Uncertainties

Cruise around to as many of the Measurement Stations as you can in 5 minutesFor each, the answer is on the backNote: Your measurement may vary, but you should have the same # of decimal places recorded and the same +/- as I doWarm-upHow to find the +/- uncertainty of measured and calculated values

IB ChemistryUncertaintiesOR have groups guess and give a +/- on their guessClosest group gets the reward, but divided by the uncertaintyExample: if group guesses 400 +/- 10, and there are 401 candies, they get it but only 40 of them (=401/10)2How many candies are in this jar?Do thisMake a guessCompare with 3 othersMake a quick bar graph of your 3 guesses and the averageDisplay graph on the blackboardWhich group had the highest precision?Precision= ability of a measurement to be consistently reproducedWhich had the highest accuracy?Accuracy= a measurements correctnessSignificant FiguresSince you work hard to be accurate, its important that you show off just how careful you were with your measurements.Examples:

76.0cm3

52.8cm3

6.59cm3 Significant FiguresSignificant Figures are values that have been measured (and deserve respect)1.98 = 3 sig figsNumbers are significant2 = 1 sig fig2.05 = 3 sig figsZeros are sig. if between numbers2.00 = 3 sig figsZeros are sig. if behind decimal0.0002 = 1 sig fig and not at the beginning2000 = 1 sig fig (but, 2000. = 4 sig figs)Zeros at the end are not significant2.000 x 103 = 4 sig figsEverything is sig. in scientific notation

Adding and subtracting- keep the same # of digits after the decimal as the value with the least #s after decimal. Ex: 2.3 + 1.444 = 2.744 = 2.7

Multiplying and Dividing- keep the same # of sig figs as the value with the leastEx: 0.002 x 3.897 = 0.007794 = 0.008

Note: Just worry about these at the end and theyre really not too bad.What is Uncertainty?Every time we measure a value, theres a certain point where we (or the instrument that were using) have to estimate or roundSo, no measurement is absolutely perfectThe imperfectness is the uncertaintyThis can be expressed with a value at the endExample: 2.5cm 0.5 means that the actual value is 2.0 3.0 2.50cm 0.05 means 2.45 - 2.55 The second value is more precise(note: uncertainties only have 1 significant figure)Finding Uncertainty- MeasuredAnalog equipment: HALF of the increment on the instrument, but you could use your judgment here, with a short justification statementEx: 76.0cm3 0.5 (or even 76.0cm3 0.2 with justification)Ex: 6.55cm3 0.05

Digital equipment: WHOLE last digit measuredEx: 1.25g 0.01gEx: pH= 6.5 0.1

Try someMeasuring mass on a digital balance:0.34g 1.9998gMeasuring temperature with digital thermometer:24oC19.6oCMeasuring temp with a manual thermometer:14.5oC Measuring volume with a burette:34.5cm3 0.01 0.0001 1 0.1 0.5 0.5Finding Uncertainty- Calculated I (Propagation of Error)Adding and Subtracting:Add uncertainties of all values usedEx:Volume change = 45.60 0.05 cm3 34.10 0.05 cm3 Could be as small as 45.55 34.15 = 11.40Could be as large as 45.65 34.05 = 11.60So = 11.50 0.1Ex #2:Mass change = 0.8 0.1 g 0.7 0.1 g

= 0.1 0.2Averaging:Half of the range of values averaged, or the , whichever is biggerEx: average these values: 3.4, 2.6, 3.2 (all 0.1)3.1

0.1

0.4

Uncertainties ALWAYS have only 1 significant figure9Try Some- Addition/Subtraction(45 1)+(23 1) =

(0.9 0.1)+(0.8 0.1)(0.5 0.1) =

Average: 9.1 0.1, 9.5 0.1, and 9.2 0.1 =68 21.2 0.3 9.2 0.2 Finding Uncertainty- Calculated IIMultiplying and DividingConvert all uncertainties into percentsAdd the percentsConvert the percent back into an absolute uncertaintyEx:Density = (4.5g 0.1)/(9cm3 1)0.1 is 2.2% of 4.51 is 11.1% of 9Density = 0.5g/cm3 13.3%13.3% of 0.5 is 0.07Answer Density = 0.5 0.07Dont forget significant figures at the endTry Some Multiplication/DivisionRate = (23.9m 0.1)/(134sec 1)

% Water = (0.049g 0.001)/(0.092 0.001) 0.1 = 0.42%, 1 = 0.75% Rate = 0.178m/sec 1.17% Rate = 0.178m/sec 0.002 0.001 = 2.0%, 0.001 = 1.1% % Water = 53% 3.1% of 53 % Water = 53% 2A Quickie WayUsually, the range of your data is much larger than the propagated uncertaintyCalculate the final value using your trials, average your trials and then add a using of the range to your final answerThis could save you a lot of converting to percents. blah blah blah along the wayExample:Example Quickie way3 values are calculated using the cumbersome % method:43.56 0.0440.99 0.02 44.03 0.03

Average= 42.86Uncertainty is half of the range or the uncertainty of the value whichever is largerThe range is 44.03-40.99= 3.04half of which is 1.52 or 2 with one sig fig2 is huge compared to the uncertainties of the values, so why did you bother with all that mess? Just skip it!Answer = 42.86 2