.
Fundamentals are the same for analytical and preparatory
separations, technique specifics differ.
Outline for this section
1. Fundamentals
A. Instrument performance characteristics (Figures of Merit)
and statistical background review.
B. Instrument Calibrations
a. Traditional (Review)
b. Standard Additions
c. Internal Standards
C. Signals, Noise, S/N
2
a. Definitions/Sources
b. Methods for S/N enhancement
General Instrument Performance Characteristics
First define the problem:
 What accuracy is required?
 What is the analyte concentration range?
 What components of the sample might interfere with the
analysis?
 Etc.
Statistics Review in Appendix 1
Appendix 1 (answers on p. 1008)
You should be able to do the following questions and problems. Some are trivial, others
not so much.
1-7, 10, 12-13, 16, 21, 24
3
1. Precision = Measurement Reproducibility
Review statistics:
4
2. Bias = systematic measurement error
3. Sensitivity = Ability to distinguish between small differences in
analyte concentration
Sensitivity Illustration
12
S = mC + SBl
10
Instrument Signal
8
6
4
2
0
0
1
2
3
4
5
6
Analyte Concentration
5
4. Detection Limit = minimum analyte concentration that can be
detected with a given confidence level.
Find the detection limit for a fluorescence analysis given the
following calibration data.
Analyte Conc. (pg/mL)
0
2
4
6
8
10
12
Fluorescence Intensity
2.1
5.0
9.0
12.6
17.3
21
24.7
Fluorescence Signal
30
y = 1.9304x + 1.5179
25
20
15
10
5
0
0
2
4
6
8
10
12
14
pg/mL
6
SUMMARY
OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.998879565
0.997760386
0.997312463
0.432847713
7
Intercept
X
Variable
1
Coefficients
1.517857143
Standard
Error
0.294936001
1.930357143
0.040900264
5. Linear Dynamic Range = Analyte concentration range from the
Limit of Quantification  concentration at which there is a nonlinear instrument response.
7
6. Selectivity = A method’s ability to selectively analyze an
analyte in the presence of other chemical species (the sample
“matrix”).
Signal = maCa + mbCb + Sbl
m = analytical sensitivity, c = concentration
Instrument Calibrations
External Standards (Traditional)
Standard Additions
Internal Standards
Section 1D pp. 11-17
Appendix 1 Section a1D.
External standards – prepared separate from the sample (what
you are familiar with).
1) Prepare standards of “exactly” known concentrations
covering the linear dynamic range
2) Prepare a blank containing everything in the sample
except the analyte
3) Obtain instrument response for standards and blank
4) Plot instrument response versus standard concentrations
8
 Plot is linear over the dynamic range
 Use linear least squares within the dynamic range to fit the
data
 For non-linear calibrations fit to appropriate function (not
ideal).
 Signal from unknown must be within range of standards (no
extrapolation)
9
What if you have a complicated sample with many species – and a
method that is not completely selective?
If you know the matrix…
If you don’t know the matrix…
Standard Additions –
This is the most common “spiking” procedure:
1. Equal volumes of unknown are pipetted into several
volumetric flasks
2. Increasing volumes of standard are added to each flask (the
standard is the same as the analyte)
3. Each flask is diluted to the same final volume
10
4. For each flask a measurement of analytical signal is obtained
(containing both unknown analyte + known amount of
additional added analyte)
To treat the data – can think about it graphically or algebraically.
11
Algebraically
What if …
 You have an instrument whose response fluctuates, or
 You have a sample preparation procedure that results in
irreproducible loss of analyte, or
 You have no way to reproducibly input a constant volume of
sample into an instrument
Internal standards calibration procedure
12
K/Li Intensity Ratio
K with Li Internal Standard Calibration
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
y = 0.00721x + 0.474
2
R = 0.995
0
100
200
300
400
500
600
ppm K
Chapter 1 Problems 9, 11
13
Signals and Noise
Sections
 5A Signal-to-Noise Ratio √
 5B Noise sources in instruments requires knowledge of
electronics (Skip)
 5C Signal-to-Noise Enhancement
5C-1 Hardware requires knowledge of electronics (Skip)
5C-2 Software methods √
5A Signal-to-Noise Ratio
Remember – every measurement has inherent uncertainty (random
error)
“Noise” is the electronic manifestation of this random error.
 It degrades measurement accuracy/precision
 Determines the detection limit
Every measurement contains 2 components:
1. Signal = response from analyte
2. Noise
Since noise is mostly independent of signal strength, the effect of
noise on the analysis depends on the signal.
A most useful figure of merit: Signal-to-Noise Ratio (S/N)
14
Noise – standard deviation of numerous measurements of signal
strength
Signal – average (mean) of numerous measurements of signal
strength
S/N =
This is nothing new.
Calculate the S/N ratio for the following titrimetric data.
Five titrations of the same amount of material required the
following volumes: 24.38 mL, 24.21 mL, 24.46 mL, 24.30 mL,
24.40 mL.
Why is S/N important? For one thing, it tells whether or not a
signal is detectable.
General Rule: A signal cannot be detected if S/N < 3.
15
To calculate S/N for 2 absorbance spectra: S/N =
Malachite Green Absorbance Spectra
0.45
Signal = 0.39
0.4
0.35
0.3
Concentrated
solution
Absorbance
0.25
0.2
Signal = 0.079
0.15
0.1
0.05
S
0
-0.05
400
Dilute solution
450
500
550
600
650
700
750
800
Wavelength (nm)
Clearly a high S/N is desirable.
Hardware devices to increase S/N (5C-1, electronics/instrument
design)
Software methods to enhance S/N. Routinely done (5C-2)
16
5C-2 Software methods to enhance S/N
1. Ensemble or signal averaging.
Make n repetitive measurements and average the result. (No
different from replicate titrimetric analyses)
In the absence of systematic error…
Find means of replicate measurements, less scatter.
Below is data from an absorbance spectrum of malachite green in a
region where there is no absorbance (i.e. noise or random error).
0.12
0.12
0.09
0.08
0.07
0.08
0.07
0.07
0.08
0.08
0.07
0.06
0.08
0.09
0.08
0.07
0.05
0.07
0.07
0.08
1. Find the mean and standard deviation for this set of 20
measurements.
2. Find the mean and standard deviation from the means
of sets of 5 measurements.
3. Compare the mean and standard deviations.
The standard deviation of the means is inversely proportional to
n , where n = number of measurements averaged to generate the
mean. (Note confidence interval equation)
Noise = random error of measurement, measured by standard
deviation.
17
There is a
averaging.
n
dependence on S/N for ensemble or signal
Vertical scale increases
as the number of scans
increases.
Random signal
fluctuations (noise)
increases with n .
Signal increases with n.
S/N increases
Summary:
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2. Boxcar Averaging
The average of a small number of adjacent data points is a better
measure of signal than all of the individual data points. (Signal
varies more slowly than noise)
Signal
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
2 pt
boxcar
x-axis
Signal
3 pt
boxcar
x-axis
unprocessed
Signal
4.5
0.733
3.5
4
0.2
0.9
1.1
2.2
3.5
4
3.6
3.8
3.3
3.1
2.9
2.4
1.8
1.2
0.8
1.5
0.55
2
3
3.5
1.65
Signal
x-axis
5
5.5
2.5
2
3.233
1.5
3.75
1
7.5
3.7
8
0.5
3.567
0
0
9.5
3.2
11.5
2.65
11
2
4
x-axis
8
6
10
12
14
16
2.8
2 pt boxcar
4
13.5
1.5
14
1.267
3.5
3
2.5
Signal
3 pt boxcar
2
4
1.5
3.5
1
3
0.5
2.5
0
Signal
0
2
4
6
8
10
x-axis
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
16
x-axis
Summary:
19
12
14
16
3. Digital Filtering
A moving boxcar average – must include an odd number of data
points.
x-axis
Signal
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
3 pt moving
boxcar
x-axis
Signal
0.2
0.9
1.1
2.2
3.5
4
3.6
3.8
3.3
3.1
2.9
2.4
1.8
1.2
0.8
2
3
4
5
6
7
8
9
10
11
12
13
14
5 pt moving
boxcar
x-axis
0.733
1.4
2.267
3.233
3.7
3.8
3.567
3.4
3.1
2.8
2.367
1.8
1.267
Signal
3
4
5
6
7
8
9
10
11
12
13
1.58
2.34
2.88
3.42
3.64
3.56
3.34
3.1
2.7
2.28
1.82
Shown below are the results of moving boxcar averages from real
spectra of many hundreds of data points.
Malachite Green Absorbance Spectra
0.09
0.08
0.07
0.06
Absorbance
0.05
0.04
0.03
0.02
0.01
0
-0.01
400
450
500
550
600
650
700
750
800
Wavelength (nm)
20
Relative Single Beam Signal Intensity
0.5 cm-1 resolution
19 pt. Boxcar averaged
2390.00
2370.00
2350.00
2330.00
2310.00
2290.00
2270.00
2250.00
Wavenumber
21
Summary:
Polynomial least squares data smoothing: similar to moving boxcar
averaging but with weighted data points.
Rather than simply averaging (an odd number) of data points, a
least squares fit of x data points to a polynomial is done. The
central point of the fitted polynomial is the new data point. This
“Savitzky-Golay” smoothing is available in most data analysis
software.
Original ref: Anal. Chem. 1964, 36, 1627.
The best solution is to eliminate, or reduce as much as possible,
noise in the first place.
There are various sources of noise (Section 5B), much of it
resulting from electronics in the instrumentation:
 Thermal
 Shot (from junctions)
 Flicker (1/f)
 Environmental*
It is good to be aware of sources of environmental noise.
22
Often low frequency signals are modulated to frequency regions
which have minimal environmental noise.
In spectroscopy the signal can be modulated by a chopper which
interrupts the light beam periodically blocking the beam. The
resulting square wave output has a frequency of the chopper.
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End of Chapter 5 problems: 1-3, 6-8, 11-12, 13a,e
(Problem 13 data exists on the website:
www.thomsonedu.com/chemistry/skoog)
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