Transcript sampling - eLisa UGM

CHAPTER 1
FUNDAMENTAL CONCEPTS
1
INSTRUMENTAL ANALYSIS
This course covers:
• The fundamentals of common analytical instruments
• Measurements with these instruments
• Interpretation of data obtained from the measurements
• Communication of the meaning of the results
2
WHAT IS ANALYTICAL CHEMISTRY
• The qualitative and quantitative characterization of matter
• The scope is very wide and it is critical to our
understanding of almost all scientific disciplines
• Characterization
• Qualitative: The identification of chemical compounds
or elements present in a sample
• Quantitative: the determination of the exact amount of
compound or element present in a sample
• Chemical Species
• Could be an element, ion or compound (organic or
inorganic)
3
CHATACTERIZATION
• Bulk Analysis
• Characterization of the entire sample
• Example: determination of the elemental composition
of a mixture (alloys)
• Surface Analysis
• Characterization of the surface of a sample
• Example: finding the thickness of a thin layer on the
surface of a solid material
• Characterization may also include Structural Analysis
and measurement of physical properties of materials
4
WET CHEMICAL ANALYSIS
• Also called Classical methods
• Separation of component of interest (analyte) from the
sample by precipitation, extraction, or distillation,
followed by gravimetric or titrimetric measurement for
quantitative analysis
• Wet analysis is time consuming and demands attention
to detail
• Volumetric Analysis
• Analysis by volume
• Gravimetric Analysis
• Analysis by mass
• Examples
• Acid-base titrations, redox titrations, complexometric
titrations, precipitation reactions
5
WET CHEMICAL ANALYSIS
• Nondestructive Analysis
• Useful when evidence needs to be preserved
• Used to analyze samples without destroying them
• Examples
• Forensic analysis
• Paintings
6
Instrumental Methods
• Involve interactions of analyte with EMR
(electromagnetic radiation)
– Radiant energy is either produced by the
analyte (e.g., Auger) or changes in EMR are
brought about by its interaction with the
sample (e.g., NMR)
• Other methods include measurement of
electrical properties (e.g., potentiometry)
7
Instruments
• Converts information stored in the physical or
chemical characteristics of the analyte into
useful information
• Require a source of energy to stimulate
measurable response from analyte
• Data domains
– Methods of encoding information electrically
– Nonelectrical domains
– Electrical domains
• Analog, Time, Digital
8
Instruments
• Detector
– Device that indicates a change in one variable in its
environment (eg., pressure, temp, particles)
– Can be mechanical, electrical, or chemical
• Sensor
– Analytical device capable of monitoring specific
chemical species continuously and reversibly
• Transducer
– Devices that convert information in nonelectrical
domains to electrical domains and the converse
9
Selecting an Analytical Method
• What accuracy is required
• How much sample is available
• What is the concentration range of the
analyte
• What components of the sample will cause
interference
• What are the physical and chemical
properties of the sample matrix
• How many samples are to be analyzed
10
THE ANALYTICAL APPROACH
• Problems continuously occur around the world in
• Manufacturing industries
• The environment
• The health sector (medicine)
• etc.
• The analytical chemist is the solution to these
problems
• The analytical chemist must understand the
• analytical approach
• uses, capabilities, and limitations of analytical
techniques
11
THE ANALYTICAL APPROACH
• Analyte
• A substance to be measured in a given sample
• Matrix
• Everything else in the sample
• Interferences
• Other compounds in the sample matrix that interfere
with the measurement of the analyte
12
THE ANALYTICAL APPROACH
• Homogeneous Sample
• Same chemical composition throughout (steel,
sugar water, juice with no pulp, alcoholic
beverages)
• Heterogeneous Sample
• Composition varies from region to region within the
sample (pudding with raisins, granola bars with
peanuts)
• Differences in composition may be visible or
invisible to the human eye (most real samples are
invisible)
• Variation of composition may be random or
segregated
13
THE ANALYTICAL APPROACH
• Analyze/Analysis
• Applied to the sample under study
• Determine/Determination
• Applied to the measurement of the analyte in the sample
• Multiple Samples
• Identically prepared from another source
• Replicate Samples
• Splits of sample from the same source
14
THE ANALYTICAL APPROACH
General Steps in Chemical Analysis
1. Defining the problem (formulating the question)
• To
be
answered
through
chemical
measurements
2. Selecting techniques (designing the analytical
method)
• Find appropriate analytical procedures
3. Sampling and sample storage
• Select representative material to be analyzed
4. Sample preparation
• Convert representative material into a suitable
form for analysis
15
THE ANALYTICAL APPROACH
General Steps in Chemical Analysis
5. Analysis (performing the measurement)
• Measure the concentration of analyte in
several identical portions
6. Assessing the data
7. Method validation
8. Documentation
16
DEFINING THE PROBLEM
• Find out the information that needs to be known
about a sample (or what procedure is being studied)
• How accurate and precise the information must be
• Whether qualitative or quantitative analysis or both is
required
• How much sample is available for study
• Whether nondestructive analysis must be employed
17
DEFINING THE PROBLEM
• Bulk analysis or analysis of certain parts is required
• Sample is organic or inorganic
• Sample a pure substance or a mixture
• Homogeneous or heterogeneous sample
• Chemical information or elemental information needed
18
DEFINING THE PROBLEM
Qualitative Analysis
• Provides information about what is present in the
sample
• If quantitative analysis is
analysis is usually done first
required,
qualitative
• Capabilities and limitations of analysis must be well
understood
19
DEFINING THE PROBLEM
Qualitative Analysis
Qualitative Elemental Analysis
• Used to identify elements present in a material
• Can provide empirical formula of organic compounds (XRay Fluorescence, AAS)
Qualitative Molecular Analysis
• Used to identify molecules present in a material
• Can be used to obtain molecular formula
• Can be used to distinguish between isomers (NMR, IR,
MS)
20
DEFINING THE PROBLEM
Qualitative Analysis
Empirical Formula
• The simplest whole number ratios of atoms of each
element present in a molecule
Molecular Formula
• Contains the total number of atoms of each element in a
single molecule of the compound
Isomers
• Different structures with the same molecular formula (nbutane and iso-butane)
21
DEFINING THE PROBLEM
Qualitative Analysis
Enantiomers
• Nonsuperimposable mirror-image isomers
• Said to be chiral
• Have the same IR, NMR, and MS
• Mostly same physical properties (boiling-point,
melting point, refractive index)
• Chiral Chromatography can be used to distinguish
between such optically active compounds (erythrose,
glyceraldehyde)
22
DEFINING THE PROBLEM
Qualitative Analysis
Mixtures of Organic Compounds
• Mixtures are usually separated before the individual
components are identified
• Separation techniques include
• GC
• LC
• HPLC
• CE
23
DEFINING THE PROBLEM
Quantitative Analysis
• The determination of the amount of analyte in a given
sample
• Often expressed in terms of concentrations
Concentration
• The quantity of analyte in a given volume or mass of
sample
• Molarity = moles/liters,
• ppm = µg/g sample
• ppb = ng/g sample,
• ppt = pg/g sample
• Percent by mass [%(m/m)],
• Percent by volume [%(v/v)]
24
DEFINING THE PROBLEM
Quantitative Analysis
• Early methods include volumetric, gravimetric, and
combustion analysis
• Automated and extremely sensitive methods are being
used today (GC, IR, HPLC, CE, XRD)
• Require micron amounts and a few minutes
• Hyphenated techniques are used for qualitative and
quantitative measurements of the components
mixtures (GC-MS, LC-MS)
25
DESIGNING THE ANALYTICAL METHOD
• Analytical procedure is designed after the problem has
been defined
• Analyst must consider
• Accuracy and precision
• Amount of sample to be used
• Cost analysis
• Turnaround time (time between receipt of sample
and delivery of results)
26
DESIGNING THE ANALYTICAL METHOD
Green chemistry processes
analytical procedures
preferred
for
modern
• The goal is to minimize waste and pollution
• Use of less toxic or biodegradable solvents
• Use of chemicals that can be recycled
• Standard methods are available in literature
(reproducible with known accuracy and precision)
27
DESIGNING THE ANALYTICAL METHOD
• Do not waste time developing a method that already
exists
• Method of choice must be reliable and robust
• Interferences must be evaluated
• Interference
• Element or compound that respond directly to
measurement to give false analyte signal
• Signal may be enhanced or suppressed
28
DESIGNING THE ANALYTICAL METHOD
Fundamental Features of Method
• A blank must be analyzed
• The blank is usually the pure solvent used for sample
preparation
• Used to identify and correct for interferences in the
analysis
• Analyst uses blank to set baseline
• Reagent blank: contains all the reagents used to
prepare the sample
• Matrix blank: similar in chemical composition to the
sample but without the analyte
29
DESIGNING THE ANALYTICAL METHOD
Fundamental Features of Method
• Methods require calibration standards (except
coulometry) used to establish relationship between
analytical signal being measured and the
concentration of analyte
• This relationship (known as the calibration curve)
is used to determine the concentration of unknown
analyte in samples
30
DESIGNING THE ANALYTICAL
METHOD
Fundamental Features of Method
• Reference (check) standards are required
• Standards
of known
concentration of analyte
composition
with
known
• Run as a sample to confirm that the calibration is correct
• Used to access the precision and accuracy of the analysis
Government and private sources of reference standards are
available (National Institute of Standards and Technology,
NIST)
31
Sampling and Sample
Preparation
32
SAMPLING
• The most important step is the collection of the
sample of the material to be analyzed
• Sample should be representative of the material
• Sample should be properly taken to provide reliable
characterization of the material
• Sufficient amount must be taken for all analysis
• Representative Sample
• Reflects the true value and distribution of analyte in
the original material
33
SAMPLING
Steps in Sampling Process
• Gross representative sample is collected from the
lot
• Portions of gross sample is taken from various parts
of material
Sampling methods include
• Long pile and alternate shovel (used for very large
lots)
• Cone and quarter
Aliquot
• Quantitative amount of a test portion of sample
solution
34
SAMPLING
• Care must be taken since collection tools and
storage containers can contaminate samples
• Make room for multiple test portions of sample for
replicate analysis or analysis by more than one
technique
• Samples may undergo
• grinding
• chopping
• milling
• cutting
35
SAMPLING
Gas Samples
• Generally considered homogeneous
• Samples are stirred before portions are taken for
analysis
• Gas samples may be filtered if solid materials are
present
Grab samples
• Samples taken at a single point in time
Composite Samples
• Samples taken over a period of time or from different
locations
36
SAMPLING
Gas Samples
Scrubbing
• Trapping an analyte out of the gas phase
• Examples
• Passing air through activated charcoal to adsorb organic
vapors
• Bubbling gas samples through a solution to absorb the
analyte
• Samples may be taken with
• Gas-tight syringes
• Ballons (volatile organic compounds may contaminate
samples)
• Plastic bags (volatile organic compounds may
contaminate samples)
• Glass containers (may adsorb gas components)
37
SAMPLING
Liquid Samples
• May be collected as grab samples or composite
samples
• Adequate
stirring
is
necessary
to
obtain
representative sample
• Stirring may not be desired under certain conditions
(analysis of oily layer on water)
• Undesired solid materials are removed by filtration or
centrifugation
• Layers of immiscible liquids may be separated with
the separatory funnel
38
SAMPLING
Solid Samples
• The most difficult to sample since least
homogeneous compared to gases and liquids
• Large amounts are difficult to stir
• Must undergo size reduction (milling, drilling,
crushing, etc.) to homogenize sample
• Adsorbed water is often removed by oven drying
39
SAMPLING
Sample Storage
• Samples are stored if cannot be analyzed
immediately
• Sample composition can be changed by interaction
with container material, light, or air
• Appropriate storage container and conditions must
be chosen
• Organic components must not be stored in plastic
containers due to leaching
• Glass containers may adsorb or release trace levels
of ionic species
40
SAMPLING
Sample Storage
• Appropriate cleaning of containers is necessary
• Containers for organic samples are washed in solvent
• Containers for metal samples are soaked in acid and
deionized water
• Containers must be first filled with inert gas to displace
air
• Biological samples are usually kept in freezers
• Samples that interact with light are stored in the dark
41
SAMPLING
Sample Storage
• Some samples require pH adjustment
• Some samples require addition of preservatives
(EDTA added to blood samples)
• Appropriate labeling is necessary
• Computer
based
Laboratory
Information
Management Systems (LIMS) are used to label
and track samples
42
SAMPLE PREPARATION
• Make samples in the physical form required by the
instrument
• Make concentrations in the range required by the
instrument
• Free analytes from interfering substances
• Solvent is usually water or organic
43
SAMPLE PREPARATION
Type of sample preparation depends on
• nature of sample
• technique chosen
• analyte to be measured
• the problem to be solved
Samples may be
• dissolved in water (or other solvents)
• pressed into pellets
• cast into thin films
• etc.
44
SAMPLE PREPARATION METHODS
Acid Dissolution and Digestion
• Used for dissolving metals, alloys, ores, glass,
ceramics
• Used for dissolving trace elements in organic materials
(food, plastics)
• Concentrated acid is added to sample and then
heated
• Choice of acid depends on sample to be dissolved and
analyte
Acids commonly used: HCl, HNO3, H2SO4 HF and HClO4
• require special care and supervision
45
SAMPLE PREPARATION METHODS
Fusion (Molten Salt Fusion)
• Heating a finely powdered solid sample with a finely
powdered salt at high temperatures until mixture
melts
• Useful for the determination of silica-containing
minerals, glass, ceramics, bones, carbides
Salts (Fluxes) Usually Used
• Sodium carbonate, sodium tetraborate (borax),
• sodium peroxide, lithium metaborate
46
SAMPLE PREPARATION METHODS
Dry Ashing and Combustion
• Burning an organic material in air or oxygen
• Organic components form CO2 and H2O vapor
leaving inorganic components behind as solid oxides
• Cannot be used for the determination of mercury,
arsenic, and cadmium
47
SAMPLE PREPARATION METHODS
Extraction
• Used for determining organic analytes
• Makes use of solvents
• Solvents are chosen based on polarity of analyte
(like dissolves like)
Common Solvents
• Hexane, xylene, methylene chloride
48
SAMPLE PREPARATION METHODS
Solvent Extraction
• Based on preferential solubility of analyte in one of two
immiscible phases
For two immiscible solvents 1 and 2
• The ratio of concentration of analyte in the two phases is
approximately constant (KD)
KD

A 1
 distribution coefficient 
A2
49
SAMPLE PREPARATION METHODS
Solvent Extraction
• Large KD implies analyte is more soluble in solvent 1
than in solvent 2
• Separatory funnel is used for solvent extraction
Percent of analyte extracted (%E)
• V1 and V2 are volumes of solvents 1 and 2
respectively

A1 V1
%E 
x 100%
A1 V1  A2 V2
%E 
100K D
K D  V2 /V1 
50
SAMPLE PREPARATION METHODS
Solvent Extraction
• Multiple small extractions are more efficient than one
large extraction
• Extraction instruments are also available
Examples
Extraction of
• pesticides, PCBs, petroleum hydrocarbons from
water
• fat from milk
51
SAMPLE PREPARATION METHODS
Other Extraction Approaches
Microwave Assisted Extraction
• Heating with microwave energy during extraction
Supercritical Fluid Extraction (SFE)
• Use of supercritical CO2 to dissolve organic
compounds
• Low cost, less toxic, ease of disposal
Solid Phase Extraction (SPE)
Solid Phase Microextraction (SPME)
• The sample is a solid organic material
• Extracted by passing sample through a bed of
sorbent (extractant)
52
Statistics
53
STATISTICS
• Statistics are needed in designing the correct
experiment
Analyst must
• select the required size of sample
• select the number of samples
• select the number of replicates
• obtain the required accuracy and precision
Analyst must also express uncertainty in measured
values to
• understand any associated limitations
• know significant figures
54
STATISTICS
Rules For Reporting Results
Significant Figures = digits known with certainty + first
uncertain digit
• The last sig. fig. reflects the precision of the
measurement
• Report all sig. figs such that only the last figure is
uncertain
• Round off appropriately (round down, round up, round
even)
55
STATISTICS
Rules For Reporting Results
• Report least sig. figs for multiplication and division
of measurements (greatest number of absolute
uncertainty)
• Report least decimal places for addition and
subtraction of measurements (greatest number of
absolute uncertainty)
• The characteristic of logarithm has no uncertainty
• Does not affect the number of sig. figs.
• Discrete objects have no uncertainty
• Considered to have infinite number of sig. figs.
56
ACCURACY AND PRECISION
• Accuracy is how close a measurement is to the true
(accepted) value
• True value is evaluated by analyzing known
standard samples
• Precision is how close replicate measurements on
the same sample are to each other
• Precision is required for accuracy but does not
guarantee accuracy
• Results should be accurate and precise
(reproducible, reliable, truly representative of
sample)
57
ERRORS
Two principal types of errors: Determinate (systematic)
and indeterminate (random)
Determinate (Systematic) Errors
• Caused by faults in procedure or instrument
• Fault can be found out and corrected
• Results in good precision but poor accuracy
May be
• constant (incorrect calibration of pH meter or mass
balance)
• variable (change in volume due to temperature
changes)
58
• additive or multiplicative
ERRORS
Examples of Determinate (Systematic) Errors
• Uncalibrated or improperly calibrated mass balances
• Improperly calibrated volumetric flasks and pipettes
• Analyst error (misreading or inexperience)
• Incorrect technique
• Malfunctioning
alignment, etc)
instrument
(voltage
fluctuations,
• Contaminated or impure or decomposed reagents
• Interferences
59
ERRORS
To Identify Determinate (Systematic) Errors
• Use of standard methods with known accuracy
and precision to analyze samples
• Run several analysis of a reference analyte whose
concentration is known and accepted
• Run Standard Operating Procedures (SOPs)
60
ERRORS
Indeterminate (Random) Errors
• Sources cannot be identified, avoided, or corrected
• Not constant (biased)
Examples
• Limitations of reading mass balances
• Electrical noise in instruments
61
ERRORS
• Random errors
measurements
are
always
associated
with
• No conclusion can be drawn with complete certainty
• Scientists use statistics to accept conclusions that
have high probability of being correct and to reject
conclusions that have low probability of being correct
• Random errors follow random
analyzed using laws of probability
distribution
and
• Statistics deals with only random errors
• Systematic errors should be detected and eliminated
62
THE GAUSSIAN DISTRIBUTION
• Symmetric bell-shaped curve representing the
distribution of experimenal data
• Results from a number of analysis from a single
sample follows the bell-shaped curve
• Characterized by mean and standard deviation
The Gaussian function is f(x)  ae
a

(x   )2
2 2
1
σ 2π
63
THE GAUSSIAN DISTRIBUTION
• a is the height of the curve’s peak
• µ is the position of the center of the peak (the mean)
• σ is a measure of the width of the curve (standard
deviation)
• T (or xt) is the accepted value
• The larger the random error the broader the
distribution
• There is a difference between the values obtained
from a finite number of measurements (N) and those
obtained from infinite number of measurements
64
THE GAUSSIAN DISTRIBUTION
f(x) = frequency of occurrence of a particular results
a
f(x)
T (xt)
Point of inflection
-3σ -2σ
-σ
μ
σ
2σ 3σ
x
65
SAMPLE MEAN ( x )
• Arithmetic mean of a finite number of observations
• Also known as the average
• Is the sum of the measured values divided by the
number of measurements
N
_
x
x
i 1
N
i

1
x1  x 2  x 3  .....  x N 
N
∑xi = sum of all individual measurements xi
xi = a measured value
N = number of observations
66
POPULATION MEAN (µ)
• The limit as N approaches infinity of the sample mean
lim
μ 
N
N
xi

i 1 N
µ = T in the absence of systematic error
67
ERROR
Error (E)  the difference between T and either x i or x
E  x i  T or E  x  T
Absolute error  Absolute value of E
E abs  x i  T or E  x  T
Total error = sum of all systematic and random errors
Relative error = absolute error divided by the true value
E rel
E abs

T
%E rel
E abs

x 100%
T
68
STANDARD DEVIATION
Absolute deviation (d i )  x i  x
Relative deviation (D) = absolute deviation divided by mean
D 
di
_
x
Percent Relative deviation [D(%)]
D(%) 
di
_
x 100%  D x 100%
x
69
STANDARD DEVIATION
Sample Standard Deviation (s)
• A measure of the width of the distribution
• Small standard deviation gives narrow distribution curve
• For a finite number of observations, N
N
s
d
i 1
 x
2
i
N 1

i 1

2
N
i
x
N 1
xi = a measured value
N = number of observations
N-1 = degrees of freedom
70
STANDARD DEVIATION
Standard Deviation of the mean (sm)
• Standard deviation associated with the mean
consisting of N measurements
s
sm 
N
Population Standard Deviation (σ)
• For an infinite number of measurements
2
N
σ
lim
N
 x
i 1
i
 μ
N
71
STANDARD DEVIATION
Percent Relative Standard Deviation (%RSD)
%RSD 
s
_
x 100
x
Variance
• Is the square of the standard deviation
• Variance = σ2 or s2
• Is a measure of precision
• Variance is additive but standard deviation is not
additive
• Total variance is the sum of independent variances
72
QUANTIFYING RANDOM ERROR
Median
• The middle number in a series of measurements
arranged in increasing order
• The average of the two middle numbers if the
number of measurements is even
Mode
• The value that occurs the most frequently
Range
• The difference between the highest and the lowest
values
73
QUANTIFYING RANDOM ERROR
• The Gaussian distribution and statistics are used to
determine how close the average value of
measurements is to the true value
• The Gaussian distribution assumes infinite number
of measurements
As N increases x  μ approaches zero
x μ
for N > 20
Random error  x  μ
• The standard deviation coincides with the point of
inflection of the curve (2 inflection points since curve is
74
symmetrical)
QUANTIFYING RANDOM ERROR
f(x)
a
Population mean (µ) = true value (T or xt)
x=µ
Points of inflection
-3σ -2σ
-σ
μ
σ
2σ 3σ
x
75
QUANTIFYING RANDOM ERROR
Probability
• Range of measurements for ideal Gaussian
distribution
• The percentage of measurements lying within the
given range (one, two, or three standard deviation on
either side of the mean)
Range
Gaussian Distribution (%)
µ ± 1σ
µ ± 2σ
µ ± 3σ
68.3
95.5
99.7
76
QUANTIFYING RANDOM ERROR
• The average measurement is reported as: mean ±
standard deviation
• Mean and standard deviation should have the same
number of decimal places
In the absence of determinate error and if N > 20
• 68.3% of measurements of xi will fall within x = µ ± σ
• (68.3% of the area under the curve lies in the range
of x)
• 95.5% of measurements of xi will fall within x = µ ± 2σ
• 99.7% of measurements of xi will fall within x = µ ± 3σ
77
QUANTIFYING RANDOM ERROR
x=µ±σ
f(x)
a
68.3%
known as the confidence level
(CL)
-3σ -2σ
-σ
μ
σ
2σ 3σ
x
78
QUANTIFYING RANDOM ERROR
x = µ ± 2σ
f(x)
a
95.5%
known as the confidence level
(CL)
-3σ -2σ
-σ
μ
σ
2σ 3σ
x
79
QUANTIFYING RANDOM ERROR
x = µ ± 3σ
f(x)
a
99.7%
known as the confidence level
(CL)
-3σ -2σ
-σ
μ
σ
2σ 3σ
x
80
QUANTIFYING RANDOM ERROR
Short-term Precision
• Analysis run at the same time by the same analyst
using the same instrument and same chemicals
Long-term Precision
• Compiled results over several months on a regular
basis
Repeatability
• Short-term precision
conditions
under
same
operating
81
QUANTIFYING RANDOM ERROR
Reproducibility
• Ability of multiple laboratories to obtain same results on
a given sample
Ruggedness
• Degree of reproducibility of results by one laboratory
under different conditions (long-term precision)
Robustness (Reliability)
• Reliable accuracy and precision under small changes in
condition
82
CONFIDENCE LIMITS
• Refers to the extremes of the confidence interval
(the range)
• Range of values within which there is a specified
probability of finding the true mean (µ) at a given CL
• CL is an indicator of how close the sample mean
lies to the population mean
µ = x ± zσ
83
CONFIDENCE LIMITS
µ = x ± zσ
If z = 1
• we are 68.3% confident that x lies within ±σ of the true
value
If z = 2
• we are 95.5% confident that x lies within ±2σ of the
true value
If z = 3
• we are 99.7% confident that x lies within ±3σ of the
true value
84
CONFIDENCE LIMITS
- For N measurements CL for µ is
μ  x  zs m
• s is not a good estimate of σ since insufficient
replicates are made
• The student’s t-test is used to express CL
• The t-test is also used to compare results from
different experiments
t
x  μ 
s
85
CONFIDENCE LIMITS
_
ts
μ  x
N
• That is, the range of confidence interval is
– ts/√n below the mean and + ts/√n above the mean
• For better precision reduce confidence interval by
increasing number of measurements
86
CONFIDENCE LIMITS
To test for comparison of Means
• Calculate the pooled standard deviation (spooled)
• Calculate t
• Compare the calculated t to the value of t from the
table
• The two results are significantly different if the
calculated t is greater than the tabulated t at 95%
confidence level (that is tcal > ttab at 95% CL)
87
CONFIDENCE LIMITS
For two sets of data with
- N1 and N2 measurements
 averages of x1 and x 2
- standard deviations of s1 and s2
s pooled 
s12 N1  1  s22 N 2  1
N1  N 2  2
x1  x2
t 
s pooled
N1N 2
N1  N 2
Degrees of freedom = N1 + N2 - 2
88
CONFIDENCE LIMITS
Using the t-test to Test for Systematic Error

 t  x μ

N
s
-A known valid method is used to determine µ for a known
sample
-- The new method is used to determine mean and standard
deviation
- t value is calculated for a given CL
- Systematic error exists in the new method if
tcal > ttab for the given CL
89
F-TEST
• Used to compare two methods (method 1 and method
2)
• Determines if the two methods are statistically different
in terms of precision
• The two variances (σ12 and σ22) are compared
• F-function = the ratio of the variances of the two sets
of numbers
σ12
F 2
σ2
90
F-TEST
• Ratio should be greater than 1 (i. e. σ12 > σ22)
• F values are found in tables (make use of two
degrees of freedom)
• Fcal > Ftab implies there is a significant difference
between the two methods
Fcal = calculated F value
Ftab = tabulated F value
91
REJECTION OF RESULTS
Outlier
• A replicate result that is out of the line
• A result that is far from other results
• Is either the highest value or the lowest value in a
set of data
• There should be a justification for discarding the
outlier
• The outlier is rejected if it is > ±4σ from the mean
• The outlier is not included in calculating the mean
and standard deviation
• A new σ should be calculated that includes outlier if
it is < ±4σ
92
REJECTION OF RESULTS
Q – Test
• Used for small data sets
• 90% CL is typically used
• Arrange data in increasing order
• Calculate range = highest value – lowest value
• Calculate gap = |suspected value – nearest value|
• Calculate Q ratio = gap/range
• Reject outlier if Qcal > Qtab
• Q tables are available
93
REJECTION OF RESULTS
Grubbs Test
• Used to determine whether an outlier should be
rejected or retained
• - Calculate mean, standard deviation, and then G
outlier  x
G
s
- Reject outlier if Gcal > Gtab
- G tables are available
94
Performing Experiment
95
PERFORMING THE EXPERIMENT
Detector
• Records the signal (change in the system that is
related to the magnitude of the physical parameter
being measured)
• Can measure physical, chemical or electrical
changes
Transducer (Sensor)
• Detector that converts nonelectrical signals to
electrical signals and vice versa
96
PERFORMING THE EXPERIMENT
Signals and Noise
• A detector makes measurements and detector
response is converted to an electrical signal
• The electrical signal is related to the chemical or
physical property being measured, which is related to
the amount of analyte
• There should be no signal when no analyte is present
• Signals should be smooth but are practically not
smooth due to noise
97
PERFORMING THE EXPERIMENT
Signals and Noise
Noise can originate from
• Power fluctuations
• Radio stations
• Electrical motors
• Building vibrations
• Other instruments nearby
98
PERFORMING THE EXPERIMENT
Signals and Noise
• Signal-to-noise ratio (S/N) is a useful tool for comparing
methods or instruments
• Noise is random and can be treated statistically
• Signal can be defined as the average value of
measurements
• Noise can be defined as the standard deviation
S
x
mean
 
N
s standard deviation
99
PERFORMING THE EXPERIMENT
Types of Noise
1. White Noise
- Two types
Thermal Noise
• Due to random motions of charge carriers (electrons)
which result in voltage fluctuations
Shot Noise
• When charge carriers cross a junction in an electrical
circuit
100
PERFORMING THE EXPERIMENT
Types of Noise
2. Drift (Flicker) Noise (origin is not well understood)
3. Noise due to surroundings (vibrations)
• Signal is enhanced or noise is reduced or both to
increase S/N
• Hardware and software approaches are available
• Another approach is the use of Fourier Transform
(FT) or Fast Fourier Transform (FFT) which
discriminates signals from noise (FT-IR, FT-NMR,
FT-MS)
101
Signals and Noise
• Signal has the information of the analyte
• Noise is the extraneous information in the
information due to electronics, spurious response,
and random events
• Signal to noise ratio
– Noise is generally constant and independent of
the signal
– The impact of noise is greatest on the lowest
signal
• The ratio of signal to noise is useful in evaluating
data
102
Signal to Noise
• Value of the signal to
noise can vary
– Values less than 3
make it hard to
detect signal
S
mean
x


N s tan dard deviation s
Sources of Noise
• Chemical Noise
– Uncontrollable variables affecting
chemistry of system under investigation
• Change in equilibria due to variations
–
–
–
–
Temperature
Pressure
Sample variation
Humidity
104
Signal to Noise Enhancement
• Hardware and software methods
– Hardware is based on instrument design
• Filters, choppers, shields, detectors,
modulators
– Software allows data manipulation
• Grounding and Shielding
– Absorb electromagnetic radiation
• Prevent transmission to the equipment
– Protect circuit with conduction material and
ground
– Important for amplification
105
Hardware
• Difference and Instrumentation Amplifiers
– Subtraction of noise from a circuit
• Controlled by a single resistor
• Second stage subtracts noise
– Used for low level signal
• Analog filtering
– Uses a filter circuit
– Restricts frequency
106
Hardware
• Modulation
– Changes low frequency signal to higher
frequency
• Signal amplified, filter with a high pass filter,
demodulation, low pass filter
• Signal Chopping
– Input signal converted to square wave by
electronic or mechanical chopper
• Square wave normalizes signal
107
Software Methods
• Ensemble Average
– Average of spectra
– Average can also
be sum of collected
spectra
• Boxcar average
– Average of points in
a spectra
108
Software Methods
109
Digital Filtering
• Numerical methods
– Fourier transform
• Time collected data converted to frequency
– NMR, IR
– Least squares smoothing
• Similar to boxcar
– Uses polynomial for fit
– Correlation
110
Signals and Noise
 Signal carries information about the analyte that is of


•
•
•
interest to us.
Noise is made up of extraneous information that is
unwanted because it degrades the accuracy and
precision of an analysis
x
1

Signal-to-Noise Ratio
s
RSD
S/N = (mean)/(Standard deviation) =
Signal-to-noise (S/N) is much more useful figure of merit than
noise alone for describing the quality of an analytical method.
The magnitude of the noise is defined as the standard deviation
s of numerous measurements and signal is given by the mean
x of the measurements.
S/N is the reciprocal of the relative standard deviation. S/N < 2
or 3  impossible to detect a signal.
111
Sources of Noise
Analysis are affected by two types of noise:
1. Chemical noise
2. Instrumental noise
Chemical noise: Arises from an uncontrollable
variables that effect the chemistry of the system being
analyzed. Examples are undetected variations in
temperature, pressure, chemical equilibria, humidity,
light intensity etc.
112
Instrumental Noise: Noise is associated with
each component of an instrument – i.e., with
the source, the input transducer, signal
processing elements and output transducer.
Noise is a complex composite that usually
cannot be fully characterized. Certain kinds of
instrumental noise are recognizable, such as:
1. Thermal or Johnson noise
2. Shot noise
3. Flicker or 1/f noise
4. Environmental noise
113
Instrumental Noise
1. Thermal Noise or Johnson Noise:
Thermal noise is caused by the thermal agitation of
electrons or other charge carriers in resistors,
capacitors, radiation transducers, electrochemical cells
and other resistive elements in an instruments. The
magnitude of thermal noise is given by
 rms = 4kTR f
where, rms = root mean square noise, f = frequency
band width (Hz), k = Boltzmann constant (1.38 x 10-23
J/K), T = temperature in Kelvin, R = resistance in ohms
of the resistive element.
Thermal noise can be decreased by narrowing the
bandwidth, by lowering the electrical resistance and by
lowering the temperature of instrument components.
114
Instrumental Noise
2. Shot Noise: Shot noise is encountered
wherever electrons or other charged particles
cross a junction.
irms = 2Ie f
Where, irms = root-mean-square current
fluctuation,
I = average direct current,
e = charge on the electron (1.60 x 10-19 C),
f = band width of frequencies.
Shot noise in a current measurement can be
minimized only by reducing bandwidth.
115
3. Flicker Noise:
• Flicker noise is characterized as having a
magnitude that is inversely proportional to the
frequency of the signal being observed.
• It is sometimes termed 1/f (one-over-f) noise.
• The cause of flicker noise are not well understood
and is recognizable by its frequency dependence.
• Flicker noise becomes significant at frequency
lower than about 100 Hz.
• Flicker noise can be reduced significantly by using
wire-wound or metallic film resistors rather than
the more common carbon composition type.
116
4. Environmental Noise:
• Environmental noise is a composite of
different forms of noise that arise from
the surroundings.
• Much environmental noise occurs
because each conductor in an
instrument is potentially an antenna
capable of picking up electromagnetic
radiation and converting it to an
electrical signal.
117
•
•
Signal-to-Noise Enhancement:
When the need for sensitivity and accuracy
increased, the signal-to-noise ratio often
becomes the limiting factor in the precision
of a measurement.
Both hardware and software methods are
available for improving the signal-to-noise
ratio of an instrumental method.
118
Hardware method:
• Hardware noise reduction is accomplished by
incorporating into the instrument design components
such as filters, choppers, shields, modulators, and
synchronous detectors.
• These devices remove or attenuate the noise without
affecting the analytical signal significantly.
• Hardware devices and techniques are as follows:
1. Grounding and Shielding:
• Noise that arises from environmentally generated
electromagnetic radiation can be substantially reduce
by shielding, grounding and minimizing the length of
conductors within the instrumental system.
119
2. Analog Filtering:
– By using low-pass and high-pass analog filters S/N
ratio can be improved.
– Thermal, shot and flicker noise can be reduced by
using analog filters.
3. Modulation:
– In this process, low frequency or dc signal from
transducers are often converted to a higher
frequency, where 1/f noise is less troublesome.
– This process is called modulation.
– After amplification the modulated signal can be
freed from amplifier 1/f noise by filtering with a highpass filter, demodulation and filtering with a lowpass filter then produce an amplified dc signal
suitable for output.
120
4. Signal chopping:
• In this device, the input signal is converted to a
square-wave form by an electronic or mechanical
chopper.
• Chopping can be performed either on the physical
quantity to be measured or on the electrical signal
from the transducer.
121
5. Lock-in-Amplifiers:
• Lock-in-amplifiers permit the recovery of signals even
when the S/N is unity or less.
• It requires a reference signal that has the same
frequency and phase as the signal to be amplified.
• A lock-in amplifier is generally relatively free of noise
because only those signals that are locked-in to the
reference signal are amplified.
• All other frequencies are rejected by the system.
122
Software Method:
• Software methods are based upon various computer
algorithms that permit extraction of signals from
noisy data. Hardware convert the signal from analog
to digital form which is then collected by computer
equipped with a data acquisition module.
• Software programs are as follows:
1. Ensemble Averaging:
• In ensemble averaging, successive sets of data stored in
memory as arrays are collected and summed point by point.
• After the collection and summation are complete, the data are
averaged by dividing the sum for each point by the number of
scans performed.
• The signal-to-noise ratio is proportional to the square root of
the number of data collected.
123
124
2. Boxcar Averaging:
• Boxcar averaging is a digital procedure for smoothing
irregularities and enhancing the signal-to-noise ratio.
• It is assumed that the analog analytical signal varies
only slowly with time and the average of a small
number of adjacent points is a better measure of the
signal than any of the individual points.
• In practice 2 to 50 points are averaged to generate a
final point.
• This averaging is performed by a computer in real
time, i.e., as the data is being collected.
• Its utility is limited for complex signals that change
rapidly as a function of time.
125
3. Digital filtering:
•
Digital filtering can be accomplished by number of
different well-characterized numerical procedure such
as (a) Fourier transformation and (b) Least squares
polynomial smoothing.
(a) Fourier transformation:
• In this transformation, a signal which is acquired in the time
domain, is converted to a frequency domain signal in which the
independent variable is frequency rather than time.
• This transformation is accomplished mathematically on a
computer by a very fast and efficient algorithm.
• The frequency domain signal is then multiplied by the frequency
response of a digital low pass filter which remove frequency
components.
• The inverse Fourier transform then recovers the filtered time
domain spectrum.
126
127
(b) Least squares polynomial data smoothing:
• This is very similar to the boxcar averaging.
• In this process first 5 data points are averaged and
plotted.
• Then moved one point to the right and averaged.
• This process is repeated until all of the points except
the last two are averaged to produce a new set of data
points.
• The new curve should be somewhat less noisy than the
original data.
• The signal-to-noise ratio of the data may be enhanced
by increasing the width of the smoothing function or by
smoothing the data multiple times.
128
129
130
Calibration Curves
131
CALIBRATION CURVES
Calibration
• The process of establishing the relationship between
the measured signals and known concentrations of
analyte
• Calibration standards: known concentrations of
analyte
• Calibration standards at different concentrations are
prepared and measured
• Magnitude of signals are plotted against
concentration
• Equation relating signal and concentration is
obtained and can be used to determine the
concentration of unknown analyte after measuring its
signal
132
CALIBRATION CURVES
• Many calibration curves have a linear range with the
• relation equation in the form y = mx + b
• The method of least squares or the spreadsheet may
be used
• m is the slope and b is the vertical (signal) intercept
• The slope is usually the sensitivity of the analytical
method
• R = correlation coefficient (R2 is between 0 and 1)
• Perfect fit of data (direct relation) if R2 is closer to 1
133
BEST STRAIGHT LINE
(METHOD OF LEAST SQUARES)
The equation of a straight line
y = mx + b
m is the slope (y/x)
b is the y-intercept (where the line crosses the y-axis)
134
BEST STRAIGHT LINE
(METHOD OF LEAST SQUARES)
The method of least squares
• finds the best straight line
• adjusts the line to minimize the vertical deviations
Only vertical deviations are adjusted because
• experimental uncertainties in y values > in x values
• calculations for minimizing vertical deviations are easier
135
BEST STRAIGHT LINE
(METHOD OF LEAST SQUARES)
m 
b 
N  x i y i    x i  y i
D
 x  y
2
i
i
  x i y i  x i
D
D  N  x i2    x i 
2
- N is the number of data points
Knowing m and b, the equation of the best straight line
can be determined and the best straight line can be
constructed
136
Calibration of Instrumental Methods
• Analytical methods require calibration
• Process that relates the measured
analytical signal to the concentration of
analyte
• 3 common methods
– Calibration curve
– Standard addition method
– Internal standard method
137
Calibration Curve
• Standards containing known concentrations of the
analyte are introduced into the instrument
• Response is recorded
• Response is corrected for instrument output obtained
with a blank
– Blank contains all of the components of the original sample
except for the analyte
• Resulting data are then plotted to give a graph of
corrected instrument response vs. analyte concentration
• An equation is developed for the calibration curve by a
least-squares technique so that sample concentrations
can be computed directly
138
Standard Addition Method
• Usually involves adding one or more
increments of a standard solution to
sample aliquots of the same size (spiking)
139
Assessing the Data
140
ASSESSING THE DATA
A good analytical method should be
• both accurate and precise
• reliable and robust
• It is not a good practice to extrapolate above the
highest standard or below the lowest standard
• These regions may not be in the linear range
• Dilute higher concentrations and concentrate lower
concentrations of analyte to bring them into the
working range
141
ASSESSING THE DATA
Limit of Detection (LOD)
• The lowest concentration of an analyte that can be
detected
• Increasing concentration of analyte decreases signal due
to noise
• Signal can no longer be distinguished from noise at a
point
• LOD does not necessarily mean concentration can be
measured and quantified
142
ASSESSING THE DATA
Limit of Detection (LOD)
• Can be considered to be the concentration of analyte
that gives a signal that is equal to 2 or 3 times the
standard deviation of the blank
• Concentration at which S/N = 2 at 95% CL or S/N = 3 at
99% CL
LOD  x blank  2σblank or LOD  x blank  3σblank
• 3σ is more common and used by regulatory methods
(e.g. EPA)
143
ASSESSING THE DATA
Limit of Quantification (LOQ)
• The lowest concentration of an analyte in a sample
that can be determined quantitatively with a given
accuracy and precision
• Precision is poor at or near LOD
• LOQ is higher than LOD and has better precision
• LOQ is the concentration equivalent to S/N = 10/1
• LOQ is also defined as 10 x σblank
144
INSTRUMENTAL ANALYSIS
1) Electroanalytical Chemistry
2) Spectrochemical Analysis
3) Chromatographic Separations
145
A Typical Instrument
Analytical
Sample
Signal
Generator
i
Signal
Transducer
V
Output
Signal
Processor
146
Types of Signals
1.
2.
3.
4.
5.
6.
Emission of Radiation
Absorption of Radiation
Scattering of Radiation
Refraction of Radiation
Diffraction of Radiation
Rotation of Radiation
7.
8.
9.
10.
11.
12.
13.
Electrical Potential
Electrical Current
Electrical Resistance
Mass-to-charge Ratio
Reaction Rate
Thermal Properties
Mass
147