Topic 11: Measurement and Topic 11: Measurement and Data ProcessingData Processing

IB Core ObjectiveIB Core Objective

11.1.2 Distinguish between 11.1.2 Distinguish between precisionprecision and and accuracyaccuracy. .

DistinguishDistinguish: Give the differences : Give the differences between two or more different between two or more different

items. (Obj. 2)items. (Obj. 2)

11.1.2 Distinguish between 11.1.2 Distinguish between precisionprecision and and accuracyaccuracy..

Accuracy: Accuracy: How close you are to the How close you are to the true valuetrue value

Precision: Precision: How reproducible your How reproducible your measurements are.measurements are.

11.1.2 Distinguish between 11.1.2 Distinguish between precisionprecision and and accuracyaccuracy..

RandomRandom SystematicSystematic

(Not precise not accurate)(Not precise not accurate) (precise but not accurate) (precise but not accurate)

Good readingGood reading

(precise and accurate)(precise and accurate)

IB Core ObjectiveIB Core Objective

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

Describe:Describe: Give a detailed account. Give a detailed account. (Obj. 2)(Obj. 2)

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

Types of error:Types of error: Random error:Random error: Is caused by Is caused by

measurement estimation when reading measurement estimation when reading equipment. If the measurements are equipment. If the measurements are inconsistent then the lab technique is poor.inconsistent then the lab technique is poor.

Systematic error: Systematic error: Is caused by Is caused by instrumentation error. Technique is good instrumentation error. Technique is good but equipment is faulty or un-calibrated. but equipment is faulty or un-calibrated. This will result in consistent but wrong This will result in consistent but wrong readings.readings.

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

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

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

IB Core ObjectiveIB Core Objective

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

Describe:Describe: Give a detailed Give a detailed account. (Obj. 2)account. (Obj. 2)

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

We will be learning more about this We will be learning more about this when we do labs.when we do labs.

This is also why we ask you to collect This is also why we ask you to collect data several times (3-5 times) for an data several times (3-5 times) for an experiment. experiment.

Repeating should increase the Repeating should increase the precision of the final result since precision of the final result since random variations can be statistically random variations can be statistically cancelled out (or dropped if it is way cancelled out (or dropped if it is way off).off).

IB Core ObjectiveIB Core Objective

11.1.4 State random uncertainty as 11.1.4 State random uncertainty as an uncertainty range (±) an uncertainty range (±)

State: State: Give a specific name, value, Give a specific name, value, or other brief answer without or other brief answer without explanation or calculation.explanation or calculation.

(Obj. 1)(Obj. 1)

11.1.4 State random uncertainty as an uncertainty 11.1.4 State random uncertainty as an uncertainty range (±)range (±)

Absolute uncertainty:Absolute uncertainty: Is the Is the measurement you are guessingmeasurement you are guessing

Ex: Ex: 25.0 cm25.0 cm33 pipette has an absolute pipette has an absolute uncertainty of uncertainty of ±±0.1cm0.1cm33

100cm100cm33 beaker has an absolute beaker has an absolute uncertainty of uncertainty of ±±1cm1cm33

11.1.4 State random uncertainty as an 11.1.4 State random uncertainty as an uncertainty range (±)uncertainty range (±)

Instruments may have the Instruments may have the tolerancetolerance (i.e. (i.e. uncertainty) clearly labeled.uncertainty) clearly labeled.

If the tolerance is not labeled on the If the tolerance is not labeled on the instrument, you will have to determine the instrument, you will have to determine the uncertainty yourself.uncertainty yourself.

A digital scale may bounce around on the A digital scale may bounce around on the last digit (i.e. between 3.759 and 3.760). last digit (i.e. between 3.759 and 3.760). The uncertainty would be The uncertainty would be ±.001. If it ±.001. If it bounces around by five on the last digit, bounces around by five on the last digit, then it would be ± .005.then it would be ± .005.

We will practice this in labs.We will practice this in labs.

IB Core ObjectiveIB Core Objective

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

State: State: Give a specific name, value, Give a specific name, value, or other brief answer without or other brief answer without explanation or calculation.explanation or calculation.

(Obj. 1)(Obj. 1)

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

Estimating the numberEstimating the number Bathroom scale BalanceBathroom scale BalanceGrape fruit 1 11.Grape fruit 1 11.55kg 1.47kg 1.4766kgkgGrape fruit 2 11.Grape fruit 2 11.55kg 1.51kg 1.5188kgkg

Certain digits: Certain digits: The numbers we knowThe numbers we knowUncertain digits: Uncertain digits: The estimated number. The The estimated number. The

bolded numbers represent the guessed digit.bolded numbers represent the guessed digit.Significant FiguresSignificant Figures The number of figures known + one guessed The number of figures known + one guessed

figure.figure. The bathroom scale has: The bathroom scale has: 2 2 sig. Figs. sig. Figs. The balance has: The balance has: 44 sig. Figs sig. Figs

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

Leading Zeros (Zeros toLeading Zeros (Zeros to thethe Left Left of the decimal of the decimal place) place) Don’t count! They are just place holders.Don’t count! They are just place holders.

ValueValue # of sig figs# of sig figs Sci. notationSci. notation

0.00560.0056

000.334g000.334g

0.010.01

0.00001050.0000105

0.00560.0056

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

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

ValueValue Sig figsSig figs

1.001.00

300.300.

300.0300.0

10001000

6.02 x 106.02 x 102323

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

Addition/Subtraction:Addition/Subtraction:When adding and subtracting data, use the When adding and subtracting data, use the

measurement with the least number of measurement with the least number of decimal places.decimal places.

ValueValue # of d.p.# of d.p. AnswerAnswer

0.0056 + 0.0056 + 1.00101.0010

5.5 – 0.135.5 – 0.135.12 x 105.12 x 1033 + + 0.100.10

1.5 – 0.00551.5 – 0.0055

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

Multiplication/ DivisionMultiplication/ DivisionWhen multiplying and dividing, your answer should When multiplying and dividing, your answer should

have the number of sig. figs as the one with the have the number of sig. figs as the one with the least number of sig figs.least number of sig figs.

ValueValue # of sig figs# of sig figs AnswerAnswer

4.56 x 1.44.56 x 1.4

.50 x 100.50 x 100

25.0 25.0 ÷ 5.00÷ 5.00

1.0 x 101.0 x 1022 ÷ 5÷ 5

IB Core ObjectiveIB Core Objective

11.2.1 State uncertainties as absolute 11.2.1 State uncertainties as absolute and percentage uncertainties.and percentage uncertainties.

State: State: Give a specific name, value, Give a specific name, value, or other brief answer without or other brief answer without explanation or calculation.explanation or calculation.

(Obj. 1)(Obj. 1)

11.2.1 State uncertainties as absolute and 11.2.1 State uncertainties as absolute and percentage uncertainties.percentage uncertainties.

Percent uncertainty: Percent uncertainty: Absolute uncertaintyAbsolute uncertainty x 100 x 100Amount usedAmount used

If we take a 30cmIf we take a 30cm33 sample in the 100cm sample in the 100cm33 beaker (with beaker (with a a ± 1 uncertainty) ± 1 uncertainty) what is the % uncertainty?what is the % uncertainty?

% uncertainty = 1/30 x 100 % uncertainty = 1/30 x 100 3.33% 3.33%

If we take a 90cmIf we take a 90cm33 sample in the 100cm sample in the 100cm33 beaker what beaker what is the % uncertainty?is the % uncertainty?

% uncertainty = 1/90 x 100 % uncertainty = 1/90 x 100 1.11% 1.11%

This is why taking small samples with a large This is why taking small samples with a large beaker is not a good idea! Use the proper beaker is not a good idea! Use the proper tool!!tool!!

IB Core ObjectiveIB Core Objective

11.2.2 Determine the 11.2.2 Determine the uncertainties in results.uncertainties in results.

Determine:Determine: Find the only possible Find the only possible answer. (Obj. 3)answer. (Obj. 3)

11.2.2 Determine the uncertainties in 11.2.2 Determine the uncertainties in results.results.

Adding/ Subtracting uncertaintiesAdding/ Subtracting uncertainties

Just add the uncertainties of each piece Just add the uncertainties of each piece of equipmentof equipment

Add the two volumes from the previous Add the two volumes from the previous exampleexample

30 (30 (±±1)1)

+90(+90(±±1)1)

120 (120 (±±2) 2) (So range is 118-122)cm (So range is 118-122)cm33..

% uncertainty = 2 % uncertainty = 2 ÷ ÷ 120 x 100 120 x 100 0.83% 0.83%

11.2.2 Determine the uncertainties in 11.2.2 Determine the uncertainties in results.results.

Multiply/Dividing uncertaintiesMultiply/Dividing uncertainties Each measurement must have the % Each measurement must have the %

uncertainty calculated.uncertainty calculated. The % uncertainties are then addedThe % uncertainties are then added The final % uncertainty is then used to The final % uncertainty is then used to

re-calculate the final absolute re-calculate the final absolute uncertainty.uncertainty.

Scale = 5.000g (Scale = 5.000g (±±0.001) 0.001)

Pipette = 50.00cmPipette = 50.00cm33 ( (±±0.01)0.01)

Graduated cylinder = 25.0cmGraduated cylinder = 25.0cm33 ( (±0.05)±0.05)

11.2.2 Determine the uncertainties in 11.2.2 Determine the uncertainties in results.results.

AnswerAnswer

0.001 0.001 ÷ 5.000 x 100 = 0.02%÷ 5.000 x 100 = 0.02%0.01 ÷ 50.00 x 100 = 0.02%0.01 ÷ 50.00 x 100 = 0.02%0.05 ÷ 25.0 x 100 = 0.2%0.05 ÷ 25.0 x 100 = 0.2%Total percentage = 0.24%Total percentage = 0.24%

If the molar mass in the end was determined If the molar mass in the end was determined to be 64.0 g/mol, thento be 64.0 g/mol, then

0.0024 x 64.0 = 0.1536,0.0024 x 64.0 = 0.1536,So final answer is 64.0 g/mol ± 0.2gSo final answer is 64.0 g/mol ± 0.2g