Transcript analytical chemistry chem 3811

INSTRUMENTAL ANALYSIS
CHEM 4811
CHAPTER 1
DR. AUGUSTINE OFORI AGYEMAN
Assistant professor of chemistry
Department of natural sciences
Clayton state university
CHAPTER 1
FUNDAMENTAL CONCEPTS
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
- The identification of chemical compounds or elements present
in a sample (qualitative)
- The determination of the amount of compound or element present
in a sample (quantitative)
CHATACTERIZATION
Qualitative Analysis
- The identification of one or more chemical species present
in a sample
Quantitative Analysis
- The determination of the exact amount of a chemical species
present in a sample
Chemical Species
- Could be an element, ion or compound (organic or inorgnic)
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
WET CHEMICAL ANALYSIS
Volumetric Analysis
- Analysis by volume
Gravimetric Analysis
- Analysis by mass
- Wet analysis is time consuming and demands attention to detail
Examples
Acid-base titrations, redox titrations, complexometric titrations,
precipitation reactions
WET CHEMICAL ANALYSIS
Nondestructive Analysis
- Useful when evidence needs to be preserved
- Used to analyze samples without destroying them
Examples
Forensic analysis
Paintings
INSTRUMENTAL ANALYSIS
- Use of automated instruments in place of volumetric methods
- Carried out by specially designed instruments which are
controlled by computers
- Samples are characterized by the interaction of electromagnetic
radiation and matter
- All the analytical steps (from sample preparation through
data processing) are automated
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
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
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
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
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
THE ANALYTICAL APPROACH
General Steps in Chemical Analysis
1. Formulating the question or defining the problem
- To be answered through chemical measurements
2. Designing the analytical method (selecting techniques)
- 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
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
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
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
DEFINING THE PROBLEM
Qualitative Analysis
- Provides information about what is present in the sample
- If quantitative analysis is required, qualitative analysis
is usually done first
- Capabilities and limitations of analysis must be
well understood
DEFINING THE PROBLEM
Qualitative Analysis
Qualitative Elemental Analysis
- Used to identify elements present in a material
- Can provide empirical formula of organic compounds
(X-Ray 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)
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
(n-butane and iso-butane)
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)
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
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)]
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)
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)
DESIGNING THE ANALYTICAL METHOD
Green chemistry processes preferred for modern
analytical procedures
- 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)
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
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
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
DESIGNING THE ANALYTICAL METHOD
Fundamental Features of Method
- Reference (check) standards are required
- Standards of known composition with known
concentration of analyte
- 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)
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
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
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
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
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)
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
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
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
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
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
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
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.
SAMPLE PREPARATION METHODS
- Specific methods are discussed in later chapters
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
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
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
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
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
 distributi on coefficien t 
A2
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 
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, petroluem hydrocarbons from water
- fat from milk
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)
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
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)
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.
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)
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)
- additive or multiplicative
ERRORS
- Two principal types of errors
- Determinate (systematic) and indeterminate (random)
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 instrument (voltage fluctuations, alignment, etc)
- Contaminated or impure or decomposed reagents
- Interferences
ERRORS
- Two principal types of errors
- Determinate (systematic) and indeterminate (random)
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)
ERRORS
- Two principal types of errors
- Determinate (systematic) and indeterminate (random)
Indeterminate (Random) Errors
- Sources cannot be identified, avoided, or corrected
- Not constant (biased)
Examples
- Limitations of reading mass balances
- Electrical noise in instruments
ERRORS
- Random errors are always associated with measurements
- 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 distribution and analyzed
using laws of probability
- Statistics deals with only random errors
- Systematic errors should be detected and eliminated
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
1
σ 2π

(x   )2
2 2
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
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
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
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
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
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
x 100%  D x 100%
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
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
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
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
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 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
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
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
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
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
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
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 under same operating conditions
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
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
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
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
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
- Refer to table 1.9 on page 37 for t-test values
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)
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
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
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
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)
- Table 1.10 on page 39 of text book
Fcal > Ftab implies there is a significant difference between
the two methods
Fcal = calculated F value
Ftab = tabulated F value
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
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
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
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
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
PERFORMING THE EXPERIMENT
Signals and Noise
Noise can originate from
- Power fluctuations
- Radio stations
- Electrical motors
- Building vibrations
- Other instruments nearby
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
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
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)
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
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
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)
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
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
BEST STRAIGHT LINE
(METHOD OF LEAST SQUARES)
xi
yi
xiyi
xi2
∑xi =
∑yi =
∑(xiyi) =
∑xi2 =
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
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
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)
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