1. CH217 Fundamentals of Analytical Chemistry
Module Leader: Dr. Alison Willows

3. Assessment Practicals 60% End of module examination 40%
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

4. 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 electronic
Please familiarise yourself with studentcentral!

5. 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

6. 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.
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.
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!
What is analytical chemistry?
Dictionary definitions
Analytical (adj) examining or tending to examine things very carefully
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 main areas of analysis: qualitative and 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. One example is a home pregnancy test which indicates the presence (positive) or lack (negative) of a pregnancy by analysing a hormone that appears in a woman's blood and urine, human chorionic gonadotropin (HCG). In this case we do not need to know how much of the hormone is present so a qualitative analysis is sufficient. A qualitative analysis may also identify substances in a sample
Quantitative analyses tell us how much of a substance is in the sample. One example is a diabetes glucose monitor that measures the amount of glucose in the blood
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
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
reporting
Analytical Documentation
Written analytical procedures are 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
Analytical Documentation for Procedures
Scope and applicability
Samples
Analytes
Ranges
Description and principle of the method
Equipment
Specification
Calibration and qualification
Range of operability
Reference materials and reagents
Preparation
Storage
Health & Safety
Sampling
Methods
Limitations
Analytical Procedure
Preparation of samples
Preparation of standards
Critical factors
Detailed description of all steps
Typical outputs; chromatograms, spectra, etc.
Recording and reporting of data
Method
Rounding and significant figures
Data treatments
Calculation of results
Calibration model
Calculation methods
Assumptions and limitations
Method performance
Statistical measures
Control charting
References & Bibliography
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

7. 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!
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!
What is analytical chemistry?
Dictionary definitions
Analytical (adj) examining or tending to examine things very carefully
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 main areas of analysis: qualitative and 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. One example is a home pregnancy test which indicates the presence (positive) or lack (negative) of a pregnancy by analysing a hormone that appears in a woman's blood and urine, human chorionic gonadotropin (HCG). In this case we do not need to know how much of the hormone is present so a qualitative analysis is sufficient. A qualitative analysis may also identify substances in a sample
Quantitative analyses tell us how much of a substance is in the sample. One example is a diabetes glucose monitor that measures the amount of glucose in the blood
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
Analytical Process
The 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
method validation
Reporting and interpretation (Results & discussion)
Drawing conclusions (answering the question!)

8. 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 main
areas of analysis:
qualitative and quantitative

9. 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.

10. 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

11. 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
Analytical Process
The 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
method validation
Reporting and interpretation (Results & discussion)
Drawing conclusions (answering the question!)

12. Analytical Process, cont.
Method validation
Reporting and interpretation (results & discussion)
Drawing conclusions (answering the question!)

13. 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
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
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.
comparing techniques statistically
Student's t test
A t test can be 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 the t test in your QS modules, please refresh your memory if you are unsure how to perform it.
Worked examples
Practice questions
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?
Worked Examples
Categories:
know basics

14. 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.

15. Valid Analytical Measurement (VAM)
Goldmine
A sampling and analysis game for Minitab can be found here
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
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.
Goldmine
A sampling and analysis game for Minitab can be found at

16. 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
comparing techniques statistically
Student's t test
A t test can be 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 the t test in your QS modules, please refresh your memory if you are unsure how to perform it.
Worked examples
Practice questions
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?
Worked Examples
Categories:
know basics

17. 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.
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.
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
Horowitz. Pure and Applied Chemistry, 1990, 62,
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.
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 calculate n.
Worked example

18. 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

19. Sampling - stages
Horwitz. Pure and Applied Chemistry, 1990, 62,

20. 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.

21. 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 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 calculate n.
Worked example

22. 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 ng ml-1 and standard deviation of 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

23. sample preparation Preparing samples for analysis
Depends on the form required for analysis
Samples may require
Moisture control
Fusion
Grinding
Extraction
Dissolving
Preconcentration/dilution
Ashing
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)
sample preparation
Preparing samples for analysis
Depends on the form required for analysis
Samples may require
1) Moisture control
2) Grinding
3) Dissolving
4) Ashing
5) Fusion
6) Extraction
7) Preconcentration/dilution
8) 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)
Remember:
The success of the analysis depends on minimising errors throughout all stages including sample preparation
Every additional step must be carefully controlled and included in error calculations
The greater the n the more confident we can be
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
(Harris ch28)
SPE uses the principles of chromatographic separation - works on ion exchange, reverse phase and normal phase
SPE can reduce solvent consumption
SPE is now often used as an efficient alternative to liquid extraction - depends on availability of selective adsorbents
cartridges are available commercially for many analyses
often used to change the buffer or matrix that the analyte is held in

24. 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
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
(Harris ch28)
SPE uses the principles of chromatographic separation - works on ion exchange, reverse phase and normal phase
SPE can reduce solvent consumption
SPE is now often used as an efficient alternative to liquid extraction - depends on availability of selective adsorbents
cartridges are available commercially for many analyses
often used to change the buffer or matrix that the analyte is held in

25. solid phase extraction

26. Sample storage
To keep samples reflective we must prevent contamination & decomposition
Problems & Solutions
Dirty containers - ensure adequate washing; use disposable containers
Type of Container - Avoid “ion-exchange” and adsorption of analyte
Light - use brown/foil-covered bottles
Air may oxidise sample - store under vacuum, or in a protective atmosphere
Moisture - keep tightly sealed
Evaporation - keep tightly sealed
Heat/cold - store in fridge/temperature controlled room
The measures chosen will depend on the analyte and its sample matrix
storage
Storing Samples
To keep samples reflective we must prevent
contamination
decomposition
Problems & Solutions
1) Dirty containers - ensure adequate washing; use disposable containers
2) Type of Container - Avoid “ion-exchange” and adsorption of analyte
3) Light - use brown/foil-covered bottles
4) Air may oxidise sample - store under vacuum, or in a protective atmosphere
5) Moisture - keep tightly sealed
6) Evaporation - keep tightly sealed
7) Heat/cold - store in fridge/temperature controlled room
The measures chosen will depend on the analyte and its sample matrix

27. 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
Calibration
Analytical methods, particularly those using instruments, frequently require calibration procedures
the reliability/drift of the method
the response to known quantities of analyte (standards) within the range used
These are to establish:
limits beyond which detection/quantitation is unreliable
measurement of samples of known concentrations
Calibration normally involves:
measurement of a relevant range of concentrations
modified calculation of errors
graphical treatment of results
a range in which the response is linear
External Standard
Prepare samples containing known quantities of analyte over a relevant range including blanks
Simplest and most common form of calibration.
Controls for sample preparation/matrix should be used, matched to the unknown samples
Linear regression with least squares analysis is used to determine response (expressed as y = bx+a)
Plot quantity/concentration of analyte vs. response
Carry out and record measurements
Repeat as and when appropriate (when it is likely that an unacceptable drift will have occurred)
May only need one calibration plot (of 5-10 samples) for 10’s to 100’s of unknown samples
Advantages
Can be easily automated
Simple statistics will provide estimates of uncertainty for the method
Requires care to match conditions and matrix to that of the unknown samples
Disadvantages
Does not control for sudden changes in method performance
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 calulate 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.
know basics
Categories:
Internal Standard
Useful for methods which are not very reproducible; e.g. Gas chromatography uses very small volumes (<1 ml) - difficult to measure accurately
1) The instrument responses to mixtures of known amounts of analyte and of a different compound (internal standard) are measured, and response factor determined
4) Response factor allows determination of analyte concentration
3) Signals from the analyte and from the internal standard are measured
2) A known amount of internal standard is added to the unknown sample.
Controls for unexpected changes in method performance
Can control for loss during sample preparation
The two compounds (standard and analyte) must be quantifiable independently and have linear responses over a range of concentrations
Requires suitable reference standard
Must account for dilution steps in calculations
Worked Example
Standard addition
Frequently used where matrix effects and interferents are prevalent e.g. atomic absorption/emission
2) “Spike” each sample with known, different amounts of standard (same analyte, including a range from 0 to ~5x expected unknown concentration)
1) Prepare samples containing equal volumes of unknown analyte concentration
3) Dilute all samples to the same volume
6) Linear regression with least squares analysis is used to determine response (expressed as y = bx+a)
5) Plot quantity/concentration of known analyte added vs. response
4) Carry out and record measurements
8) Repeat for each unknown sample
7) Concentration of unknown = - (x-intercept) = a/b
Controls for matrix effects
Must be careful to account for dilution steps in calculations
May use more unknown sample than other methods
Requires several measurements for each unknown

28. 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)
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)
Advantages
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
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 calulate 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.
Categories:
know basics

29. External Standard Advantages
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

30. 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.

31. 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
Internal Standard
Useful for methods which are not very reproducible; e.g. Gas chromatography uses very small volumes (<1 ml) - difficult to measure accurately
1) The instrument responses to mixtures of known amounts of analyte and of a different compound (internal standard) are measured, and response factor determined
2) A known amount of internal standard is added to the unknown sample.
3) Signals from the analyte and from the internal standard are measured
4) Response factor allows determination of analyte concentration
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
Worked Example

32. 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

33. 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.
Absorbance
Caffeine Theophyline
solution
caffeine
Theophyline
Conc./mg.l-1
Peak area A 1
20000
50000 B 2
38400
48000 c 4
89600
56000

34. 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

35. Internal Standard-Worked Example
Response factor allows determination of analyte concentration in sample:
 Original concentration = 1.39 x 20/10
= 2.78mg.L-1

36. 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
Standard addition
Frequently used where matrix effects and interferents are prevalent e.g. atomic absorption/emission
1) Prepare samples containing equal volumes of unknown analyte concentration
2) “Spike” each sample with known, different amounts of standard (same analyte, including a range from 0 to ~5x expected unknown concentration)
3) Dilute all samples to the same volume
4) Carry out and record measurements
5) Plot quantity/concentration of known analyte added vs. response
6) Linear regression with least squares analysis is used to determine response (expressed as y = bx+a)
7) Concentration of unknown = - (x-intercept) = a/b
8) Repeat for each unknown sample
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
Worked Example

37. 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

38. 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
0.150 2
0.312 3 4
0.446 6
0.580 5 8
0.762

39. 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
0.150 2
0.312
0.8 3 4
0.446
1.6 6
0.580
2.4 5 8
0.762
3.2

40. 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 = x 25/10 = ~ 2.03mg.L-1

41. validation Standards Performance parameters Errors in Analysis
Record Keeping
standards
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.
Example: An analytical balance will be calibrated periodically using calibrated weights. These weights are regularly checked against a set of weights held at a reference laboratory. The reference laboratory's weights will be checked periodically against the national standard kilogram (held at the National Physical Laboratory, NPL). 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.
The UK National Standard Kilogram - a cylinder of platinum-iridium alloy and numbered '18' - is kept in a basement vault at NPL. It is stored in an air-tight enclosure, only exposed to the air via two micropore filters. Conditions in the basement are very stable - although not temperature controlled - with the temperature remaining in the range 19 °C ±1 °C throughout the year. While the temperature in the vault is monitored, the storage temperature of the kilogram is not critical provided it remains within a few degrees of 19 °C. If is gets too cold condensation may form on the surface - resulting in physisorption of water into the surface layers. If it gets too hot the rate of surface contamination and adsorption of hydrocarbons from the surrounding air may increase.
Where and how is the UK's National Standard Kilogram stored? (FAQ - Mass & Density)
From
Standard solutions can be used to help with calibration and to compare results against to establish the accuracy of a technique.
High purity
Primary standards should meet the following requirements:
Primary standards are highly purified compounds that are used, directly or indirectly, to establish the concentration of standard solutions.
Stability toward air
Reasonable solubility in titration medium
Ready availability at reasonable cost
Absence of hydrate water so composition does not change with variations in humidity
Reasonably large molar mass so that relative error associated with weighing the standard is minimised
often a less pure compound has to be used:
There are few compounds that meet these criteria. So
secondary standard
React rapidly with the analyte
Be sufficiently stable that its concentration needs to be determined only once
The ideal standard solution should:
Undergo selective reaction with simple balanced equation
React more or less completely with the analyte for good end points
Few reagents meet all of these requirements
Certified Reference Materials (CRM) - specially prepared samples containing an analyte at a pre-determined concentration . hey are often used to analyse the performance of a method or laboratory and are used as part of a quality control procedure.
Performance parameters
Precision – measure of agreement between observed values obtained by repeated application of the same analytical procedure
Accuracy – measure of agreement between a single analytical result and the true value
Selectivity – measure of the discriminating power of an analytical procedure in differentiating between the analyte and other components in the test 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
Limit of detection – calculated amount of analyte in the sample which corresponds to 3 times the sd of the blank 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)
Linearity – a measure of the linearity of the calibration
Standard deviation and relative standard deviation (RSD) – measures of the spread in the observed values as a result of random errors
Ruggedness – insensibility of the method for variations during execution
Range – concentration range to which the technique is applicable
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
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
Repeatability – expected maximum difference between two results of identical test samples obtained under identical conditions
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
(Miller and Miller Chapters 1-3, Harris Chapters 3 & 4)
Even the simplest analytical experiment is likely to have more than ten stages, each of which may introduce errors
The best way to minimise errors is by careful experimental design
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. It is also a good idea to keep a copy of the notebook (preferably in a separate location). Many employers have their own prescribed 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.
title and date
In general for each experiment include:
objectives
method
hazard assessment, if necessary
reaction scheme, if applicable
conclusion
results and calculations, including any instrument readouts and graphs

42. “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.
standards
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.
Example: An analytical balance will be calibrated periodically using calibrated weights. These weights are regularly checked against a set of weights held at a reference laboratory. The reference laboratory's weights will be checked periodically against the national standard kilogram (held at the National Physical Laboratory, NPL). 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.
From
Where and how is the UK's National Standard Kilogram stored? (FAQ - Mass & Density)
The UK National Standard Kilogram - a cylinder of platinum-iridium alloy and numbered '18' - is kept in a basement vault at NPL. It is stored in an air-tight enclosure, only exposed to the air via two micropore filters. Conditions in the basement are very stable - although not temperature controlled - with the temperature remaining in the range 19 °C ±1 °C throughout the year. While the temperature in the vault is monitored, the storage temperature of the kilogram is not critical provided it remains within a few degrees of 19 °C. If is gets too cold condensation may form on the surface - resulting in physisorption of water into the surface layers. If it gets too hot the rate of surface contamination and adsorption of hydrocarbons from the surrounding air may increase.
Standard solutions can be used to help with calibration and to compare results against to establish the accuracy of a technique.
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
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
Certified Reference Materials (CRM) - specially prepared samples containing an analyte at a pre-determined concentration . hey are often used to analyse the performance of a method or laboratory and are used as part of a quality control procedure.

43. Example
An analytical balance will be calibrated periodically using calibrated weights.
These weights are regularly checked against a set of weights held at a reference laboratory.
The reference laboratory's weights will be checked periodically against the national standard kilogram (held at the National Physical Laboratory, NPL).
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.

44. 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 .

45. 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

46. 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

47. 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
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
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

48. 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

49. 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
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
(Miller and Miller Chapters 1-3, Harris Chapters 3 & 4)
Even the simplest analytical experiment is likely to have more than ten stages, each of which may introduce errors
The best way to minimise errors is by careful experimental design
types of error
Three main types of error
e.g. dropping a key sample, instrumental breakdown
Gross: So serious the experiment must be abandoned
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.
May be personal, instrumental or methodological
Typical sources of error
Random
b) Weight - sensitivity of the balance
a) Volume - not reading the burette reproducibly
a) Volume
Systematic
incomplete drainage of pipette/burette
”indicator errors”
glassware not exact
lab temperature
air buoyancy effect
vessel at different temperature to balance
b) Weight
Both
Interfering species
Incomplete reaction, decomposition or moisture absorbance of sample/analyte
Incomplete transference between vessels
With good tools and careful measurement, traditional methods (gravimetry, titrimetry) are generally more accurate than instrumental method.
Error Avoidance
After considering each stage of the process, employ:
Random Errors
sufficient repeated measurements (replicates) (see also later notes for estimating required replicates)
a more accurate balance
improved technique (e.g. reading burette volumes)
a different scale (g are easier to weigh than mg)
temperature controls
replicates in different glassware
Systematic errors
difference weighing
a different/additional method
purified reagents
“reference standards” and “blank” measurements
interlaboratory trials
Systematic errors are not always obvious - but the methods above can often be used to detect them!
Categories:
know basics
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)
Size of the uncertainty dictates how many significant figures to quote (see next page)
Analytical results are quoted as a mean ± uncertainty
s and RSD should be quoted with the relevant n
Calculating uncertainty
Problem: This can be very complex, and it is difficult to include systematic errors
Combine all known errors (e.g. weighing, glassware, reagent purity) to give an estimate of uncertainty
1) Bottom-up 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.
2) Top-down method
Often quoted as a indicators of uncertainty
Measures of Spread
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 (see later)
significant figures
You should have covered this in more detail in BY131 (also see Harris )
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 ±0.02
Rules
The last digit will always have uncertainty associated with it (unless the data is discrete)
Generally only the last digit should have uncertainty associated with it
Zeros at the end of a number imply you know the value ends in 0 (4.56 is not the same as 4.560)
Use literature examples and common sense if you are unsure!
If you are worried about loss of information you may put an extra digit as a subscript (e.g )
Calculations should be carried out without rounding - only round up the answer
propagation of errors
Propagation of Uncertainty (Harris Ch.3-5)
“bottom up” estimation of uncertainty
Necessary to calculate combined errors for:
estimating uncertainty for results based on two or more values each with its own uncertainty
e.g. For data reported as ratios
- we cannot simply add the errors - sometimes they will cancel each other out
Value = (sample result (±error) : control result (±error))
How do we combine uncertainties?
e.g. x = (a/b) + c
combine one stage at a time
can use simple formulae to combine uncertainties
2) Combine the result with c to get uncertainty in x
1) Combine a and b uncertainty, then
NOTE: The methods described here are only used for random errors, and assume that systematic errors have been identified and eliminated
limit of detection & limit of quantitation
The concentration which gives an instrument signal (y) significantly different from the blank (or background) signal
Limit of Detection (LOD)
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
The concentration above which precise quantitative measurement is possible
Limit of Quantitation (LOQ)
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
Measuring LOD/LOQ
1) Practically
Perform the analysis on matched solutions containing no analyte
BUT this can be very time- and reagent- consuming
Calculate the mean (yB) and standard deviation (sB) of the signals/measurements obtained
2) Mathematically
This is more accurate than using the single blank value included as part of the calibration process, and eliminates the need for repetition
Use sy/x as an estimate of sB
Use the calculated value of the intercept (a) as an estimate of yB
Sensitivity vs. Detectivity
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
LOD and LOQ are measures of detectivity and are dependent on both the slope and the intercept of the calibration plot

50. 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.
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.
Typical sources of error
May be personal, instrumental or methodological
Random
a) Volume - not reading the burette reproducibly
b) Weight - sensitivity of the balance
Systematic
a) Volume
glassware not exact
”indicator errors”
incomplete drainage of pipette/burette
lab temperature
b) 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.
Error Avoidance
After considering each stage of the process, employ:
Random Errors
improved technique (e.g. reading burette volumes)
a more accurate balance
sufficient repeated measurements (replicates) (see also later notes for estimating required 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!
Categories:
know basics

51. Typical sources of error
May 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.

52. Error Avoidance After 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!

53. Accuracy and precision
Accurate and Precise
Precise but not accurate
Accurate but not precise
Inaccurate and Imprecise

54. 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
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 (see next page)
Calculating uncertainty
1) 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
2) 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.
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 (see later)
Categories:
know basics

55. 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.

56. 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

57. significant figures
You should have covered this in more detail in BY131 (also see Harris )
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 (±0.02) x 102 not 93400, and not ±0.02
significant figures
You should have covered this in more detail in BY131 (also see Harris )
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 ±0.02
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 )
Use literature examples and common sense if you are unsure!
Categories:
know basics

58. 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 )
Use literature examples and common sense if you are unsure!

59. 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 ratios
Value = (sample result (±error) : control result (±error))
- we cannot simply add the errors - sometimes they will cancel each other out
propagation of errors
Propagation of Uncertainty (Harris Ch.3-5)
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 ratios
Value = (sample result (±error) : control result (±error))
- we cannot simply add the errors - sometimes they will cancel each other out
How do we combine uncertainties?
can use simple formulae to combine uncertainties
combine one stage at a time
e.g. x = (a/b) + c
1) Combine a and b uncertainty, then
2) 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

60. 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:

61. 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?
So,

62. How do we combine uncertainties?
We can use simple formulae to combine uncertainties
Combine one stage at a time
e.g. x = (a/b) + c
1) Combine a and b uncertainty, then
2) 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

63. 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:
Method:
Calculate x
Calculate ex
Quote result as x ± ex
Square of absolute uncertainties are added (even if result is subtracted)

64. 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 (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 ml = 17.83ml
Absolute uncertainty, ex =
Volume =17.83 (±0.03)ml

65. 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:
Method:
Calculate x
Convert absolute uncertainties to relative uncertainties
Calculate %ex
Convert %ex to ex
Quote result as x ± ex

66. Example question Calculate x Relative uncertainties:
Calculate 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
Relative uncertainties:

67. Example question cont.
Combine
Convert to absolute uncertainty
So,

68. 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:
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

69. 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

70. Example question, cont. Multiply by b Convert to absolute uncertainty
(using correct s.f.)

71. 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

72. 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!

73. 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 = cm3 and Tb = 0.04 cm3. m is known absolutely.

74. y = xm/(Ts - Tb) Look at subtraction first
Measured volume Ts - Tb = ml = 14.97ml
Calculate eTs-Tb
Convert to %eTs-Tb

75. 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

76. Calculate y
Convert relative uncertainty of y to absolute
So,

77. 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
limit of detection & limit of quantitation
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
Limit of Quantitation (LOQ)
The concentration above which precise quantitative measurement is possible
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
Measuring LOD/LOQ
1) 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
2) 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
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

78. 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

79. 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

80. 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

81. 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.
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. It is also a good idea to keep a copy of the notebook (preferably in a separate location). Many employers have their own prescribed 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.
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

82. 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
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. It is also a good idea to keep a copy of the notebook (preferably in a separate location). Many employers have their own prescribed 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.
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

83. 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
reporting
Analytical Documentation
Written analytical procedures are 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
Analytical Documentation for Procedures
Scope and applicability
Samples
Analytes
Ranges
Description and principle of the method
Equipment
Specification
Calibration and qualification
Range of operability
Reference materials and reagents
Preparation
Storage
Health & Safety
Sampling
Methods
Limitations
Analytical Procedure
Preparation of samples
Preparation of standards
Critical factors
Detailed description of all steps
Typical outputs; chromatograms, spectra, etc.
Recording and reporting of data
Method
Rounding and significant figures
Data treatments
Calculation of results
Calibration model
Calculation methods
Assumptions and limitations
Method performance
Statistical measures
Control charting
References & Bibliography
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