uncertainties salters a2 1. 2 salters b there is guidance as to what the error is acknowledged to be...
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Uncertainties
Salters A2
1
2
Salters B
There is guidance as to what the error is acknowledged to be if it is not stated on the apparatus
It is generally taken to be the smallest unit on the scale being used
eg if a balance weighs to 0.01g the error uncertainty is taken as +/- 0.01g
Salters B
There is guidance as to what the error is acknowledged to be if it is not stated on the apparatus
It is generally taken to be the smallest unit on the scale being used
eg if a balance weighs to 0.01g the error uncertainty is taken as +/- 0.01g
Uncertainty Variation – Why?
• Example:
• Electronic set top balance • Reading is 2.05g• What range of values could it actually be?
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Deciding on precision – Volumetric glassware
CLASS: Class B has twice the tolerance of class A
CLASS: Class B has twice the tolerance of class A
Maximum volume/cm3Maximum volume/cm3
Tolerance / ± xcm3
Tolerance / ± xcm3
Temperature for true volumeTemperature for true volume
Flask
Graduated pipette
StandardStandard
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Volumetric equipment – class B
Flasks:Flasks:Capacity/ cm3 Accuracy limit / ±
cm3
5, 10 0.0515 0.06
20,25 0.0850 0.12
100, 250 0.20500 0.50
Standards: DIN, ISO and BS) BS1792:1982(93)http://www.reagecon.com/TechPapers/volumetricglassware.pdf
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Volumetric equipment – class BBulb pipettes:Bulb pipettes: Capacity/ cm3 Accuracy limit / ±
cm3
1 0.0162 0.025 0.03
10 0.04 25 0.0650 0.10
Standards: One Mark Bulb pipettes: DIN, ISO, BS)(ISO648)http://www.reagecon.com/TechPapers/volumetricglassware.pdf
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Volumetric equipment – class BGraduated pipettes:Graduated pipettes: Capacity/ cm3 Accuracy limit / ±
cm3
1 0.0125 0.06
10 0.1025 0.20
Standards: Graduated pipettes:(USP, DIN, ISO, BS)(ISO835http://www.reagecon.com/TechPapers/volumetricglassware.pdf
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Volumetric equipment – class B
BuretteBuretteCapacity/ cm3 Accuracy limit / ±
cm3
10 0.04025 0.0650 0.10
100 0.26
http://www.titrations.info/pipette-burette
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Volumetric equipment – Calculated example
The uncertainty associated with a grade B 25 cm3 pipette is 0.06 cm3 or 0.24% . This is calculated as follows:
The uncertainty associated with a grade B 25 cm3 pipette is 0.06 cm3 or 0.24% . This is calculated as follows:
%24.0%100cm 25
0.06cm
100%x valueEffective
Tolerance
3
3
x
10
For a 250 cm3 volumetric flask the uncertainty is 0.20 cm3.For a 250 cm3 volumetric flask the uncertainty is 0.20 cm3.
%080.0%100cm 250
0.20cm
100%x Value Effective
yuncertaint Absolute
3
3
x
Volumetric equipment
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For volume measurements, the precision of a 25 cm3 measuring cylinder is 0.1 cm3:For volume measurements, the precision of a 25 cm3 measuring cylinder is 0.1 cm3:
0.25% 100%x cm 20
cm 0.05%
3
3
U
Eg for 20cm3 of a solution:Eg for 20cm3 of a solution:
100%x Value Effective
Precision21
Measuring Cylinder
e.g. for 1.27g of iodine:e.g. for 1.27g of iodine:
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For mass measurements, the precision of a 2d.p. balance is 0.01g:For mass measurements, the precision of a 2d.p. balance is 0.01g:
0.394% 100%x 1.27g
0.005g% U
100%x valueEffective
Precision 21
Mass
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Total % uncertainty =
% U of mass or% U of volume (measuring cylinder or pipette)+ % U of volumetric flask
Total % uncertainty =
% U of mass or% U of volume (measuring cylinder or pipette)+ % U of volumetric flask
Making a solution
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Example 1
250 cm3 of 0.2M iron (III) chloride solution250 cm3 of 0.2M iron (III) chloride solution
%037.0%100515.13
005.0% x
g
gU
MassMass
%080.0%100250
20.0%
3
3
xcm
cmU
Volume (volumetric flask)
Volume (volumetric flask)
%117.0%080.0%037.0% TUTotalTotal
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Example 2
250 cm3 of 0.2M HCl250 cm3 of 0.2M HCl
%7.0%1000.7
05.0%
1.2%
%5.0%1000.10
05.0%
3
3
3
3
xcm
cmU
xcm
cmUVolume
(10 cm3 measuring cylinder
Volume (10 cm3 measuring cylinder
%080.0%100250
20.0%
3
3
xcm
cmUVolume
(flask)Volume (flask)
%28.1%080.0%2.1% TUTotalTotal
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Comment:
The overall percentage uncertainty in measuring a volume of reagent for dilution is higher because three pieces of equipment were used (even if one was the same, it was used twice), and this piece of equipment had a lower precision than for the dilution of the solid reagent.
In general, the more equipment that is used, the greater the %U for that procedure.In general, the more equipment that is used, the greater the %U for that procedure.
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For titration measurements, the uncertainty in each reading is:For titration measurements, the uncertainty in each reading is:
valuefinalin % valueinitialin % UU
The % U in the titre is:The % U in the titre is:
Titrations
100%x Value Effective
Precision21
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Comment:
Clearly, if the initial burette reading is 0.0 cm3, then it is unreasonable to include this in the calculation since it would return an infinite error.
To overcome this, use 2 x %U in final burette reading.
It is the same reasoning that tells you that the uncertainty in measuring a piece of paper with a mm-precision ruler is ± at either end, ie 2 x precision.
infinity0.0
05.03
3
cm
cm
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Comment:
The burette itself has an inherent error over the whole volume range (0.10cm3 for a 50 cm3 burette).
This could be included in the overall error by adding the %U due to this:
%100Titre
) Abs%
Ua10.00.50
)(
3
3
33
3
x) (cm
U (cmU
bsolutecmxcm
cmtitre
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Multiple additions
Multiple additions from a burette when it is not refilled can be treated as though the burette had been refilled.
Multiple additions from a burette when it is not refilled can be treated as though the burette had been refilled.
Adding to the reaction mixture from several burettes containing different substances:
%U from each burette must be calculated and the values added together
Adding to the reaction mixture from several burettes containing different substances:
%U from each burette must be calculated and the values added together
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Standard Curves
When creating a standard curve, the % U of each measurement and for the colorimeter must be added together to obtain the overall % U for the curve.
When creating a standard curve, the % U of each measurement and for the colorimeter must be added together to obtain the overall % U for the curve.
This may produce a high overall %U but remember, this is the MAXIMUM possible %UThis may produce a high overall %U but remember, this is the MAXIMUM possible %U
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Example: Standard Curve
Salicylic acid/mol dm-3
Volume FeCl3/cm3
Volume Salicylic acid/cm3
Volume Water/cm3
0 10 0 100.004 10 2 80.008 10 4 60.012 10 6 40.016 10 8 20.020 10 10 0
Volumes added using 3 burettes. Salicylic acid dilutions used 50cm3 volumetric flasks and 1cm3 pipettesVolumes added using 3 burettes. Salicylic acid dilutions used 50cm3 volumetric flasks and 1cm3 pipettes
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Uncertainty in standard curve
Dilution of salicylic acid: 50cm3 ± 0.12cm3 volumetric flaskDilution of salicylic acid: 50cm3 ± 0.12cm3 volumetric flask
%2.1%10050
12.0 5%
3
3
x
cm
cmxU
Transfer of salicylic acid: 1.0cm3 ± 0.012cm3 pipetteTransfer of salicylic acid: 1.0cm3 ± 0.012cm3 pipette
%6%1001
012.0 5%
3
3
x
cm
cmxU
Note, 5 volumes of 1cm3 were used in the whole curve
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Uncertainty in standard curve
INITIAL burette reading – salycilic acidINITIAL burette reading – salycilic acid
%7.5%1002
05.0%100
4
05.0
%1006
05.0%100
8
05.0%100
10
05.0%
3
3
3
3
3
3
3
3
3
3
xcm
cmx
cm
cm
xcm
cmx
cm
cmx
cm
cmU
FINAL burette reading – salycilic acidFINAL burette reading – salycilic acid
%7.5%1002
05.0%100
4
05.0
%1006
05.0%100
8
05.0%100
10
05.0%
3
3
3
3
3
3
3
3
3
3
xcm
cmx
cm
cm
xcm
cmx
cm
cmx
cm
cmU
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Uncertainty in standard curve
INITIAL burette reading – Iron (III) ChlorideINITIAL burette reading – Iron (III) Chloride
%3%10010
05.0 6%
3
3
x
cm
cmxU
FINAL burette reading –Iron (III) Chloride FINAL burette reading –Iron (III) Chloride
%3%10010
05.0 6%
3
3
x
cm
cmxU
Note, 6 volumes of 10cm3 were used
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Uncertainty in standard curve
INITIAL burette reading - waterINITIAL burette reading - water
%7.5%1002
05.0%100
4
05.0
%1006
05.0%100
8
05.0%100
10
05.0%
3
3
3
3
3
3
3
3
3
3
xcm
cmx
cm
cm
xcm
cmx
cm
cmx
cm
cmU
FINAL burette reading – waterFINAL burette reading – water
%7.5%1002
05.0%100
4
05.0
%1006
05.0%100
8
05.0%100
10
05.0%
3
3
3
3
3
3
3
3
3
3
xcm
cmx
cm
cm
xcm
cmx
cm
cmx
cm
cmU
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Uncertainty in standard curve
ColorimeterColorimeter
%33%10063.0
005.0%100
52.0
005.0%100
37.0
005.0
%10026.0
005.0%100
16.0
005.0%100
02.0
005.0%
xxx
xxxU
Total % Uncertainty = (1.2 + 6+ 3+3+5.7+5.7+5.7+5.7+33)%
= 69% (2sf is enough)
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Example 2: Gas Syringe
Precision of gas syringe – 1cm3.Precision of gas syringe – 1cm3.
100%x Value Effective
Precision%
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U
Find the uncertainties for all other measurements, eg balance, making solutions and the measurement of your independent variable (e.g.time) add to the %U of the gas syringe.
Find the uncertainties for all other measurements, eg balance, making solutions and the measurement of your independent variable (e.g.time) add to the %U of the gas syringe.
For the single curve resulting from one value of your variable, add together all of your %U to give you the overall %U for that experiment.
For the single curve resulting from one value of your variable, add together all of your %U to give you the overall %U for that experiment.
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Example 2: Gas Syringe
%33%10063.0
005.0%100
52.0
005.0%100
37.0
005.0
%10026.0
005.0%100
16.0
005.0%100
02.0
005.0%
xxx
xxxU
If a gas syringe method is used to measure a rate of reaction at different substrate concentrations or other condition, then the error for your reaction rate curve should, theoretically be the sum of all %U from the individual curves from which the initial rate (gradient) was taken.
The %U from the smallest values, closest to the origin, are likely to be the highest, and so it is not unreasonable to add together the largest individual uncertainties from each individual curve in order to approximate an overall maxiumum %U in the derived reaction rate curve if that is your intent.
However, this calculation is not really necessary of you are looking for the order of a reaction, since the shape of the resulting curve is all you need.
Improvements to technique
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http://www.titrations.info/pipette-burette
The bottom of the concave meniscus must be precisely on a calibration mark. To make reading of the meniscus position easier we can use piece of paper with a horizontal black stripe, about an inch and half wide.
If the paper is held half an inch behind a burette with the stripe about a half an inch below the meniscus, the solution surface seems to be black and is much easier to see.
Precision for burettes and graduated pipettes