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