This course is concerned with instrumental methods of analysis

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Chapter 1

• This course is concerned with instrumental
  methods of analysis
• These methods use various chemical and physical
  properties of analytes that can be measured
  instrumentally to determine qualitative (what is
  there) and quantitative (how much is there)
  information about these analytes

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first 6 are spectroscopic-involve interaction of
light and matter next 4 are electrochemical-measur
ement of voltage, current, or resistance mass
spectrometry several other types
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• Chromatography and electrophoresis are considered
  instrumental techniques because they use many of
  the techniques mentioned above in separating
  (electrophoresis) and detecting (both) analytes
  after separation
• As can be seen from topics list and laboratory
  schedule, we will cover many of the spectroscopic
  techniques, some electrochemistry,
  chromatography, and mass spectrometry

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Course Objectives

• basic theory behind each technique
• instrument design and components
• types of analytes than can be analyzed by a
  particular technique
• qualitative and/or quantitative uses of a
  technique
• limitations of each technique, including
• precision - agreement among repeat measurements
• accuracy - agreement of measurements with true
  value
• comparisons of techniques so intelligent choices
  can be made between them

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General instrument examples
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transducer changes signal from nonelectrical to
electrical domains (and vice versa) detector is
the more general term, i.e. all transducers are
detectors but not all detectors are transducers
signal processing include amplification,
attenuation (decreasing signal), filtering,
integration, differentiation, etc. No matter
what type of instrument or method, quantitative
analyses require some sort of calibration curve
in which signal (A, V, i, conductivity, emission,
etc.) is plotted on y axis against known
concentrations of analyte on x axis
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• errors, absolute and relative, must also be
  considered
• determinate errors - in principle can be
  accounted for, always high or always low (method,
  operator, instrument)
• indeterminate - random and uncontrollable
• Random means error will be high and low ()
• Are preferred type of error because
• they can be treated statistically
• means analyst is getting the most out of the
  instruments and methods

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Precision

• precision agreement among repeat measurements
  absolute error is the standard deviation of the
  determination.
• It determines number of significant digits in
  result.
• example report the following number and its
  standard deviation to the correct number of
  significant figures
• 45.6879 0.07895 mM

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Precision

• relative error in precision coefficient of
  variation (CV)
• (absolute error/value) x 100
• Why important?
• compare relative errors in the following
• 3.495 0.034 and 10.678 0.034

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Accuracy

• accuracy absolute error is difference between
  determined value and true value
• relative error in accuracy (actual value
  true value)/ true value x 100
• ex. determine absolute and relative errors in
  accuracy between determined value 4.58 mM and its
  accepted value of 4.62 mM

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Method Selection
To select a method one must 1. define problem
(section 1E-1) 2. determine other performance
criteria (table 1-4)
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• 1. What accuracy and precision are required?
• 2. How much sample is available?
• ex. at least 5 mL needed for a flame AA
  measurement
• 3. What is the concentration range of the
  analyte?
• ex. ppm flame AA, ppb graphite furnace AA
• 4. What sample components will cause
  interference?
• ex. PO43- in AA analysis of calcium
• 5. What are chemical and physical properties of
  sample matrix?
• 6. How many samples are to be analyzed?

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Matrix
rigorous definition of matrix all constituents
of a sample including analyte (other
constituents are called concomitants) if
analyte concentration is very low (so it does
not measurably affect other constituents) then
matrix is often defined as everything else in
sample except analyte(s)
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Table 1-4 (modified)
Speed Ease and convenience Skill required of
operator Cost of instrumentation (to buy and
use) Availability of instrumentation Per-sample
cost
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Accuracy Determination
Also must consider ways of determining
accuracy and other performance characteristics
in table 1-3 (p.11)
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Accuracy Determination

• Accuracy determined in one of three ways
• analysis of standard reference material
• intermethod comparison
• spike recovery

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analysis of standard reference material

• reference material containing analyte in matrix
  essentially identical to that of unknown sample
  is analyzed.
• If stated amount of analyte in reference
  standard is obtained within experimental error,
  method is accurate

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intermethod comparison

• Identical samples are analyzed by method in
  question and a method known to be accurate and
  independent of method being tested.
• Results are then plotted against each other.
• If slope of graph is equal to one (within
  experimental error) then method is accurate.
• This can be used for unstable analytes.

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spike recovery

• Known amount of the analyte is added to a known
  amount of sample and analyzed.
• If 100 of this spike is recovered (within
  experimental error) then method is considered
  accurate.
• Is not recommended for unstable analytes.

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This s is for multiple measurements of same number
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This is not the way s is calculated when
concentration is determined from a calibration
curve. We will discuss this when calibration
curves are covered below.
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Sensitivity

• ability to discriminate between small differences
  in analyte concentration.
• Limited by two factors
• 1) slope of calibration curve
• 2) precision of method

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signal
concentration
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calibration sensitivity

• slope of calibration curve S mc Sbl
• independent of concentration
• does not take precision into account

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analytical sensitivity (g)

• g m/sS
• 1) relatively insensitive to amplification
• 2) independent of measurement units

often concentration dependent because sS often
varies with concentration

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Detection Limit (LOD)

• minimum concentration or mass that can be
  detected at a known confidence level
• depends primarily on ratio of analytical signal
  size to size of standard deviation of blank
  signal
• also is a function of slope of calibration curve

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Detection Limit

• Sm Sbl ksbl
• Sm Minimum Signal
• Sbl mean blank signal measured 20 to 30 times
  over extended period of time
• sbl standard deviation of blank k 3

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Detection Limit

• use m from calibration curve of analyte
• S mc Sbl
• to convert Sm to cm (note that Sbl and Sbl
  are different)
• cm (Sm - Sbl )/m
• (Sbl ksbl - Sbl) / m
• 3sbl/ m

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Detection Limit

• use m from calibration curve of analyte
• S mc Sbl
• to convert Sm to cm (note that Sbl and Sbl
  are different)
• cm (Sm - Sbl )/m
• (Sbl ksbl - Sbl) / m
• 3sbl/ m

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Detection Limit

• use m from calibration curve of analyte
• S mc Sbl
• to convert Sm to cm (note that Sbl and Sbl
  are different)
• cm (Sm - Sbl )/m
• (Sbl ksbl - Sbl) / m
• 3sbl/ m LOD

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Detection Limit example

• A method requires reaction of sample with
  enzyme and then DNPH reagent. 20 blanks were
  analyzed with one batch of enzyme. Another 20
  blanks were analyzed with another batch of enzyme
  one month later. Standard deviations of sets were
  same so results pooled to determine Sbl, sbl, Sm,
  and (with slope of calibration curve) LOD
• Sbl 24.5 mAUs sbl 0.534 mAUs m
  52.9 mAUs/mM

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Concentration range

• Dynamic range range from lowest concentration
  at which quantitative measurements can be made
  (LOQ) to point where curve begins to deviate from
  linearity (LOL)

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Figure 1-7
10sbl
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Bias

• measure of determinate error in method
• Bias m xt
• where m is population mean of analyte
  concentration in a standard reference sample
  (usually determined from minimum of 20
  measurements) and xt is true value.

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Selectivity

• degree to which method is free from interference
  by other species in matrix
• interference can add to or subtract from signal.
  
• ex. ion selective electrodes

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Calibration Curves

• All instrumental methods (except gravimetry
• and coulometry) require calibration curve to
• relate measured signal to concentration
• (amount) of analyte

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• Titrations do not require calibration curves They
  are not mentioned in your text because when used
  to determine amounts or concentrations,
  titrations can be done without instrumentation
  (just burette, flask, and indicator needed)

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Calibration Curves

• Calibration curve which is usually linear.
• Why?
• vs
• Ease of error analysis
• Constant sensitivity
• Fewer data points needed

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Calibration Curves

• Three types of calibration curves
• External standard
• Standard Addition
• Internal Standard

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External standard

• constructed by measuring signals of several known
  concentrations of analyte and then plotting
  signal vs. concentration
• known analyte solutions must have a similar
  matrix to that of sample
• signal magnitude should not be a function of
  small sample volumes that may be difficult to
  reproduce Ex. GC
• this procedure works well for simple matrices
• error in result (concentration of unknown) is
  determined by equation from appendix 1

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External Standard

• Calibration curve prepared from known
  concentrations
• Unknown solution measured

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Concentration of unknown 1.71 ppm
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Standard Addition

• known amounts of analyte are added directly to
  sample to try to account for matrix effects
• two main types of standard addition use either a
  constant total volume or a changing total volume.

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Standard Addition Constant Total V

• Analysis Conditions
• constant total volume
• constant volume of unknown analyte
• varying volume of added analyte of known
  concentration to each sample
• linear response of instrument to concentration y
  mx b

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Standard Addition Constant Total V

• S signal k proportionality constant
• Vs volume of standard cs concentration of
  standard
• Vt total volume
• Vx volume of unknown cx unknown
  concentration

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Standard Addition Constant Total V

• all variables are constants except S and Vs
  therefore this is a straight line equation where
  
• m and b

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Standard Addition Constant Total V

• Plot S vs Vs for several different Vs
• Determine m and b
• find cx using ratio of b to m
• After rearranging -

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Standard Addition Example
Six samples. Each contains 5.00 mL of unknown
copper solution, x mL of added 50.0 ppm copper
solution, and each sample is diluted to a final
volume of 10.00 mL.
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2.000 ppm
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Concentration of unknown 1.71 ppm
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Standard addition vs external standard

• How to determine if standard addition is needed?
• Have to do analysis both ways and see if external
  standard analysis gives numbers that are always
  too high or too low

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Standard addition vs external standard

• Why isnt standard addition always used instead
  of external calibration?
• Compare time involved for the preceding example
  which was an AA analysis

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Standard addition vs external standard

• External standard calibration curve analysis
• One calibration curve (usually 4 to 6 points)
• Single measurement for each sample
• Standard Addition analysis
• At least two measurements for each sample
• Based on above information after 4 to 6 samples
  external standard analysis is faster

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Standard addition vs external standard

• External standard is more efficient if many
  samples and fast analysis time for each sample
• Standard addition only used under these
  conditions if external standards do not give
  correct answers

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Standard addition vs external standard

• Voltammetric analyses almost always use standard
  addition because
• each measurement that requires emptying and
  refilling cell takes several minutes
• Addition of known to solution that has already
  been deoxygenated allows for quick measurement
• Electrode surface is very sensitive to changes in
  solutions

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Two point standard addition, constant total V

• Can be done with only two points using the
  unknown and one addition to sample
• Unknown concentration is determined from
• where S1 is signal of diluted unknown and S2 is
  signal of diluted unknown plus standard

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Two point standard addition, changing total V

• Signal from known V of unknown concentration is
  measured (S1)
• Signal after known V of standard added to this
  unknown sample (S2)
• Unknown concentration determined from

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Internal Standard

• Corrects for random instrumental and method
  fluctuations
• Ex. Methods in which signal depends on the sample
  volume used such as GC
• Methods in which T variations can affect signal
  such as Atomic Emission (AE) spectroscopy

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Internal Standard

• A constant known amount of a substance that is
  similar to, but not the same as, analyte is added
  to all standards and unknown samples
• Signals for calibration curve generated from
  ratio of analyte signal to internal standard
  signal
• Ratio of unknown analyte signal to internal
  standard signal is used to determine analyte
  concentration from calibration curve.

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Internal Standard Example

• GC-MS analysis of octane using nonane as internal
  standard
• 5 octane standards from 1.00 to 10.00 mg/mL each
  containing 3.00 mg/mL nonane
• Octane analyte containing 3.00 mg/mL nonane

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Internal standard example data
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Octane concentration 1.81 mg/mL
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Octane concentration 2.04 mg/mL
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Error analysis for these methods

• How to find error in concentration of an unknown
  determined by external standard calibration
  curve?
• Review least squares
• y mx b
• Simple least squares assumes a constant error in
  y value (measurement signal) and no error in x
  axis values (concentration)

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• Residual is vertical deviation of each data point
  from line
• Line generated by least squares minimizes sum of
  the squares of residuals for all points

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Least Squares Equations

• To determine slope, intercept, and errors these
  three quantities are very useful

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• sr standard deviation about regression
  (standard error of the estimate)
• N number of points in calibration curve

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• sc standard deviation in results
  (concentrations) from curve
• M number of replicate analyses of an unknown
• N number of points in calibration curve
• mean of signals from analysis of
  unknown
• mean value of y signals used in
  calibration curve

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External Standard

• Calibration curve prepared from known
  concentrations
• Unknown solution measured

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Concentration of unknown 1.71 ppm
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Excel version
Block out 2x5 matrix of cells linest(ys,xs,true
,true) hold down control and shift buttons and
then hit enter
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Error Analysis for standard addition

• Review propagation of error for random errors

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Error Analysis for standard addition
cx is not determined by reading signal from
straight line
unknown signals are actually part of calibration
curve
determine sx in cx by assuming no error in cs or
Vx and that all error comes from b and m
Use propagation of error equation from Table a1-6
to come up with
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Excel version
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Internal standard example data
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Octane concentration 1.81 mg/mL
Error analysis
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Octane concentration 2.04 mg/mL
error analysis