ACSI 2022 HL Measurement and Data Processing (Teacher) (1)

IBDP Chemistry HL/ Measurement and Data Processing Page 1 Anglo − Chinese School (Independent) Year 5 (2022) IBDP Chemistry HL (IBDP syllabus Topic 11) 11.1 Uncertainties and errors in measurement and results (SL and HL) - Essential Idea: all measurement has a limit of precision and accuracy, and this must be taken into account when evaluating experimental results 11.2 Graphical techniques (SL and HL) - Graphs are a visual representation of trends in data TOPIC 11 MEASUREMENT AND DATA PROCESSING TEACHER COPY – WITH SUGGESTED SOLUTIONS

IBDP Chemistry HL/Measurement and Data Processing Page 2 11.1 Uncertainties and Errors in Measurement and Results  Nature of Science: • Making quantitative measurements with replicates to ensure reliability – precision, accuracy, systematic, and random errors must be interpreted through replication. (3.2, 3.4) Understandings: • Qualitative data includes all non- numerical information obtained from observations not from measurement. • Quantitative data are obtained from measurements, and are always associated with random errors/uncertainties, determined by the apparatus, and by human limitations such as reaction times. • Propagation of random errors in data processing shows the impact of the uncertainties on the final result. • Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction. • Repeat trials and measurements will reduce random errors but not systematic errors. Applications and skills: • Distinction between random errors and systematic errors. • Record uncertainties in all measurements as a range (+) to an appropriate precision. • Discussion of ways to reduce uncertainties in an experiment. • Propagation of uncertainties in processed data, including the use of percentage uncertainties. • Discussion of systematic errors in all experimental work, their impact on the results and how they can be reduced. • Estimation of whether a particular source of error is likely to have a major or minor effect on the final result. • Calculation of percentage error when the experimental result can be compared with a theoretical or accepted result. • Distinction between accuracy and precision in evaluating results. Guidance: • The number of significant figures in a result is based on the figures given in the data. When adding or subtracting, the final answer should be given to the least number of decimal places. When multiplying or dividing the final answer is given to the least number of significant figures. • Note that the data value must be recorded to the same precision as the random error. • SI units should be used throughout the programme. International–mindedness: • As a result of collaboration between seven international organizations, including IUPAC, the International Standards Organization (ISO) published the Guide to the Expression of Uncertainty in Measurement i n 1995. This has been widely adopted in most countries and has been translated into several languages. Theory of knowledge: • Science has been described as a self –correcting and communal public endeavour. To what extent do these characteristics also apply to the other areas of knowledge?

IBDP Chemistry HL/Measurement and Data Processing Page 3 Aims: • Aim 6: The distinction and different roles of Class A and Class B glassware could be explored. • Aim 8: Consider the moral obligations of sci entists to communicate the full extent of their data, including experimental uncertainties. The “cold fusion” case of Fleischmann and Pons in the 1990s is an example of when this was not fulfilled. 11.2 Graphical Techniques  Nature of Science: • The idea of correlation – can be tested in experiments whose results can be displayed graphically. (2.8) Understandings: • Graphical techniques are an effective means of communicating the effect of an independent variable on a dependent variable, and can lead to determination of physical quantities. • Sketched graphs have labelled but unsc aled axes, and are used to show qualitative trends, such as variables that are proportional or inversely proportional. • Drawn graphs have labelled and scal ed axes, and are used in quantitative measurements. Applications and skills: • Drawing graphs of experimental results including the correct choice of axes and scale. • Interpretation of graphs in terms of the relationships of dependent and independent variables. • Production and interpretation of best -fit lines or cu rves through data points, including an assessment of when it can and cannot be considered as a linear function. • Calculation of quantities from graphs by measuring slope (gradient) and intercept, including appropriate units. International–mindedness: • Charts and graphs, which largely transcend language barriers, can facilitate c ommunication between scientists worldwide. Aims: • Aim 7 : Graph-plotting software may be used, including the use of spreadsheets and the derivation of best-fit lines and gradients.

IBDP Chemistry HL/Measurement and Data Processing Page 4 Quantitative Chemistry: Errors and uncertainties in chemistry 11.1.1 Why do we learn about Errors and Uncertainties in Chemistry? 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 sciences. The evaluation of the reliability of the data upon which conclusions can be drawn is at the heart of a wider scientific method, which is explained in section 3 of the “Nature of science” part of the subject guide. The treatment of errors and uncertainties is also directly relevant to the internal assessment criteria of: • Exploration (“The methodology is highly appropriate to address the research question because it takes into consideration all, or nearly all, of the significant factors that may influence the relevance, reliability and sufficiency of the collected data.”) • Analysis (“The report shows evidence of full and appropriate consideration of the impact of measurement uncertainty on the analysis.”) • Evaluation (“Strengths and weaknesses of the investigation, such as limitations of the data and sources of error, are discussed and provide evidence of a clear understanding of the methodological issues involved in establishing the conclusion.”) Expectations (SL and HL): Within practical work, students should be able to: • design procedures that allow for relevant data to be collected, in which systematic errors are minimized and random errors are reduced through the choice of appropriate techniques and measuring instruments , and by incorporating sufficient repeated measurement where appropriate • make a quantitative record of uncertainty range • state the results of calculations to the appropriate number of significant figures . Th e number of significant figures in any answer should reflect the number of significant figures in the given data • propagate uncertainties through a calculation to determine the uncertainties in calculated results and state them as absolute and/or percentage uncertainties. Only a simple treatment is required. For functions such as addition and subtraction, absolute uncertainties can be added; for multiplication, division and powers, percentage uncertainties can be added. If one uncertainty is much larger than the others, the approximate uncertainty in the calculated result can be taken as due to that quantity alone • determine from graphs, physical quantities (with units) by measuring and interpreting a slope (gradient) or intercept. When constructing graphs from experimental data