errors and uncertainties in chemistry internal assessment the consideration and appreciation of the...

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).

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.

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.

• Random uncertainties or errors arise

from the inadequacies or limitations in the instrument.

• 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.

Random uncertainties

1.5 ± 0.1

uncertainty of the measurement due to the limitation of the instrument

Random uncertainties

1.5 ± 0.1 in

Means that the true value can be in between 1.4 and 1.6

• Random uncertainties

What is the length of the object?

1.52 in ???

No, you can estimate only ONE DIGIT, NOT TWO!

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!!!

For uncertainties of the digital equipments,

± the smallest digit that could be measured on that equipment.

Uncertainties in measurements…

2.000 ±0.001 g

While making measurements…

• always remember to estimate ONE MORE DIGIT!!!

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

Significant figures(carry meaning contributing

to its precision)…

Total # of digits that we’re certain

of+ # of the digit

estimated (1)

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

How can we reduce the random errors?

• repeat measurements, 5 TRIALS AT LEAST!

• use more precise measuring equipment (?????)

MOST EFFECTIVE!!!

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?

More precise equipment is…

• the one that gives more digits to the right of the decimal point in measurements.

Precision vs Accuracy in measurements

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?

• 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

Accuracy• is usually calculated as “PERCENTAGE

ERROR.”

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:

Precision vs Accuracy in measurements

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