Choice of method
The General Analytical Problem
1. Accuracy: the best method is not always the most accurate
•
frequently, we do not know what the "right" answer is, so we can't actually know
this
Select sample
Extract analyte(s) from matrix
2. Precision
• in most cases, we rely on precision as our guide
3. Sensitivity
• related to the detection limit, or Minimum Detectable Quantity (MDQ)
Separate analytes
4. Selectivity
is the method subject to interferences from other species besides the analyte?
5. Speed
• faster is always better (equipment time, analysts time, etc. - how many samples
can be analyzed per day?)
6. Cost and Legal acceptance
Detect, identify and
quantify analytes
Determine reliability and
significance of results
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Mean
Errors in Chemical Analysis
N
Defined as follows:
∑ xi
x =
i=1
N
Where xi = individual values of x and N = number of replicate
measurements
Impossible to eliminate errors.
How reliable are our data?
Data of unknown quality are useless!
Median
•Carry out replicate measurements
•Analyse accurately known standards
•Perform statistical tests on data
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The middle result when data are arranged in order of size (for even
numbers the mean of middle two). Median can be preferred when
there is an “outlier” - one reading very different from rest. Median
less affected by outlier than is mean.
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Illustration of “Mean” and “Median”
Precision
Results of 6 determinations of the Fe(III) content of a solution, known to
contain 20 ppm:
Relates to reproducibility of results..
How similar are values obtained in exactly the same way?
Useful for measuring this:
Deviation from the mean:
modulus
d i = xi − x
Note: The mean value is 19.78 ppm (i.e. 19.8ppm) - the median value is 19.7 ppm
individual value
mean value
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Illustrating the difference between
“accuracy” and “precision”
Accuracy
Measurement of agreement between experimental mean and
true value (which may not be known!).
Measures of accuracy:
Low accuracy, low precision
Low accuracy, high precision
High accuracy, low precision
High accuracy, high precision
Absolute error: E = xi - xt (where xt = true or accepted value)
Relative error:
x −x
t × 100%
E = i
r
x
t
(latter is more useful in practice)
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Types of Error in Experimental Data
Three types:
(1) Random (indeterminate) Error
Data scattered approx. symmetrically about a mean value.
Affects precision - dealt with statistically (see later).
(2) Systematic (determinate) Error
Several possible sources - later. Readings all too high
or too low. Affects accuracy.
(3) Gross Errors
Usually obvious - give “outlier” readings.
Detectable by carrying out sufficient replicate
measurements.
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Systematic errors can be
constant (e.g. error in burette reading less important for larger values of reading) or
proportional (e.g. presence of given proportion of
interfering impurity in sample; equally significant
for all values of measurement)
Error Sources of Systematic
1. Instrument Error
Need frequent calibration - both for apparatus such as
volumetric flasks, burettes etc., but also for electronic
devices such as spectrometers.
2. Method Error
Due to inadequacies in physical or chemical behaviour
of reagents or reactions (e.g. slow or incomplete reactions)
3. Personal Error
e.g. insensitivity to colour changes; tendency to estimate
scale readings to improve precision; preconceived idea of
“true” value.
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Principles of Separation Science
SEPARATION
of what may be a large number of components
Minimise instrument errors by careful recalibration and good
maintenance of equipment.
Minimise personal errors by care and self-discipline
Method errors - most difficult. “True” value may not be known.
Three approaches to minimise:
• analysis of certified standards
• use 2 or more independent methods
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• analysis of blanks
IDENTIFICATION
of these components (often called SPECIATION)
QUANTITATIVE MEASUREMENT
of the amount of each of them
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3
General Classification
Chromatography
Most general and common
separation technique
Liquid chromatography
(LC). Mobile phase: liquid
Specific Method
Liquid/liquid
Liquid/bonded phase
Discovered 1905 - Mikhail Tswett - Russian botanist
Liquid/solid
Stationary Phase Type of
Equilibrium
Liquid adsorbed
on solid
Partition
(immiscible liquids)
Organic species
Partition (liquid/
bonded to solid surface bonded surface)
Solid
Adsorption
Developed 1940’s-50’s - Martin and Synge (U.K.)
General Principle:Gas chromatography
(GC). Mobile phase : gas
Sample contained in a mobile phase, which is carried
through or over a stationary phase. The components of
the mixture are partitioned between the phases.
Separation because of differing affinities of components
for the stationary phase.
Some components stay longer in the stationary phase - and hence move more slowly.
Size exclusion
Liquid in polymeric
solid
Partition/sieving
Ion exchange
Ion-exchange resin
Ion exchange
Gas/liquid
Liquid adsorbed
on solid
Partition
(gas/liquid)
Gas/solid
Supercritical fluid
chromatography
Mobile phase: SF
Solid
Organic species
bonded to solid
surface
Adsorption
Partition
(supercritical fluid/
bonded surface)
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Column Chromatography
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TLC Thin Layer Chromatography
UV detection of spots
Coloured spots
For qualitative determination of reaction, and used in conjunction with column
chromatography for identification of fractions
Routinely used in synthetic labs for cleaning up reaction products
Solid phase: silica
Mobile phase: organic solvent
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Some useful terms:
A typical column chromatographic experiment
Mixture of A and B at top of column.
Carried down by mobile phase
Process of flushing mixture down the column = ELUTION
Mobile phase described as
ELUENT
Material leaving column is
ELUATE
Affinity for stationary phase: B > A
Detector at end of column records
nothing until time t3, when A emerges,
and t4, when B emerges.
Plot of detector response versus time
is called a CHROMATOGRAM
Plot is called a chromatogram.
Peak positions used to identify
components; peak areas to determine
amounts of each analyte.
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BAND BROADENING AND RESOLUTION
This shows two ways of
improving resolution (b) increased separation or
(c) decreased band width.
Details later on influencing
band widths.
This shows the concentration profiles of A and B at times
t1 and t3 in the column separation shown earlier.
Note: If there was always an equilibrium distribution between
mobile and stationary phases, there would be much less
band broadening - but this would take excessively long times.
Separation increases with time, but so do peak widths.
Simply increasing column length does not necessarily
give better separation (resolution).
Usually competition between speed and resolution.
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5
Retention Time
Gas Chromatography (GC)
Non-retained species: time to pass
down column = tM (dead time - time
for mobile phase to pass down column)
Time for analyte to pass down
column = tR = RETENTION TIME
Average linear velocity of mobile phase:
u=
L
Mobile phase - carrier gas + vapour of analyte
Stationary phase - (usually) involatile liquid on inert solid support
Carrier gas - must be inert to analytes and stationary phase - usually He, H2, N2 or CO2
tM
Types of column - Capillary (or “open tubular”) - fused silica tube (i.d. ~0.3 mm), with
inside wall coated with stationary phase. Length of column 10 - 100 m. High
resolution, but slow, and can only inject small samples on to column.
Packed - shorter (~1 m), wider (i.d.. 2 - 5 mm), with stationary phase
supported on small particles (~0.1 - 0.2 mm in diameter). Less resolving power
but quicker, and can cope with larger samples.
(where L = length of column packing)
Average linear velocity of analyte molecules:
Usually gas-liquid chromatography (GLC) - but shorter abbreviation preferred
ν =
L
tR
From these we can deduce the relationship between
migration rate and partition ratio
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Schematic diagram of a gas chromatograph
Stationary Phases
Must have:
(1) low volatility
(2) thermal stability
(4) chemical inertness
(5) solvation properties giving suitable values for resolution of components
Commonest are polysiloxanes:
R
R3Si
O
Si O
n
SiR3
R
Nature of R varied to give different polarities.
e.g. All R = Me : non-polar column. Best for non-polar analytes (hydrocarbons, PAH’s etc.)
or R = 50% Me, 50% cyanopropyl - increased polarity - best for alcohols, acids etc.
Greater polarity from polyethylene glycols:
HO C C
H2 H2
Detectors
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O C C
H2 H2
will discuss these later (and applications of GC in real
analytical problems).
n
OH
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6
General Elution Problem in GC
Choice of stationary phase
• In general, polarity of stationary phase should match
(a) - low temperature (450C) - good resolution
initially - but too slow later.
that of sample components.
• In this case, order of elution is determined by boiling
points of eluents.
(b) - higher temperature (145oC) - much faster
but poor resolution for early-eluting species.
In general - best results for temperatures near
boiling point of analyte.
General polarity series: aliphatic hydrocarbons < olefins <
aromatic hydrocarbons < halides < sulphides < ethers < nitro
cpds. < esters / aldehydes / ketones < alcholols / amines <
sulphones < sulphoxides < amides < carboxylic acids < water
If there is a wide range of boiling points in the
sample - then the best results \re obtained by
temperature programming as shown in (c),
for the same mixture, where the temperature
steps are as shown.
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Liquid Chromatography (LC)
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Schematic HPLC Apparatus
Especially high-performance liquid chromatography (HPLC).
The term “high-performance” refers to the
use of packed columns with very small
packing particles (diam. 5-10 µm) giving greatly enhance resolution.
Note: several types of LC. In
addition to partition (as described
so far) - there are also ionexchange and size-exclusion
chromatography using liquid
mobile phases. We will concentrate
only on partition.
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Rather complicated! High pressures needed to push mobile phase through finelypacked column. “Sparging” = sweeping dissolved gases out of mobile phase using a
stream of inert gas.
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HPLC resources
http://kerouac.pharm.uky.edu/ASRG/HPLC/hplcmytry.html
Simple HPLC uses mobile phase of constant composition isocratic elution.
For more complex mixtures - programme a changing (stepwise or continuous)
mobile phase composition during the run - gradient elution. In HPLC this is
the usual solution to the general elution problem (solved in GC by temperature
programming
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Pumps
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Columns
Needed because HPLC performed at high pressure.
Usually stainless steel (to withstand pressure), 1 - 5 mm diameter, ~5 µm packing.
Ideally need a steady flow - achieved using syringe pump. This has limited capacity.
Very efficient but limited length (cf. GC) because of pressure drop.
Packing - usually silica
Often need a reciprocating pump:
Stationary phase - could be involatile liquid (like those in packed-column GC).
More usual now to use similar chemical species actually bonded to the silica
(longer column life), e.g.
Unlimited capacity but pulsed flow. Therefore
need to include a ballast
volume (pulse damper) to
even this out.
Me
Si O
Si R
R can be non-polar (C8 or C18
hydrocarbon chain) or polar (amine,
nitrile etc.).
Me
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Detectors
Stationary phase polar, mobile phase non-polar
= NORMAL PHASE CHROMATOGRAPHY.
In both GC, HPLC – great effort to separate analytes.
When the separated analytes leave the column, we need to detect them.
Stationary phase non-polar, mobile phase polar
= REVERSED PHASE CHROMATOGRAPHY.
What are the criteria for an ideal detector?
It should be:
UNIVERSAL (i.e. detects everything)
In normal phase, least polar analyte elutes first.
SENSITIVE (i.e. detects a very small amount of everything)
It should have a LINEAR RESPONSE (i.e. linear relationship between
intensity of response and amount of analyte).
In reversed phase, most polar analyte elutes first.
It should give STRUCTURAL INFORMATION (i.e. tell you what the
analyte is, even if you didn’t know beforehand).
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Selective Detectors
Very many possibilities - some of the more common:-
Spectroscopic methods used particularly
where structural information is important.
- thermionic detection (mainly for N, P)
- fluorescence
- light-scattering
- electron-capture detection (ECD) - especially for elements with high
electron affinities (e.g. halogens)
- UV - single wavelength or scanning
Need to be careful not to use large detector
cells (causes loss of chromatographic
resolution) - especially when linking
successive detectors.
- FTIR
- mass spectrometry
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O
Detector Parameters
H3C
O
Sensitivity - defined in terms of
minimum detectable quantity (MDQ) the amount of material giving a
signal/noise ratio of ~3.
CH3
N
N
N
N
CH3
Some Real-Life
Examples
of
Chromatographic
Analyses
Linear dynamic range -need
linearity of response over at
least the range of amounts to be
analysed.
Detectors should have an MDQ
of <1 ng. Many do much better,
e.g. 270 fg of 2,3’,4’-trichlorobiphenyl using ECD. On-line FTIR
gives a value of 95 pg for
caffeine.
Linear dynamic range should cover at
least 4 - 5 orders of magnitude.
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2. An Environmental Example
(C.Aguilar, F.Borrull and R.M.Marcé, J. Chromatography, A, 1997, 771, pp. 221-231)
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Many pesticides contain halogens, e.g. lindane (hexachlorocyclohexane),
aldrin:
Cl
Cl
Pesticides - persistent pollutants - highly toxic.
Cl2
Increasingly strict regulation (EU directive - <0.1 µg/l for drinking
water, <1-3 µg/l for surface water).
Cl
Cl
and heptachlor:
Report on analysis of water samples taken from delta of River Ebro
(northern Spain). Concentrate samples by passing 500 ml samples
through adsorbent material – then wash off with small amount of
organic solvent (hexane/ethyl acetate).Samples then subjected to
GC, with MS detection, and also using electron capture detection
(ECD).
Cl
Cl
Cl2
Cl
Cl
ECD: irradiate carrier gas with β-electrons (from 63Ni). This
generates a large number of low-energy electrons, which give
a current on applying a voltage. In presence of analytes which
can capture electrons (e.g. halogen-containing compounds) the
current is reduced. A very sensitive method for such compounds.
Cl
These are particularly suitable for ECD detection.
The GC-MS and GC-ECD chromatograms, and the mass spectrum of lindane
are shown on the next slides
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GC-ECD chromatogram of water from delta
of River Ebro (N. Spain)
GC-MS chromatogram of water from delta of
River Ebro (N. Spain)
lindane
aldrin
standard
standard
heptachlor
lindane
aldrin
malathion
heptachlor
Time (min)
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Time (min)
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Mass spectra of lindane: standard (a) and sample (b)
181
111
The GC-ECD chromatogram shows greatly increased sensitivity for chlorinated
species, but no structural information (assignments by comparison with standards).
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(a)
N.B. Malathion (in the GC-MS) is a non-chlorinated species.
Concentrations (in µg/l) and relative standard deviations (%) are as follows
145
181
111
(b)
Lindane
Heptachlor
Aldrin
Malathion
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MS
Conc
2.1
1.7
1.5
4.3
RSD
9
13
11
10
ECD
Conc
2.1
1.7
1.5
N/A
RSD
8
11
9
N/A
145
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Note that all are at the top end of, or above, the EU recommended levels for surface
water – and would require extensive treatment to bring down to the levels for
drinking water.
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Case Studies in HPLC
1.
HPLC-MS chromatogram of a beef extract
Heterocyclic amines in beef extracts.
(P.Pais et al., J. Chromatography, A, 778 (1997), pp 207 – 218)
Evidence for the formation of carcinogenic heterocyclic amines on
pyrolysis (cooking!) of protein-rich foods, e.g. meats. Recent HPLC
study of a beef extract, with MS detection.
The peaks were identified as follows from the accompanying mass spectra:
2. Glu-P-1
1. TriMeIQx
NH2
N
N
Me
N
N Me
Me
N
Me
3. Harman
N
NH2
4. Norharman
NH2
Me
Me
The total ion chromatogram of the extract shown on next overhead:
N
N
5. AαC
N
N
N
N
NH2
H
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Gramivimetric Analysis
The concentrations of the largest components were:
•
3. (Harman)
4. (Norharman)
A quantitative method for determining concentration of a species in
solution.
• React solution species with (usually excess) of a soluble
compound and obtain a non-soluble precipitate.
129.5 ± 16.8 ng/g
74.0 ± 7.4 ng/g
Good for metals e.g.
These are small amounts - but large enough to be a cause for concern
with these potent carcinogens.
Ag+aq + Cl-aq → AgClsolid
The precipitate needs to be washed and dried, them carefully
weighed. Allows determination of Ag+ conc. in original solution.
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Very Classical Method – as old as Chemistry itself!
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Since silver chlorides are insoluble, can use Ag to determine chloride salt conc.
A common method for determining the amount of chloride in a sample is to
precipitate out the chloride with a solution of silver nitrate (gravimetric
analysis), according to the following reaction
Molecular weight of AgCl = 148.3 g mol-1
Therefore 0.2212 g of AgCl = 1.5 x 10-3 moles
Keep in mind reaction stochiometry, we can clearly see that 1 mole of insoluble
product requires 1 mole of MgCl2
MgCl2(aq) + 2 AgNO3(aq) → 2AgCl(s) + Mg(NO3)2(aq)
MgCl2(aq) + 2 AgNO3(aq) → 2AgCl(s) + Mg(NO3)2(aq)
20.00 ml of a solution of magnesium chloride was treated with excess silver
nitrate. Once filtered, dried, and weighed the mass of silver chloride found
was 0.2212 g. What was the original concentration of the magnesium
chloride solution?
So, providing silver nitrate is in excess, and reaction goes to completion, we can
see that original solution contained 1.5 x 10-3 moles of MgCl2 / 20 ml.
Concentrations are generally (not always expressed in mol dm-3
1 dm-3 = 1 litre
Therefore, 0.75 x 10-3 moles of MgCl2 in 20 ml, will be 50 x (1000 / 20) greater in
1 dm-3:
Original concentration of MgCl2 = 0.0375 dm-3
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Please, NOT M
Next, determine the number of moles each of N2H4 and N2O4 which have molar
masses of 32.04524 and 92.01108 g mol-1, respectively.
Limiting Reagents
Cu2S reacts with O2 to form Cu2O and SO2,
n N2H4 =
2Cu 2S(s) + 3O2 (g) → 2SO 2 (g) + 2Cu 2O(s)
Suppose you have 3 moles each of Cu2S and O2: How much SO2 is produced?
n N 2O4 =
• 2 moles of Cu2S will react with the 3 moles of O2 leaving 1 mole of Cu2S
• O2 is called the limiting reagent because it is used up in the reaction before any of
the other reactants are used up allowing no further reaction
e.g. A fuel mixture used in the early days of rocketry is composed of two liquids,
hydrazine (N2H4) and dinitrogen tetroxide (N2O4), which ignite on contact to form
nitrogen gas and water vapour. How many grams of nitrogen gas form when
1.00x102 g N2H4 and 2.00x102 g N2O4 are mixed?
=
1.00 × 102 g
= 3.12 mol
32.04524 g mol-1
2.00 × 10 2 g
= 2.17 mol
92.01108 g mol-1
2 mol N 2 H 4 reacts with 1 mol N 2 O 4
1
1 mol N 2 H 4 reacts with mol N 2O 4
2
3.12 mol N 2 H 4 reacts with
1
× 3.12 = 1.56 mol N 2 O4
2
So once all of the N2H4 reacts, there is still some N2O4 left over
ie. 2.17-1.56=0.61 mol excess N2O4.
Solution: The first step is to write down an equation and balance it.
N 2 H 4 (l) + N 2O4 (l) → N 2 (g) + H 2O(g)
balanced
m N 2 O4
MM N 2O4
=
From the balanced equation it is readily seen that:
• with no more oxygen left absolutely no more Cu2S will react
2N 2 H 4 (l) + N 2O4 (l) → 3N 2 (g) + 4H 2O(g)
mN2H4
MM N 2 H 4
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Therefore N2H4 is the limiting reagent.
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From the balanced equation
2 mol N 2 H 4 yields 3 mol N 2
1 mol N 2 H 4 yields
3
mol N 2
2
x mol N 2 H 4 yields
3
x mol N 2
2
3.12 mol N 2 H 4 yields
3
× 3.12 = 4.68 mol N 2
2
So 4.68 mol N2 is produced from our mixture of rocket fuel.
m N2 = n N2 × MM N 2 = 4.68 mol × 28.01348 g mol -1 = 131 g
131 g of N2 is produced from the mixture of rocket fuel.
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