Chapter 1
Introduction
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1A Classification of analytical methods
• Classical Methods：wet chemistry
Separation by precipitation, extraction, distillation
• Qualitative analyses：the separated components were then treated
with reagents that yielded products that could be recognized by
colors, boiling or melting points, solubilities in a series of solvents,
odors, optical activities, or refractive indexes.
• Quantitative analyses：the amount of analyte was determined by
gravimetric or by volumetric measurements.
• Example：Acid-base titrations, redox titrations, complexometric
titrations, precipitation reactions
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1A Classification of analytical methods
• Instrumental Method by interaction with
a. Electromagnetic radiation：emission, absorption
b. Potential / current Magnetic (NMR) / electric field
(mass spectrometry)
c. Chemicals separation - chromatography
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1A Classification of analytical methods
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1C Instruments For Analysis
• Example：IR
Sample
Attenuated light
Lamp
Figure 1-1 Block diagram showing the overall process of an instrumental
measurement.
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Data Domains
• The measurement process is aided by a wide variety of
devices that convert information from one form to
another.
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Figure 1-3 A block diagram of a fluorometer showing (a) a general diagram of the instrument,
(b) a diagrammatic representation of the flow of information through various data domains in
the instrument, and (c) the rules governing the data-domain transformations during the
measurement process.
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1D Selecting an Analytical Method
• To select an analytical method intelligently, it is essential to define
clearly the nature of the analytical problem. In general, the following
points should be considered when choosing an instrument for any
measurement.
1. Accuracy and precision required
2. Available sample amount
3. The concentration range of the analyte
4. Interference in sample
5. Physical and chemical properties of the sample matrix
6. Number of samples to be analyzed
7. Speed, ease, skill, and cost of analysis
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Figures of Merit
• Precision：random error
• Bias : systematic error
• Sensitivity
• Detection limit
• Concentration range
(Dynamic range)
• Selectivity
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Precision
• How close the same measurements are to one another. The degree of
mutual agreement among data that have been obtained in the same
way. Precision provides a measure of the random or indeterminate
error of an analysis.
• Absolute standard deviation (s)
• relative standard deviation (sr), RSD
𝐬𝐫 =
𝐬
𝐱ത
, 𝑥 is the average
• Standard deviation of the mean (Sm), Sm = S / 𝑵
• Coefficient of variation, CV =
• Variance：S2
𝑺
𝑿
× 100%
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Bias
• Bias measures the systematic, or determinate error of an
analytical method.
• bias = 𝑥 - xt
where, 𝑥 is the population mean and xt is the true value
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Sensitivity
• The sensitivity of an instrument is a measure of its ability to
discriminate between small differences in analyte concentration.
• Two factors limit sensitivity：(1) the slope of the calibration
curve and the (2) reproducibility or precision of the measuring
device.
• The slope of the calibration curve at the concentration of
interest is known as calibration sensitivity.
• Of the two methods that have equal precision, the one that has
the steeper calibration curve will be the more sensitive.
• With such curves, the calibration sensitivity is independent of
the concentration
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Sensitivity
S = mC + Sbl
S = measured signal
m = calibration sensitivity
(Slope of line)
C = analyte concentration
Sbl = blank signal
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Sensitivity
• Analytical sensitivity (𝛄)：𝛄 = m/ss
m= slope of the calibration curves
ss = standard deviation of the measurement
• The analytical sensitivity offers the advantage of being relatively
insensitive to amplification factors.
• EX: gain of an instrument 5X → increase in m 5X → increase in
ss 5X ss → analytical sensitivity constant
• A second advantage of analytical sensitivity is that it is
independent of the measurement units for S.
• Disadvantage: analytical sensitivity is that it is often concentration
dependent because ss may vary with concentration.
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Detection Limit (Limit of detection, LOD)
• The minimum concentration of analyte that can be detected with a
specific method at a known confidence level.
• LOD is determined by S/N (Signal-to-noise ratio)
• NoiseUnwanted baseline fluctuations in the absence of analyte signal
(standard deviation of the background)
• 𝑆𝑚 = 𝑆𝑏𝑙 + 𝑘𝑠𝑏𝑙
• Sm = minimum distinguishable analytical signal (S/N = 3)
• 𝑆𝑏𝑙 = mean blank signal, 𝑠𝑏𝑙 = standard deviation, 𝑠𝑏𝑙 .
• The detection limit is given by : 𝑪𝒎 =
𝑺𝒎 −ഥ
𝑺𝒃𝒍
𝒎
• Cm = minimum concentration (LOD)
• m = sensitivity (slope of calibration curve)
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Example 1-2
A least-squares analysis of calibration data for the determination of
lead based on its flame emission spectrum yielded the equation
S = 1.12 cPb + 0.312
where cPb s is the lead concentration in ppm, and S is a measure of
the relative intensity of the lead emission line. The follow-ing
replicate data were then obtained:
Calculate (a) the calibration sensitivity, (b) the analytical sensitivity
at 1 and 10 ppm of Pb, and (c) the detection limit.
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Example 1-2
Solution
(a) By definition, the calibration sensitivity is the slope m = 1.12.
(b) At 10 ppm Pb, γ = m/ss = 1.12/0.15 = 7.5.
At 1 ppm Pb , γ = m/ss = 1.12/0.025 = 45.
Note that the analytical sensitivity is quite concentration
dependent. Because of this, it is not reported as often as the
calibration sensitivity.
(c) Applying Equation 1-12, S = 0.0296 + 3 × 0.0082 = 0.054
Substituting into Equation 1-13 gives :
Cm =
0.054 −0.0296
1.12
= 0.022 ppm Pb
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Dynamic Range
• The lowest concentration at which quantitative measurements can
be made (limit of quantitation, LOQ) to the concentration at which
the calibration curve departs from linearity (limit of linearity, LOL).
• LOQ equals ten times the standard deviation of repetitive
measurements on a blank (10 Sbl).
• LOQ = 𝑆𝑏𝑙 + 10 Sbl
• Dynamic range is the range over which the detector still responds to
changing concentration
• An analytical method should have a dynamic range,
•
usually 2-6 orders of magnitude. (102 ~ 106)
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Dynamic Range
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Selectivity
• The selectivity of an analytical method refers to the degree to
which the method is free from interference by other species
contained in the sample matrix.
• No analytical method is free from interference from other species,
and steps need to be taken to minimize the effects of these
interferences.
• The selectivity coefficient is a measure of how well the method
responds to interfering species in comparison to the analyte. It
can range from zero, indicating no interference, to values greater
than one.
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Selectivity
• Analyte A；interfering species：B and C
• If CA, CB, and CC are the concentrations of the three species and
mA, mB, and mC are their calibration sensitivities,
• the total instrument signal S
S = mA CA + mB CB + mC CC + Sbl
• selectivity coefficient for A with respect to B, kB,A
kB,A = mB / mA
• for A with respect to C ：kC,A = mC / mA
S = mA (CA + kB,A CB + kC,A CC) + Sbl
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Calibration of Instrumental Methods
• All types of analytical methods require calibration for
quantitation.
• Calibration is a process that relates the measured analytical signal
to the concentration of the analyte.
• We can’t just run a sample and know the relationship between
signal and concentration without calibrating the response
• The three most common calibration methods are:
1. Calibration curve
2. Standard addition method
3. Internal standard method
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1D-2 external-Standard Calibration
• Several standards (with different concentrations) containing exactly
known concentrations of the analyte are measured, and the
responses are recorded.
• A plot is constructed to graph instrument signal versus analyte
concentration.
• Sample (containing unknown analyte concentration) is run; if the
response is within the LDR of the calibration curve, then
concentration can be quantitated.
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1D-2 external-Standard Calibration
• The calibration curve relies on the accuracy of standard
concentrations.
• It depends on how closely the matrix of the standards resembles
that of the sample to be analyzed.
• If matrix interferences are low, calibration curve methods are OK.
• If matrices for samples and standards are not the same, calibration
curve methods are not good.
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1D-3 Standard Addition Methods
• The better method to use when matrix effects can be substantial
• Standards are added directly to aliquots of the sample; therefore
matrix components are the same.
• Procedure：
✓ Obtain several aliquots of the sample (all with the same volume).
✓ Spike the sample aliquots → add different volumes of standards
with the same concentration to the aliquots of the sample
✓ Dilute each solution (sample + standard) to a fixed volume
✓ Measure the analyte concentration
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Standard Addition Methods
• Instrumental measurements are made on each solution to get
instrument response (S).
• If the instrument response is proportional to the concentration
S=
𝒌𝑽𝒔𝑪𝒔
𝑽𝒕
+
𝒌𝑽𝒙𝑪𝒙
𝑽𝒕
✓ Vx =Volume of sample = 25 mL (suppose)
✓ Vs = Volume of standard = variable (5, 10, 15, 20 mL)
✓ Vt = Total volume of the flask = 50 mL
✓ Cs = Concentration of standard
✓ Cx = concentration of analyte in aliquot
✓ k = proportionality constant
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Standard Addition Methods
• A plot of S as a function of Vs is a straight line of the form,
• S = mVs+b
✓ slope, m = (kCs) / Vt
✓ intercept, b = (kVxCx) / Vt
✓ b/m = VxCx / Cs
✓ Cx = bCs / mVx
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Standard Addition Methods
• In the interest of saving time or sample, it is possible to perform
standard addition analysis by using only two increments of the
sample.
• A single addition of Vs mL of the standard would be added to one
of the two samples
• S1 = (kVxCx)/Vt
• S2 = (kVxCx)/Vt + (kVsCs)/Vt
Cx =
𝑺𝟏𝑪𝒔𝑽𝒔
(𝑺𝟐 − 𝑺𝟏) 𝑽𝒙
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Example 1-1
Ten millimeter aliquot of a natural water sample were pipetted into
50.00 mL volumetric flasks. Exactly 0.00, 5.00, 10.00, 15.00, 20,00
mL of a standard solution containing 11.1 ppm pf Fe3+ were added
to each, following by an excess of thiocyanate ion to give the red
complex Fe(SCN)2+. After dilution to volume, the instrument
response S for each of the five solutions, measured with a
colorimeter, was found to be 0.240, 0.437, 0.621, 0.809, and 1.009,
respectively. (a) What was the concentration of Fe3+ in the water
sample? (b) Calculate the standard deviation in the
concentration of Fe3+.
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Example 1-1
Solution
Unknown
(a) Cs = 11.1 ppm, Vs = 10.00 mL, Vt = 50.00 mL
m = 0.03820, b = 0.2412
As = 0.03820 Vs + 0.2412
Cx =
𝑏𝐶𝑠
𝑚𝑉𝑥
=
(0.2412)(11.1 𝑝𝑝𝑚 𝐹𝑒 3+ )
(0.03820/𝑚𝐿)(100𝑚𝐿)
= 7.01 ppm Fe3+
(b) Sm = 3.07 × 10-4 and Sb = 3.76 × 10-3
Sc = Cx
𝑆𝑚 2
𝑚
+
𝑆𝑏 2
𝑏
= 7.01
3.07 × 10−4 2
0.03820
+
3.76 ×10−3 2
0.2412
= 0.12 ppm Fe3+
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1D-4 The Internal-Standard Method
• An internal standard is a substance that is added in a constant
amount to all samples, blanks, and calibration standards in an
analysis.
• Calibration involves plotting the ratio of the analyte signal to the
internal-standard signal as a function of the analyte concentration
of the standards.
• This ratio for the samples is then used to obtain their analyte
concentrations from a calibration curve.
• If properly chosen and used, an internal standard can compensate
for several types of random and systematic errors.
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The method detection limit
• The method detection limit (MDL) is defined as the minimum
concentration of a substance that can be measured and reported
with 99% confidence that the analyte concentration is greater than
zero and is determined from the analysis of a sample in a given
matrix containing the analyte.
• This procedure is designed for applicability to a wide variety of
sample types ranging from reagent (blank) water-containing
analytes to wastewater-containing analytes.
• The MDL for an analytical procedure may vary as a function of
sample type.
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