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Topic 11. Measurement and data processing SL SL. Uncertainty and error in measurement All measurements have always some degree of uncertainty.

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Presentation on theme: "Topic 11. Measurement and data processing SL SL. Uncertainty and error in measurement All measurements have always some degree of uncertainty."— Presentation transcript:

1 Topic 11. Measurement and data processing SL SL

2 Uncertainty and error in measurement All measurements have always some degree of uncertainty.

3 E.g. How to read a pipettes volume: The right way to read a pipette a. But is it not possible to hit the line exact every time => Random uncertainty. Some time little too much and sometime little to little. By repeating experiments/measurements you can reduce the random uncertainties.

4 If the volume is important in an experiment then you should use the right kind of equipment to reduce the random uncertainty. E.g. a measuring cylinder is more accurate than a beaker. Why?

5 If you use method b. The wrong way => Systematic error. The volume will always be to low, can’t be reduced by repeating measurements It is always important to calibrate equipment to reduce the systematic errors.

6 Precision and Accuracy a.Neither accurate nor precise (large random uncertainty) b.Precise but not accurate. (Small random uncertainty, large systematic error) c.Both precise and accurate (Small random and systematic error)

7 Random uncertainty as an uncertainty range (±) The scale on burettes is normally divided in 0.1 ml lines. That gives you an uncertainty of 0.05 ml. So when you have measured a volume, the true volume can be 0.05 ml more or less. E.g. 15.6 ± 0.05 ml

8 Significant figures. The number of significant figures in any answer should reflect the number of significant figures in given data.

9 Uncertainties in calculated results 15.6 ± 0.05 ml. The absolute uncertainty = 0.05 ml 0.05/15.6 = 0.003 => Percentage uncertainty =0.3%

10 Determine the uncertainties in results Only a simple treatment is required Addition and subtraction: absolute uncertainties can be added V 1 =15.6 ± 0.05 ml V 2 =13.2 ± 0.05 ml The absolute uncertainties = 0.05 ml V tot = V 1 + V 2 = 15.6 ± 0.05 + 13.2 ± 0.05 ml= 28.8 ± 0.10 ml

11 Determine the uncertainties in results. Only a simple treatment is required Multiplication, division and powers: percentages uncertainties can be added V=15.6 ± 0.05 dm 3 0.05/15.6 = 0.003 => Percentage uncertainty =0.3% c = 2.00 ± 0.005 mol/dm 3 0.005/ 2.00 = 0.0025 => Percentage uncertainty =0.25 % n=c*V= 2.00 *15.6 = 31.2 mol Percent uncertainty 0.3 + 0.25 = 0.55 % Absolute uncertainty 0.0055*31.2=0.17 Answer n= 31.2 ± 0.17 mol

12 Graphical techniques Axis should be labelled with quantity divided by units. E.g. mass / g On the x-axis you shall have the independent variable. The variable that you can decide over/can control. In the experiment you will collect values at different independent values. This collected values are called dependent values.

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14 You shall set the scale on the axis so you use most of the paper:

15 The best fit line will also work as uncertainty analysis.

16 The equation of a straight line: y = mx + c Determining the slope/gradient: Gradient = (y 2 –y 1 )/(x 2 -x 1 ) =  y  x


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