Chapter 11 Notes Chapter 11.1 All measurement has a limit of precision and accuracy, and this must be taken into account when evaluating experimental results.

Terms for this section Uncertainty Significant figures Addition/subtraction Multiplication/division Analogue vs digital instruments Errors Random errors Systematic errors Accuracy vs precision Percentage Uncertainty Error Propagation of uncertainty Addition/subtraction Mulitplication/division

Uncertainty in measurement Uncertainty of the measurement is dependent on the instrument used Analogue instruments Many state the degree of uncertainty If not stated, the uncertainty is +/- half the smallest division Ex: if the graduated cylinder shows 40.0 ml, then the reported data with uncertainty should be 40.0 +/- 0.5 ml Digital instruments +/- the smallest scale division Ex: if scale shows 37.02 g, then the reported uncertainty should be 37.02 +/- 0.01 g

Experimental Errors: Random Random error occurs when: If there is an equal probability of an error being too high or too low. Exs: Readability of instrument Insufficient data Effects of changes in surroundings (such as air currents or temp) Observer misinterpreting reading Can be reduced by repeated measurements Should be repeatable and reproducible

Experimental Errors: Systematic Systematic occurs when: There is a poor experimental design or procedure A specific directional result of data occurs. Exs: Measuring volume from top of meniscus rather than bottom = vol levels that are too high Overshooting volume of a liquid delivered in a titration = vol too high Using indicator whose end-point does not correspond to equivalence point Heat loss in exothermic rxn = smaller temp changes Cannot be reduced by repeated measurements

Accuracy Vs Precision Accuracy: Smaller systematic error, greater accuracy Closer to accepted value Precision: Smaller random uncertainties, greater precision Closer to each others’ values (reproducible) These should be discussed along with types of error (systematic and random) in all lab report conclusions!!! Also, compare results in labs to literature values whenever possible in labs!!!

Percentage Uncertainties vs Percentage Error Uncertainties can be expressed as a value or as a percentage Fractional uncert = absolute uncertainty meas. value Ex: 0.5/25.7 = +/-0.02 Percentage uncert = absolute uncertainty meas. value *100 Ex: 0.5/25.7 = +/- 2% Percentage error is how close your value is to the accepted value (or literature value) Percentage error = accepted value - experimental value accepted value *100

Propagation of Uncertainties: Addition and Subtraction Note: Uncertainties need to match the end decimal of the measurement. Ex: 26.0 +/- 0.5 g When adding or subtracting measurements, the uncertainties, find the max and min of the ranges and the average of the possible values. And, Add the uncertainties Ex: measurements – 23.5 +/- 0.1 g, 28.2 +/- 0.1 g 23.5: 23.6 or 23.4 28.2: 28.3 or 28.1 Max mass difference = 28.3-23.4 = 4.9 Min mass difference = 28.1-23.6 = 4.5 Mass difference is then = 4.7 +/- 0.2 g

Propagation of Uncertainties: Multiplication and Division

Significant Figures: Addition and Subtraction The number of decimal places determines the sig figs (precision of calculated value) Solve: (Assume digital measurements) 36.7 + 56.4 = _____ +/- _____ 2.37 + 23.11 = _____ +/- _____ 3.212 - 0.255 = _____ +/- _____ 2.3 - 0.002 = _____ +/- _____

Read page 538 for lab conclusions/evaluations If you calculated the possible max and min, how does this compare to the absolute uncertainty? 40.5*19.5 = (remember, 3 sig figs) 39.5*20.5 = Are they within range? 800 +/- 30 mm2 Read page 538 for lab conclusions/evaluations