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CH217Fundamentals of Analytical
Chemistry
Module Leader: Dr. Alison Willows
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Assessment Practicals 60%
Practical 1: online quiz during lab session
Practicals 2 & 3: electronic reports, see lab scripts
End of module examination 40% In addition you are also required to:
Complete the guided study (not assessed)
Attend all the labs Attend at least 80% lectures/workshops
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Studentcentral
Module content and assignments are available through studentcentral
You will be required to submit your coursework electronically via studentcentral
The guided study will be an electronic test on studentcentral
Feedback on assessments will also be electronicPlease familiarise yourself with
studentcentral!
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Recommended reading
The module descriptor tells you what you should know by the end of this module
The information given in lectures and on studentcentral is only a guideline to aid your study
Please refer to the module learning handbook and studentcentral for a list of recommended books and other useful resources.
You will not achieve a good grade in this module without doing additional reading outside of the lectures
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Principles of Analytical design
DTI's Valid Analytical Measurement programme
The six principles of good analytical practice Analytical measurements should be made to satisfy an
agreed requirement. Analytical measurements should be made using methods
and equipment which have been tested to ensure they are fit for purpose.
Staff making analytical measurements should be both qualified and competent to undertake the task.
There should be a regular independent assessment of the technical performance of a laboratory
Analytical measurements made in one location should be consistent with those elsewhere.
Organisations making analytical measurements should have well defined quality control and quality assurance procedures.
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Role of analytical chemistry in science
Do I need analytical chemistry?Analytical chemistry might: enable you to pass your course help you to understand other
modules be useful in your career be interesting help with your final year project change your life!
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What is analytical chemistry?
Dictionary definitions Analytical (adj) examining or tending to examine things very
carefully Chemistry(noun) 1.(the part of science which studies) the
basic characteristics of substances and the different ways in which they react or combine with other substances. 2. INFORMAL understanding and attraction between two people
Cambridge Advanced Learner's dictionary Analytical chemistry encompasses any
type of test that provides information on the amount or identification of the chemical composition of a sample.
This breaks down into two mainareas of analysis: qualitative and quantitative
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Qualitative vs.. Quantitative Qualitative analyses give a
positive/negative or yes/no answer. This tells us whether a substance (the analyte) is present but doesn't tell us how much is there. A qualitative analysis may also identify substances in a sample
Quantitative analyses tell us how much of a substance is in the sample.
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When and where is analytical chemistry used?
Food industry - wine production; contaminants; process lines
Medical - blood analysis; imaging; Pharmaceutical - drug analysis Environmental - water, gas & soil analysis Engineering - materials characterisation Crime - forensics (CSI) Sport & leisure - pool chlorination; drugs
tests Research
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Analytical Process
Formulating the question Selecting analytical procedures Conducting the analysis
Sampling Sample preparation calibration of method Sample analysis
Collection and processing of data and calculation of errors
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Analytical Process, cont.
Method validation Reporting and interpretation (results
& discussion) Drawing conclusions (answering the
question!)
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Method selection Valid Analytical Measurement (VAM)
A result is fit for purpose when its uncertainty maximises its expected utility (cost, usually)
reducing uncertainty generally increases the cost of analysis
most users have tight budgets uncertainty in measurement should be as large as
can be tolerated to keep costs down other factors can affect fitness for purpose
sensitivity of technique sample throughput accuracy and precision that is obtainable sample type and preparation
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VAM, cont
Ultimately, the results are fit for purpose if they meet the specific needs of the customer, the customer is confident in the results and they represent value for money.
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Valid Analytical Measurement (VAM)
Goldmine A sampling and analysis game for
Minitab can be found here
http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/goldmine.asp
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Comparing techniques statistically
The F test and Student's t test F test -Is there a significant difference between
the precision of two methods? i.e. are the standard deviations of the two methods significantly different?
Student’s t test - used to decide if two sets of results are "the same" or to compare a set of results with a known value.
You will have learnt these tests in your QS modules, please refresh your memory if you are unsure how to perform it.
You will be expected to be able to compare a set of results with a known value, compare two sets of matched results and compare two sets of unmatched results, please see me if you can not do this
Further information and worked examples are available on the CH217 studentcentral website
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Samples - sampling strategy
Probably the most important stage in any analysis.
If the sample taken is not representative of the original material everything you do next is worthless.
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Sample nomenclature
lot - quantity of material which is assumed to represent a single population for sampling purposes
batch - quantity of material known (or assumed) to have been produced under uniform conditions
increments - portions of material obtained using a sampling device from lot/batch
primary/gross sample - combination of increments
composite/aggregate sample - combination of primary samples
laboratory sample - portion of material delivered to lab for analysis
test (analytical) portion - material actually submitted for analysis
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Sampling - stages
Horwitz. Pure and Applied Chemistry, 1990, 62, 1193-1208.
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Obtaining a representative sample
Usually the lot is not homogeneous but may be randomly heterogeneous (different
compositions occur on a small scale and randomly) or
segregated heterogeneous (large patches of different compositions)
A representative sample will not reflect the composition of the target exactly but will be adequate enough to be 'fit for purpose'. There will always be a degree of uncertainty from sampling.
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Sampling - n numbers How many replicate samples do we need to
analyse? Often in biology you will come across n=6 for all
analyses. so where does this come from?
Confidence limits - met in QS modules
Rearrange to make n the subject
Use the acceptable error and confidence level (to find t) to calculate n.
n
tsx
2
22
x
stn
x
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Sampling - n numbers Worked Example The concentration of lead in the bloodstream was measured
for a sample of children from a large school near a busy main road. A preliminary sampling of 50 children gave a mean concentration of 10.12 ng ml-1 and standard deviation of 0.64 ng ml-1. How big does the sample need to be to give an error of less than ±0.1 ng ml-1 with 95% confidence?
For 95% confidence t = 1.96 (n = ∞)
So 160 children would need to be tested
2
22
x
stn
2
22
1.0
64.096.1 1604.157
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sample preparation Preparing samples for analysis
Depends on the form required for analysisSamples may require
Moisture control Grinding Dissolving Ashing Fusion
Extraction Preconcentration/
dilution Derivatisation
or a combination of several of these Instruments such as microwave ovens, sonicating baths,
pressure vessels (digestion bombs) and extraction cartridges may also be used.
Please see recommended reading for further details on these preparation techniques (ch28 Harris)
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solid phase extraction
Analyte is removed from sample by passing a solution over a solid.
Analyte is adsorbed, or absorbed by the solid and the remaining liquid can be discarded
Analyte is eluted by use of a stronger solvent
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solid phase extraction
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Sample storage To keep samples reflective we must prevent
contamination & decompositionProblems & Solutions1. Dirty containers - ensure adequate washing; use
disposable containers2. Type of Container - Avoid “ion-exchange” and
adsorption of analyte3. Light - use brown/foil-covered bottles4. Air may oxidise sample - store under vacuum, or in a
protective atmosphere5. Moisture - keep tightly sealed6. Evaporation - keep tightly sealed7. Heat/cold - store in fridge/temperature controlled room
The measures chosen will depend on the analyte and its sample matrix
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Calibration Analytical methods, particularly those using instruments, frequently require calibration procedures
These are to establish: the response to known quantities of analyte (standards)
within the range used the reliability/drift of the method limits beyond which detection/quantitation is unreliable
Calibration normally involves: measurement of samples of known concentrations measurement of a relevant range of concentrations a range in which the response is linear graphical treatment of results modified calculation of errors
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External Standard
Simplest and most common form of calibration. Prepare samples containing known quantities of
analyte over a relevant range including blanks Controls for sample preparation/matrix should be
used, matched to the unknown samples Carry out and record measurements Plot quantity/concentration of analyte vs.
response Linear regression with least squares analysis is
used to determine response (expressed as y = bx+a)
Repeat as and when appropriate (when it is likely that an unacceptable drift will have occurred)
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External StandardAdvantages May only need one calibration plot (of 5-10
samples) for 10’s to 100’s of unknown samples Can be easily automated Simple statistics will provide estimates of
uncertainty for the method
Disadvantages Requires care to match conditions and matrix to
that of the unknown samples Does not control for sudden changes in method
performance
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External standard You will have done this in more detail in
BY131
You should be able to use linear regression to calculate the line of best fit and the errors in the calibration line to calculate the concentration of the analyte and its error from this information (see sec 5.4, 5.5, 5.6 in Miller & Miller)
The ability to do this is assumed in this module.
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Internal Standard Useful for methods which are not very
reproducible; e.g. Gas chromatography uses very small volumes (<1 ml) - difficult to measure accurately
The instrument responses to mixtures of known amounts of analyte and of a different compound (internal standard) are measured, and response factor determined
A known amount of internal standard is added to the unknown sample.
Signals from the analyte and from the internal standard are measured
Response factor allows determination of analyte concentration
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Internal Standard
Advantages Can control for loss during sample
preparation Controls for unexpected changes in
method performance
Disadvantages Requires suitable reference standard The two compounds (standard and
analyte) must be quantifiable independently and have linear responses over a range of concentrations
Must account for dilution steps in calculations
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Internal Standard-Worked Example Measurement of caffeine concentration by HPLC, using
theophyline as an internal standard. Standard solutions containing a range of known amounts of both caffeine and theophyline are prepared. These are subjected to HPLC and the relative instrument response (area under each peak) is determined, and response factor determined.
Abs
orb
ance Caffeine Theophyline
solution
caffeine Theophyline
Conc./mg.l-1
Peak area
Conc./mg.l-1 Peak area
A 1 20000 1 50000
B 2 38400 1 48000
c 4 89600 1 56000
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Internal Standard-Worked Example Response Factor
In reality there would be some variation and multiple calibration samples would be used to determine precision of response factor
A 10ml of a 1mg.L-1 internal standard is added to 10ml of an
unknown sample . Instrument signals measured: Analyte: 30,000,
Internal Standard: 27,000
conc.standard
signalStandardF
concAnalyte
signalAnalyte
.
4.01
56000
4
89600)
4.01
48000
2
38400)
4.01
50000
1
20000)
FFc
FFb
FFa
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Internal Standard-Worked Example Response factor allows determination of analyte
concentration in sample:
Original concentration = 1.39 x 20/10
= 2.78mg.L-1
1.39.1
4.030000
.
Lmgx
0.5
27000
x
conc.standard
signalStandardF
concAnalyte
signalAnalyte
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Standard addition Frequently used where matrix effects and interferents are prevalent e.g. atomic absorption/emission
Prepare samples containing equal volumes of unknown analyte concentration
“Spike” each sample with known, different amounts of standard (same analyte, including a range from 0 to ~5x expected unknown concentration)
Dilute all samples to the same volume Carry out and record measurements Plot quantity/concentration of known analyte added
vs.. response Linear regression with least squares analysis is used
to determine response (expressed as y = bx+a) Concentration of unknown = - (x-intercept) = a/b Repeat for each unknown sample
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Standard addition
Advantages Controls for matrix effects Controls for unexpected changes in method
performance
Disadvantages Requires several measurements for each
unknown May use more unknown sample than other
methods Must be careful to account for dilution steps in
calculations
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Standard addition - Worked Example
Measurement of Copper concentration by atomic absorption spectrometry
Five 10ml solutions of unknown (approx. 2mg.L-1) copper concentration were prepared and to these was added: 0, 2, 4, 6 and 8 cm3 of 10mg.L-1 standard analyte solution in water (one volume to each flask). All samples diluted to 25cm3 with water and mixed well. The solutions were then measured using AAS and the results recorded
Solution
Added volume/ cm3
Absorbance
1 0 0.150
2 2 0.312
3 4 0.446
4 6 0.580
5 8 0.762
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Calculate concentration of copper added to solution, using c1V1 = c2V2
i.e. 2 cm3 added: 10 x 2/1000 = c2 x 25/1000
c2 = 0.8 mg.L-1 etc
Plot quantity/concentration of known analyte added vs. response,
and plot line using linear regression with least square analysis
(expressed as y = bx+a)
Solution
Added volume/ cm3
Absorbance
Added concentration/ mg.l-1
1 0 0.150 0
2 2 0.312 0.8
3 4 0.446 1.6
4 6 0.580 2.4
5 8 0.762 3.2
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Conc. of unknown in samples = - (x-intercept) = a/b
= 0.813mg.L-1
NB: 10cm3 aliquots of the original solution were diluted to
25cm3 in the samples, so concentration of original solution
= 0.813 x 25/10 = 2.0325 ~ 2.03mg.L-1
Standard addition plot
-1 0 1 2 3 4
0.2
0.4
0.6
0.8
1.0
x-intercept = -ve concentration of unknown
Concentration added to sample
(mg.L-1)
Ab
sorb
ance
Slope Y-intercept X-intercept
0.1865 ± 0.0060280.1516 ± 0.01181-0.8129
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validation
Standards Performance parameters Errors in Analysis Record Keeping
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“How long is a piece of string?”
The results from any analytical measurement depends upon and is traceable to the measurement standards used in the process. These include standards for mass, volume and amount of a chemical species.
Equipment is usually periodically calibrated using standards that can be traced back to an International Primary Standard.
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Example1. An analytical balance will be calibrated periodically using
calibrated weights. 2. These weights are regularly checked against a set of
weights held at a reference laboratory. 3. The reference laboratory's weights will be checked
periodically against the national standard kilogram (held at the National Physical Laboratory, NPL).
4. This national standard kilogram is occasionally compared to the international standard kilogram.
Each stage introduces a measurement uncertainty which has to be taken into account. This means that the standards used in a laboratory will always have a greater uncertainty associated with them than those from the reference laboratories.
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Standard solutions Standard solutions can be used to help
with calibration and to compare results against to establish the accuracy of a technique.
The two main grades of standard are: Primary Secondary
Certified Reference Materials (CRM) - specially prepared samples containing an analyte at a pre-determined concentration .
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Primary standards
Primary standards are highly purified compounds that are used, directly or indirectly, to establish the concentration of standard solutions.
Primary standards should meet the following requirements: High purity Stability toward air Absence of hydrate water so composition does not
change with variations in humidity Ready availability at reasonable cost Reasonable solubility in titration medium Reasonably large molar mass so that relative error
associated with weighing the standard is minimised
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Secondary standards There are few compounds that meet these
criteria. So often a less pure compound has to be used: secondary standard
The ideal standard solution should: Be sufficiently stable that its concentration needs to be
determined only once React rapidly with the analyte React more or less completely with the analyte for good
end points Undergo selective reaction with simple balanced
equation
Few reagents meet all of these requirements
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Performance parameters Accuracy – measure of agreement between a single
analytical result and the true value Precision – measure of agreement between observed
values obtained by repeated application of the same analytical procedure
Selectivity – measure of the discriminating power of an analytical procedure in differentiating between the analyte and other components in the test sample
Sensitivity – the change of the measured signal as a result of one unit change in the content of the analyte (calculated from the calibration line)
Limit of Detection – calculated amount of analyte in the sample which corresponds to 3 times the sd of the blank sample
Limit of Quantitation – minimum content of the analyte that can be quantitatively determined with reasonable statistical confidence. Equivalent to 6 time the sd of the blank sample
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Linearity – a measure of the linearity of the calibration Range – concentration range to which the technique is
applicable Ruggedness – insensibility of the method for variations
during execution Standard deviation and relative standard
deviation (RSD) – measures of the spread in the observed values as a result of random errors
Repeatability – expected maximum difference between two results of identical test samples obtained under identical conditions
Within-lab reproducibility – expected maximum difference between two results obtained by repeated application of the analytical procedure to an identical test sample under different conditions (e.g. different operator, different days) but in the same laboratory
Between-lab reproducibility - expected maximum difference between two results obtained by repeated application of the analytical procedure to an identical test sample in different laboratories (e.g. different operators, different instrumentation in different labs on different days using same method
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Errors in Analysis
The key to any successful analysis is ensuring that it will “answer the question”
No analysis can be absolutely error-free All analyses must be designed to produce
acceptable levels of errors and uncertainty The best way to minimise errors is by
careful experimental design
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types of error Three main types of error
Gross: So serious the experiment must be abandoned. e.g. dropping a key sample, instrumental breakdown
Random: When an experiment is repeated as exactly as possible, the replicate results will differ due to random errors. Estimates of random errors gives the precision or reproducibility of the analysis.
Systematic: An experimental method gives a reproducible under- or overestimate of the real result. Total of all systematic errors gives the bias of an analysis.
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Typical sources of errorMay be personal, instrumental or methodological Random
Volume - not reading the burette reproducibly Weight - sensitivity of the balance
Systematic Volume - glassware not exact; ”indicator errors”;
incomplete drainage of pipette/burette; lab temperature Weight - vessel at different temperature to balance; air
buoyancy effect Both
Incomplete transference between vessels Incomplete reaction, decomposition or moisture
absorbance of sample/analyte Interfering species
With good tools and careful measurement, traditional methods (gravimetry, titrimetry) are generally more accurate than instrumental method.
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Error AvoidanceAfter considering each stage of the process, employ: Random Errors
improved technique (e.g. reading burette volumes) a more accurate balance sufficient repeated measurements (replicates) a different scale (g are easier to weigh than mg)
Systematic errors replicates in different glassware temperature controls difference weighing “reference standards” and “blank” measurements purified reagents a different/additional method interlaboratory trials
Systematic errors are not always obvious - but the methods above can often be used to detect them!
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Accuracy and precision
Accurate and Precise
Inaccurate and Imprecise
Accurate but not precise
Precise but not accurate
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accuracy & precision
Uncertainty - A measure of both precision and accuracy, i.e. is an indicator of overall errors associated with the method.
May be quoted using s, RSD or CI (should state which) s and RSD should be quoted with the relevant n
Analytical results are quoted as a mean ± uncertainty
Size of the uncertainty dictates how many significant figures to quote
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Calculating uncertainty
Bottom-up method Combine all known errors (e.g. weighing, glassware,
reagent purity) to give an estimate of uncertainty Problem: This can be very complex, and it is difficult to
include systematic errors
Top-down method Conduct multiple replicates of the experiment, varying
as many conditions that cause bias as possible - operator, reagent source, glassware etc. - then mathematically estimate the uncertainty.
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Measures of Spread Often quoted as a indicators of uncertainty
Range: Difference between highest and lowest values Standard Deviation (s): A good measure of precision. A
small s means that the data is more precise than data with a large s - but not necessarily more accurate
Variance (s2): The square of the standard deviation
Coefficient of Variation (CV) OR Relative Standard Deviation (RSD): A relative error estimate expressed as a % of the mean of the measurements. Used to compare the precision of methods with different units/ranges.
Confidence interval (CI): A range which has a high statistical likelihood (e.g.95%) of containing the true value
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significant figures
You should have covered this in more detail in BY131 (also see Harris 3.1-3.3)
Don’t just write down all the digits your calculator gives you!
Quote the minimum number of digits needed to write a value in scientific notation without loss of accuracy
e.g. 9.34 (±0.02) x 102 not 93400, and not 9.34567 ±0.02
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Rules Generally only the last digit should have
uncertainty associated with it The last digit will always have uncertainty
associated with it (unless the data is discrete) Zeros at the end of a number imply you know the
value ends in 0 (4.56 is not the same as 4.560) Calculations should be carried out without
rounding - only round up the answer If you are worried about loss of information you
may put an extra digit as a subscript (e.g. 4.562) Use literature examples and common sense if
you are unsure!
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propagation of errors
Necessary to calculate combined errors for: “bottom up” estimation of uncertainty estimating uncertainty for results based on two or more
values each with its own uncertainty
e.g. For data reported as ratiosValue = (sample result (±error) : control result
(±error)) - we cannot simply add the errors - sometimes they
will cancel each other out
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Relative and Absolute uncertainties
Uncertainties of a measurement x can be quoted as absolute – ex (in same units as x) Relative - %ex ( a percentage of x)
Conversion:
%100e
%e
%100 valueMeasured
yuncertaint Absoluteyuncertaint Relative
xx
x
%100
xee
100%
valueMeasuredyuncertaint Relativeyuncertaint Absolute
xx
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Example Question
A sample weight was measured as 5.1g. The balance used was known to be accurate to 0.02g. What is the relative uncertainty associated with this measurement?
%100e
%e
%100 valueMeasured
yuncertaint Absoluteyuncertaint Relative
xx
x
%10010.5
0.02g%ex
g
%4.0%ex
%4.010.5 weightsample g So,
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How do we combine uncertainties?
We can use simple formulae to combine uncertainties
Combine one stage at a timee.g. x = (a/b) + c 1) Combine a and b uncertainty, then2) Combine the result with c to get uncertainty in x
NOTE: The methods described here are only used for random errors, and assume that systematic errors have been identified and eliminated
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Combining uncertainties - addition and subtraction
Where the calculation to find x includes addition or subtraction e.g. x = a+b-c
We need to combine the absolute uncertainties for a, b and c, i.e. Combine ea eb and ec
Uncertainty in x: 222cbax eeee
Method: Calculate x Calculate ex
Quote result as x ± ex
Square of absolute uncertainties are added (even if
result is subtracted)
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Example question
Uncertainty in reading a burette: You measure a volume by subtracting the initial
reading from the final reading. Initial reading is 0.05 (0.02) ml Final reading is 17.88 (0.02) ml If the uncertainty in each reading is known to be
0.02ml what is the volume measured and its overall uncertainty Measured volume is 17.88 - 0.05ml = 17.83ml
Absolute uncertainty, ex =
mlml
ml
mlmlee if
03.002.0
108
02.002.0
8
4
2222
Volume =17.83 (±0.03)ml
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Combining uncertainties – multiplication and division
Where the calculation to find x includes multiplication or division e.g. x = (a×b)/c
We need to combine the relative uncertainties for a, b and c, i.e. Combine %ea %eb and %ec
Uncertainty in x: 222 %%%% cbax eeee Method:
Calculate x Convert absolute uncertainties to relative uncertainties Calculate %ex
Convert %ex to ex
Quote result as x ± ex
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Example questionCalculate the value and uncertainty of x where: x=
(a.b)/c and: a = 1.76 ( 0.03), b = 1.89 ( 0.02) and c =
0.59 ( 0.02)
Calculate x
xe
x
645
020590
020891030761
.
......
Relative uncertainties:
%7.1
76.1
10003.0100%ea
a
ea
%1.1
89.1
10002.0100e% b
b
eb
%4.3
59.0
10002.0100%ec
c
ec
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Example question cont. Combine
Convert to absolute uncertainty
So,
%.4
%66.15
%4.3%1.1%7.1
%%%%RelativeCombined
0
222
23
22
21
eeeex
3
0
2.0
100
64.5.4
100
%in xty UncertainAbsolute
xex
2.06.52.064.5 3 x
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Combining uncertainties – powers and roots
Where the calculation to find x includes a power or root e.g. x = ab or x = √a
Using relative uncertainties Uncertainty in x:
ax ebe %%
Method: Express roots as ab e.g. √a = a½
Calculate x Convert ea to %ea
Calculate %ex by multiplying by b Convert %ex to ex
Quote result as x ± ex
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Example question
Calculate the value and uncertainty of x where: x=
a3 and a = 1.76 ( 0.03)
Express as x = ab
Calculate x
Convert absolute uncertainty to relative
uncertainty
303.076.1 x
53 4.576.1 x
%.1
%10076.1
03.0%
7
ae
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Example question, cont. Multiply by b
Convert to absolute uncertainty
So,
(using correct s.f.)
%.5
3%7.1%
1
xe
82.0
%100
45.5%1.5
xe
3.05.5 x
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Combining uncertainties - constants
Where a constant k is part of the calculation, and has no
uncertainty associated with it.
Rule of thumb: If you are uncertain about the effect of
k, include it as a term with an associated uncertainty
of 0 Case 1: k is added or subtracted
Value and uncertainty of x where x = k + a or x = a - k
k does not affect the absolute uncertainty - but will affect relative
uncertainty
Case 2: k is multiplied or divided Value and uncertainty of x where x = ka or a/k
k affects the absolute uncertainty - but not the relative uncertainty
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Combining uncertainties – combinations
Solve each type of combination separately, one at a time
e.g x = (a + b) c
• Combine errors for a + b to get absolute ea+b
• Convert ea+b to %ea+b using (a + b) as the measured value
• Convert ec to %ec and combine with %ea+b to get %ex
• Calculate x
• Convert %ex to ex
• Answer is expressed as x± ex
NOTE: All these examples give ex (absolute uncertainty) as an answer. You may be asked to calculate just %ex (relative uncertainty)
Read the question carefully!
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Example question
A 50cm3 burette can be read to ± 0.02cm3. In a particular analysis the result is calculated using the formula
y = xm/(Ts - Tb)
where y is the analyte concentration, in mol.dm-3, and Ts and Tb and the sample and blank titres respectively in cm3. Calculate the uncertainty in the final result when:x = (0.150 ± 0.002) mol.dm-3, m=300, Ts = 15.01 cm3 and Tb = 0.04 cm3. m is known absolutely.
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y = xm/(Ts - Tb) Look at subtraction first
Measured volume Ts - Tb = 15.01 - 0.04ml = 14.97ml
Calculate eTs-Tb
Convert to %eTs-Tb
38
4
2222
03.002.0
108
02.002.0
cm
eee TbTsTbTs
%18.0
%10097.14
028.0
%100%
7
bs
TTTT TT
ee bs
bs
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Now look at constant y = xm/(Ts-Tb) m only affects absolute uncertainties for y To calculate ey we will be using relative uncertainties
(division) Convert ex to %ex
Combine relative uncertainties
%3.1
%100150.0
002.0
%100%
3
x
ee xx
%.
.
..
%%%
4
227
22
31
801
331180
xTbTsy eee
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Calculate y
Convert relative uncertainty of y to absolute
So,
3
1 .0.3
97.14
30015.0
dmmol
TT
xmy
bs
30 .04.0
%100
01.334.1
%100
%
dmmol
yee yy
3.04.001.3 dmmoly
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Limit of Detection (LoD)
The concentration which gives an instrument signal (y) significantly different from the blank (or background) signal
This is generally calculated as: Concentration x which gives rise to a signal of yB
+ 3sB
where yB and sB are the mean and s.d. of blank solutions
NB the method used may vary according to the purpose of the analysis - so it should always be quoted
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Measuring LOD/LOQ Practically
Perform the analysis on matched solutions containing no analyte
Calculate the mean (yB) and standard deviation (sB) of the signals/measurements obtained
BUT this can be very time- and reagent- consuming
Mathematically Use the calculated value of the intercept (a) as an
estimate of yB
Use sy/x as an estimate of sB
This is more accurate than using the single blank value included as part of the calibration process, and eliminates the need for repetition
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Sensitivity vs. Detectivity
LOD and LOQ are measures of detectivity and are dependent on both the slope and the intercept of the calibration plot
Sensitivity is a measure of instrument response to changes in concentration across the entire linear range and is only dependent on the slope of the plot
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Limit of Quantitation (LoQ)
The concentration above which precise quantitative measurement is possible
This is generally calculated as:
Concentration x which gives rise to a signal of yB + 10sB
This calculation is often conducted in different ways - again the method used should always be quoted
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Record Keeping Ensure results are recorded in a laboratory
notebook even if they are available electronically. Enough information should be included to ensure
a colleague can repeat the experiment using only your notes.
Keep a copy of the notebook (preferably in a separate location).
Many employers have their own methods for laboratory record keeping and usually require that each page is signed and dated by both the employee and their line manager. This is useful when it comes to intellectual property rights.
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Record Keeping
In general for each experiment include: title and date objectives reaction scheme, if applicable hazard assessment, if necessary method results and calculations, including any
instrument readouts and graphs conclusion
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Reporting - Analytical Documentation
Used to allow other competent analysts to reproduce the method. Sufficient detail is required to obtain consistent results. Trained and competent personnel are still required even when a full detailed document is available
Please see studentcentral website for further details
Drawing conclusions In a written report of an experiment you must come to some
conclusion about the work Use the information from the statistical tests and performance
parameters Pull together all the information Keep the wording ‘analytical’ i.e. use ‘accurate’ and ‘precise’
correctly, and don’t over-generalise Make informed judgements about the technique and compare
to other possible techniques