created with mindgenius business 2005® ch217 fundamentals of analytical chemistry ch217...

Created with MindGenius Business 2005®

CH217Fundamentals of Analytical

Chemistry

Module Leader: Dr. Alison Willows


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


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!


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


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 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


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.


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

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, cont.

Method validation Reporting and interpretation (results

& discussion) Drawing conclusions (answering the

question!)


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


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.


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

http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/goldmine.asp


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


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.


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


Sampling - stages

Horwitz. Pure and Applied Chemistry, 1990, 62, 1193-1208.


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.


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


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


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)


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


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


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


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 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


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.


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

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


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


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


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


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

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


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


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


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


validation

Standards Performance parameters Errors in Analysis Record Keeping


“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.


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.


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 .


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


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


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


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


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 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.


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!


Accuracy and precision

Accurate and Precise

Inaccurate and Imprecise

Accurate but not precise

Precise but not accurate


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


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.


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


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


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!


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


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


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,


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


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)


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


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



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


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


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



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


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


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


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!


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.


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


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


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


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


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


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


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


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

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


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

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