INSTRUMENTAL ANALYSIS CHEM 4811 CHAPTER 1 DR. AUGUSTINE OFORI AGYEMAN Assistant professor of...
-
Upload
edmund-dennis-harvey -
Category
Documents
-
view
236 -
download
1
Transcript of INSTRUMENTAL ANALYSIS CHEM 4811 CHAPTER 1 DR. AUGUSTINE OFORI AGYEMAN Assistant professor of...
INSTRUMENTAL ANALYSIS CHEM 4811
CHAPTER 1
DR. AUGUSTINE OFORI AGYEMANAssistant professor of chemistryDepartment 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)
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
CHATACTERIZATION
WET CHEMICAL ANALYSIS
Volumetric Analysis- Analysis by volume
Gravimetric Analysis- Analysis by mass
- Wet analysis is time consuming and demands attention to detail
ExamplesAcid-base titrations, redox titrations, complexometric titrations,
precipitation reactions
Nondestructive Analysis- Useful when evidence needs to be preserved
- Used to analyze samples without destroying them
ExamplesForensic analysis
Paintings
WET CHEMICAL ANALYSIS
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
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
INSTRUMENTAL ANALYSIS
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 theanalytical approach
uses, capabilities, and limitations of analytical techniques
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
THE ANALYTICAL APPROACH
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
- 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 GCLC
HPLCCE
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 sampleppb = 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)
DEFINING THE PROBLEM
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)
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 sampleMatrix 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)
DESIGNING THE ANALYTICAL METHOD
- 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 acidand 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
SAMPLING
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
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
- 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 finelypowdered salt at high temperatures until mixture melts
- Useful for the determination of silica-containing minerals, glass, ceramics, bones, carbides
Salts (Fluxes) Usually UsedSodium 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 SolventsHexane, 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)
2
1D A
AtcoefficienondistributiK
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
100%x
VAVA
VA%E
2211
11
12D
D
/VVK
100K%E
SAMPLE PREPARATION METHODS
Solvent Extraction
- Multiple small extractions are more efficient than one large extraction
- Extraction instruments are also available
ExamplesExtraction 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)
SAMPLE PREPARATION METHODS
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
- 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
ERRORS
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
2
2
2
)(x
aef(x) is function Gaussian The
2πσ
1a
- 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
THE GAUSSIAN DISTRIBUTIONf(
x)
a
μx
-σ σ-2σ-3σ 2σ 3σ
f(x) = frequency of occurrence of a particular results
T (xt)
Point of inflection
- 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
N321
N
1ii_
x.....xxxN
1
N
xx
∑xi = sum of all individual measurements xi
xi = a measured valueN = number of observations
SAMPLE MEAN )x(
- The limit as N approaches infinity of the sample mean
µ = T in the absence of systematic error
N
1i
i
N
x
N
limμ
POPULATION MEAN (µ)
Total error = sum of all systematic and random errors
Relative error = absolute error divided by the true value
ERROR
T
EE abs
rel 100%xT
E%E abs
rel
xorxeither and T between difference the (E)Error i
TxEorTx E i
TxEorTx E
Eof valueAbsolute error Absolute
iabs
Relative deviation (D) = absolute deviation divided by mean
STANDARD DEVIATION
_i
x
dD
100%xD100%xx
dD(%) _
i
Percent Relative deviation [D(%)]
xx)(ddeviationAbsolute ii
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
xi = a measured valueN = number of observationsN-1 = degrees of freedom
1N
xx
1N
ds
2N
1ii
N
1i
2i
STANDARD DEVIATION
Population Standard Deviation (σ)- For an infinite number of measurements
N
μx
N
limσ
2N
1ii
Standard Deviation of the mean (sm)- Standard deviation associated with the mean
consisting of N measurements
N
ssm
STANDARD DEVIATION
100xx
s%RSD _
Percent Relative Standard Deviation (%RSD)
STANDARD DEVIATION
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
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
zeroapproachesμxincreasesNAs
for N > 20μx
- The standard deviation coincides with the point of inflection of the curve (2 inflection points since curve is symmetrical)
μxerrorRandom
QUANTIFYING RANDOM ERROR
f(x)
a
μx
-σ σ-2σ-3σ 2σ 3σ
Population mean (µ) = true value (T or xt)
x = µ
Points of inflection
QUANTIFYING RANDOM ERROR
Range
µ ± 1σµ ± 2σ µ ± 3σ
Gaussian Distribution (%)
68.395.599.7
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)
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
f(x)
a
μx
-σ σ-2σ-3σ 2σ 3σ
68.3%known as the confidence level
(CL)
x = µ ± σ
QUANTIFYING RANDOM ERROR
f(x)
a
μx
-σ σ-2σ-3σ 2σ 3σ
95.5%known as the confidence level
(CL)
x = µ ± 2σ
QUANTIFYING RANDOM ERROR
f(x)
a
μx
-σ σ-2σ-3σ 2σ 3σ
99.7%known as the confidence level
(CL)
x = µ ± 3σ
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
QUANTIFYING RANDOM ERROR
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
µ = x ± zσ
If z = 1we are 68.3% confident that x lies within ±σ of the true value
If z = 2we are 95.5% confident that x lies within ±2σ of the true value
If z = 3we are 99.7% confident that x lies within ±3σ of the true value
CONFIDENCE LIMITS
- 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
s
μxt
mzsxμ
- For N measurements CL for µ is
CONFIDENCE LIMITS
N
tsxμ_
- 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
- standard deviations of s1 and s2
2NN
1Ns1Nss
21
2221
21
pooled
21
21
pooled
21
NN
NN
st
xx
Degrees of freedom = N1 + N2 - 2
CONFIDENCE LIMITS
21 xandxofaverages
Using the t-test to Test for Systematic Error
- 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
s
Nμxt
CONFIDENCE LIMITS
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 σ2
2) are compared
F-function = the ratio of the variances of the two sets of numbers
22
21
σ
σF
- Ratio should be greater than 1 (i. e. σ12 > σ2
2)
- 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 valueFtab = tabulated F value
F-TEST
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
Grubbs Test
- Used to determine whether an outlier should be rejected or retained
- Calculate mean, standard deviation, and then G
s
xoutlierG
REJECTION OF RESULTS
- 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
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
deviationstandard
mean
s
x
N
S
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)
PERFORMING THE EXPERIMENT
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 areprepared 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
- 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
CALIBRATION CURVES
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)
D
yxyxNm iiii
D
xyxyxb iiii
2i
2i2i xxND
- N is the number of data points
Knowing m and b, the equation of the best straight line canbe determined and the best straight line can be constructed
BEST STRAIGHT LINE(METHOD OF LEAST SQUARES)
xi
∑xi =
yi
∑yi =
xiyi
∑(xiyi) =
xi2
∑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
blankblankblankblank 3σxLODor2σxLOD
- 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