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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 Characterizat

ion - 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 Concentratio

n - 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)

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

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) Determina

te (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) Indetermi

nate (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 DISTRIBUTION

- a is the height of the curves peak - µ is

the position of the center of the peak (the

mean) - s 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

T (xt)

f(x)

Point of inflection

µ

-s

s

-2s

-3s

2s

3s

x

SAMPLE MEAN

- 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

?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

µ T in the absence of systematic error

ERROR

Total error sum of all systematic and random

errors Relative error absolute error divided

by the true value

STANDARD DEVIATION

Relative deviation (D) absolute deviation

divided by mean

Percent Relative deviation D()

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

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

Population Standard Deviation (s) - For an

infinite number of measurements

STANDARD DEVIATION

Percent Relative Standard Deviation (RSD)

Variance - Is the square of the standard

deviation - Variance s2 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

for N gt 20

- The standard deviation coincides with the point

of inflection of the curve (2 inflection points

since curve is symmetrical)

QUANTIFYING RANDOM ERROR

Population mean (µ) true value (T or xt)

a

x µ

f(x)

Points of inflection

µ

-s

s

-2s

-3s

2s

3s

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 µ 1s µ 2s µ 3s

Gaussian Distribution () 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 gt 20 - 68.3 of measurements of xi will fall

within x µ s - (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 2s -

99.7 of measurements of xi will fall within x

µ 3s

QUANTIFYING RANDOM ERROR

x µ s

a

68.3 known as the confidence level (CL)

f(x)

µ

-s

s

-2s

-3s

2s

3s

x

QUANTIFYING RANDOM ERROR

x µ 2s

a

95.5 known as the confidence level (CL)

f(x)

µ

-s

s

-2s

-3s

2s

3s

x

QUANTIFYING RANDOM ERROR

x µ 3s

a

99.7 known as the confidence level (CL)

f(x)

µ

-s

s

-2s

-3s

2s

3s

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 zs

CONFIDENCE LIMITS

µ x zs If z 1 we are 68.3 confident that

x lies within s of the true value If z 2 we

are 95.5 confident that x lies within 2s of the

true value If z 3 we are 99.7 confident that

x lies within 3s of the true value

CONFIDENCE LIMITS

- For N measurements CL for µ is

- s is not a good estimate of s since

insufficient replicates are made - The students

t-test is used to express CL - The t-test is

also used to compare results from different

experiments

CONFIDENCE LIMITS

- That is, the range of confidence interval is

ts/vn below the mean and ts/vn 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 gt ttab at 95 CL)

CONFIDENCE LIMITS

For two sets of data with - N1 and N2

measurements - standard deviations of s1 and s2

Degrees of freedom N1 N2 - 2

CONFIDENCE LIMITS

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 gt 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 (s12 and s22) are

compared F-function the ratio of the variances

of the two sets of numbers

F-TEST

- Ratio should be greater than 1 (i. e. s12 gt

s22) - F values are found in tables (make use of

two degrees of freedom) - Table 1.10 on page 39

of text book Fcal gt 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 gt 4s from the

mean - The outlier is not included in

calculating the mean and standard deviation - A

new s should be calculated that includes outlier

if it is lt 4s

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 gt 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

- Reject outlier if Gcal gt 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

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 gt in x values - calculations for

minimizing vertical deviations are easier

BEST STRAIGHT LINE (METHOD OF LEAST SQUARES)

- 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)

xiyi ?(xiyi)

xi2 ?xi2

xi ?xi

yi ?yi

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

- 3s 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

sblank

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