Errors and uncertainties in chemistry internal assessment The consideration and appreciation of the...
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![Page 1: Errors and uncertainties in chemistry internal assessment The consideration and appreciation of the significance of the concepts of errors and uncertainties.](https://reader036.fdocuments.us/reader036/viewer/2022070305/5514316a550346dd488b5fea/html5/thumbnails/1.jpg)
Errors and uncertainties in chemistry internal assessment
• The consideration and appreciation of the significance of the concepts of errors and uncertainties helps to develop skills of inquiry and thinking that are not only relevant to the group 4 experimental sciences
• The treatment of errors and uncertainties is directly relevant in the internal assessment criteria of:– data collection and processing, (recording raw data
and presenting processed data)– conclusion and evaluation, aspects 1, 2 and 3
(concluding, evaluating procedure(s), and improving the investigation).
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Within internal assessment students should be able to do the following:
• make a quantitative record of uncertainty range (±)
• state the results of calculations to the appropriate number of significant figures.
• propagate uncertainties through a calculation so
as to determine the uncertainties in calculated results and to state them as absolute and/or percentage uncertainties.
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Random and systematic errors
• Systematic errors arise from a problem in the experimental set-up that results in the measured values always deviating from the “true” value in the same direction, that is, always higher or always lower.
• Examples of causes of systematic error are miscalibration of a measuring device or poor insulation in calorimetry experiments.
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• Random uncertainties or errors arise
from the inadequacies or limitations in the instrument.
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• Random uncertainties
What is the length of the object?
The ruler has scale markings every inch. You must divide each inch to 10 equal parts w/ your eyes and estimate the length of the object to the nearest 1/10 of an inch.
ANSWER: 1.5 or 1.4 or 1.6. We’re not certain about the first place after the decimal place.Hence we should record this value as 1.5 ± 0.1.
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Random uncertainties
1.5 ± 0.1
uncertainty of the measurement due to the limitation of the instrument
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Random uncertainties
1.5 ± 0.1 in
Means that the true value can be in between 1.4 and 1.6
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• Random uncertainties
What is the length of the object?
1.52 in ???
No, you can estimate only ONE DIGIT, NOT TWO!
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Uncertainties in measurements…
• form the random errors in the investigations
• will always be determined as 1/10th of the LEAST CERTAIN DIGIT on the MANUAL EQUIPMENTS!!!
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For uncertainties of the digital equipments,
± the smallest digit that could be measured on that equipment.
Uncertainties in measurements…
2.000 ±0.001 g
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While making measurements…
• always remember to estimate ONE MORE DIGIT!!!
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Random uncertainties
1.5 in
Total # of digits that we’re certain of + the # of the
digit estimated (1)= total # of significant figures in that measurement
digit we’re certain of digit we
estimated
2 sf
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Significant figures(carry meaning contributing
to its precision)…
Total # of digits that we’re certain
of+ # of the digit
estimated (1)
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Can we eliminate the random errors?
• No, we can only reduce them.
• the uncertainty is reduced, but it can never be completely eliminated. When recording raw data, estimated uncertainties should always be indicated for all measurements
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How can we reduce the random errors?
• repeat measurements, 5 TRIALS AT LEAST!
• use more precise measuring equipment (?????)
MOST EFFECTIVE!!!
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Learning check
top Ruler: ........1.5 ± 0.1 in bottom Ruler: 1.46 ± 0.01in
What is the length of the object on both rulers?
Which ruler is more precise?
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More precise equipment is…
• the one that gives more digits to the right of the decimal point in measurements.
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Precision vs Accuracy in measurements
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Precision vs Accuracy in measurements
• The theoretical value of R (ideal gas law constant)=8.314 J/molK
• Student A found it as 8.34 ± 0.03 J/molK
• Student B found it as 8.513 ± 0.006 J/molK
Which one is more accurate and which one is more precise?
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• Student A found it as 8.34 ± 0.03 J/molK
(more accurate)
• Student B found it as 8.513 ± 0.006 J/molK
(more precise)
Precision vs Accuracy in measurements
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Accuracy• is usually calculated as “PERCENTAGE
ERROR.”
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8.314 - 8.34
8.314
= 0.31 %
8.314 - 8.513
8.314
= 2.39 % (less accurate)
AccuracyLet’s determine the accuracy of the student A’s and B’s results by calculating the % errors:
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Precision vs Accuracy in measurements
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C. Estimating the uncertainity ( propogation of errors )
Device Example Uncertainity
Analogue scale Ruler,voltmeter,ammeter ,graduated cylinder, thermometer, watch, stopwatch,meters with moving pointers.
1/10th of the smallest scale division
Digital scale Top-pan balances , digital meters,voltmeter,pH meter
the smallest scale division
Reflex time of a person 0.2 seconds