Topic 11: Measurement and Data Processing

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• Topic 11 Measurement and Data Processing
• IB Core Objective
• 11.1.2 Distinguish between precision and
  accuracy.
• Distinguish Give the differences between two or
  more different items. (Obj. 2)

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11.1.2 Distinguish between precision and accuracy.

• Accuracy How close you are to the true value
• Precision How reproducible your measurements
  are.

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11.1.2 Distinguish between precision and accuracy.

• Random Systematic
• (Not precise not accurate) (precise
  but not accurate)
• Good reading
• (precise and accurate)

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IB Core Objective

• 11.1.1 Describe and give examples of random
  uncertainties and systematic errors.
• Describe Give a detailed account. (Obj. 2)

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11.1.1 Describe and give examples of random
uncertainties and systematic errors.

• Types of error
• Random error Is caused by measurement estimation
  when reading equipment. If the measurements are
  inconsistent then the lab technique is poor.
• Systematic error Is caused by instrumentation
  error. Technique is good but equipment is faulty
  or un-calibrated. This will result in consistent
  but wrong readings.

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11.1.1 Describe and give examples of random
uncertainties and systematic errors.

• A random uncertainty can arise from inadequacies
  or limitations in the instrument, such as
  pinpointing the reading of a burette or graduated
  cylinder.

Examples of a systematic error can be from
reading a burette from the wrong direction,
reading the top of the meniscus instead of the
bottom, or using equipment that is not well
calibrated.
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IB Core Objective

• 11.1.3 Describe how the effects of random
  uncertainties may be reduced.
• Describe Give a detailed account. (Obj. 2)

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11.1.3 Describe how the effects of random
uncertainties may be reduced.

• We will be learning more about this when we do
  labs.
• This is also why we ask you to collect data
  several times (3-5 times) for an experiment.
• Repeating should increase the precision of the
  final result since random variations can be
  statistically cancelled out (or dropped if it is
  way off).

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IB Core Objective

• 11.1.4 State random uncertainty as an uncertainty
  range ()
• State Give a specific name, value, or other
  brief answer without explanation or calculation.
• (Obj. 1)

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11.1.4 State random uncertainty as an uncertainty
range ()

• Absolute uncertainty Is the measurement you are
  guessing
• Ex 25.0 cm3 pipette has an absolute
  uncertainty of 0.1cm3
• 100cm3 beaker has an absolute uncertainty of
  1cm3

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11.1.4 State random uncertainty as an uncertainty
range ()

• Instruments may have the tolerance (i.e.
  uncertainty) clearly labeled.
• If the tolerance is not labeled on the
  instrument, you will have to determine the
  uncertainty yourself.
• A digital scale may bounce around on the last
  digit (i.e. between 3.759 and 3.760). The
  uncertainty would be .001. If it bounces around
  by five on the last digit, then it would be
  .005.
• We will practice this in labs.

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IB Core Objective

• 11.1.5 State the results of calculations to the
  appropriate number of significant figures
• State Give a specific name, value, or other
  brief answer without explanation or calculation.
• (Obj. 1)

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11.1.5 State the results of calculations to the
appropriate number of significant figures

• Estimating the number
• Bathroom scale
  Balance
• Grape fruit 1 11.5kg
  1.476kg
• Grape fruit 2 11.5kg
  1.518kg
• Certain digits The numbers we know
• Uncertain digits The estimated number. The
  bolded numbers represent the guessed digit.
• Significant Figures
• The number of figures known one guessed
  figure.
• The bathroom scale has 2 sig. Figs.
• The balance has 4 sig. Figs

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11.1.5 State the results of calculations to the
appropriate number of significant figures

• Leading Zeros (Zeros to the Left of the decimal
  place) Dont count! They are just place holders.

Value of sig figs Sci. notation
0.0056
000.334g
0.01
0.0000105
0.0056
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11.1.5 State the results of calculations to the
appropriate number of significant figures

• Trailing Zeros (Zeros to the Right End of the
  number) Only count when the number contains a
  decimal place.

Value Sig figs
1.00
300.
300.0
1000
6.02 x 1023
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11.1.5 State the results of calculations to the
appropriate number of significant figures

• Addition/Subtraction
• When adding and subtracting data, use the
  measurement with the least number of decimal
  places.

Value of d.p. Answer
0.0056 1.0010
5.5 0.13
5.12 x 103 0.10
1.5 0.0055
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11.1.5 State the results of calculations to the
appropriate number of significant figures.

• Multiplication/ Division
• When multiplying and dividing, your answer should
  have the number of sig. figs as the one with the
  least number of sig figs.

Value of sig figs Answer
4.56 x 1.4
.50 x 100
25.0 5.00
1.0 x 102 5
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IB Core Objective

• 11.2.1 State uncertainties as absolute and
  percentage uncertainties.
• State Give a specific name, value, or other
  brief answer without explanation or calculation.
• (Obj. 1)

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11.2.1 State uncertainties as absolute and
percentage uncertainties.

• Percent uncertainty Absolute uncertainty x 100
• Amount used
• If we take a 30cm3 sample in the 100cm3 beaker
  (with a 1 uncertainty) what is the
  uncertainty?
• uncertainty 1/30 x 100 ? 3.33
• If we take a 90cm3 sample in the 100cm3 beaker
  what is the uncertainty?
• uncertainty 1/90 x 100 ? 1.11
• This is why taking small samples with a large
  beaker is not a good idea! Use the proper tool!!

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IB Core Objective

• 11.2.2 Determine the uncertainties in results.
• Determine Find the only possible answer. (Obj. 3)

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11.2.2 Determine the uncertainties in results.

• Adding/ Subtracting uncertainties
• Just add the uncertainties of each piece of
  equipment
• Add the two volumes from the previous example
• 30 (1)
• 90(1)
• 120 (2) ? (So range is 118-122)cm3.
• uncertainty 2 120 x 100 ? 0.83

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11.2.2 Determine the uncertainties in results.

• Multiply/Dividing uncertainties
• Each measurement must have the uncertainty
  calculated.
• The uncertainties are then added
• The final uncertainty is then used to
  re-calculate the final absolute uncertainty.
• Scale 5.000g (0.001)
• Pipette 50.00cm3 (0.01)
• Graduated cylinder 25.0cm3 (0.05)

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11.2.2 Determine the uncertainties in results.

• Answer
• 0.001 5.000 x 100 0.02
• 0.01 50.00 x 100 0.02
• 0.05 25.0 x 100 0.2
• Total percentage 0.24
• If the molar mass in the end was determined to be
  64.0 g/mol, then
• 0.0024 x 64.0 0.1536,
• So final answer is 64.0 g/mol 0.2g