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Prepared by Lawrence Kok

Tutorial on Uncertainty Calculation, Error analysis and Standard deviation for rate of reaction.

IB Chemistry, Uncertainty, Error Analysis, Standard Deviation

Uncertainty Calculation for Rate and Concentration of reaction.Rate = 1/time, Time for X to disappear. ( Iodine Clock Reaction)

• 3 Methods for Uncertainty Calculation for Rate (0.10M) KI.

• Average time is (5.28 + 4.75 + 4.47) / 3 = 4.83

• 1st % Uncertainty MethodUncertainty time = Uncertainty (stop watch + reaction time) ( 0.01 + 0.09 ) = ( 0.10 )Time = 4.83 ±( 0.10 )

• 2nd Max-min range MethodUncertainty time = (Max time - Min time)/2, = ( 5.28 - 4.47 )/2 = 0.41Time = 4.83 ±0.41

1st % Uncertainty MethodUncertainty time = (4.83 ± 0.10)Rate = 1/ time, 1/ 4.83 = 0.207

2nd Max-min range MethodUncertainty time = ( 4.83 ± 0.41)Rate = 1/time, 1/ 4.83 = 0.207

3 Methods used for Uncertainty Calculation for Rate

1st % Uncertainty Method• % Uncertainty time = (0.1/4.83) x100 %=2.07• % Uncertainty Rate = % Uncertainty time• % Uncertainty Rate = 2.07% Rate = (0.207 ± 2.07)% Rate = 0.207 ± 0.004

2nd Max-min range Method•% Uncertainty time = (0.41/ 4.83) x 100% = 8.48%•% Uncertainty Rate = % Uncertainty time•%Uncertainty Rate = 8.48%Rate = 0.207 ± 8.48%Rate = 0.207 ± 0.017

3rd Max /Min Rate Method

• Max Rate = 1/ Minimum time, 1/ 4.47 = 0.220• Min Rate = 1/ Maximum time, 1/ 5.28 = 0.190• Ave rate = 1/ Ave time, 1/ 4.83 = 0.207Uncertainty Rate = 0.207 ± ( 0.220 --- 0.190 )

Uncertainty Cal for Conc, 30ml 0.1M KI (2 Methods used)

1st % Uncertainty Method• Pipette uncertainty = ± 0.4 and Total Volume used = 30ml

• %Uncertainty Vol KI = (0.4/ 30) x100%=1.3%• % Uncertainty Vol Water = 0%• %Uncertainty Conc = % Uncertainty Vol KI only• %Uncertainty Conc = 1.3%

1st % Uncertainty Method• %Uncertainty Conc = %Uncertainty Vol KI + %Uncertainty Vol Water

Calculation Absolute Uncertainty• Conc = 0.10 ± 1.3%• Conc = 0.100 ± 0.001

2nd Max/Minimum Method

Preparing 0.053M from 0.1M KI using pipette.Pipette uncertainty = ± 0.4Max Conc KI = Max Vol KI and Min Vol of water used

M x V (dil) = M x V (conc)M x (15.8 + 14.2) = 0.1 x (15.8)M = 0.1 x ( 15.8 ) / ( 15.8+ 14.2 )M = 0.053

Max Conc KI = Max Vol KI + Min Vol water Max Vol KI = 15.8 ± 0.4 = 16.2Min Vol water = 14.2 ± 0.4 = 13.8

M x V (dil) = M x V (conc)Max Conc KI = (0.1 x 16.2) / ( 16.2 + 13.8 )Max Conc = 0.054

Min Conc = Min Vol KI and Max Vol water usedMin Vol KI = 15.8 ± 0.4 = 15.4Max Vol water = 14.2 ± 0.4 = 14.6

M x V (dil) = M x V (conc)M x (15.4 + 14.6) = 0.1 x (15.4)M = 0.1 x ( 15.4 ) / ( 15.4 + 14.6 )M = 0.051Min Conc = 0.051Uncertainty Conc = 0.053 ± ( 0.054 --- 0.051)

Uncertainty Calculation, 2 fold Serial dilution using 3% H2O2

Two Methods used1st % Uncertainty Method

For 1.5% :Total % Uncertainty is 1.6%, Answer = 1.5 ± 1.6%Propagation of error involved

Absolute Uncertainty for 1.5 ± 1.6% = (1.50 ± 0.02)%

2nd Max/ Min Method

For 2 fold Serial dilution on 3% H2O2

M x V (dil) = M x V (conc)M x (1.5 +1.5) = 3% x 1.5M = 1.5%

Max Conc H2O2 when Min Conc H2O2 whenMax Vol H2O2 used = 1.51 Min Vol H2O2 used = 1.49Min Vol water used = 1.49 Max Vol water used = 1.51

Max Conc H2O2 Min Conc H2O2 M x V (dil) = M x V (conc) M x V (dil) = M x V (conc) M x (1.51 + 1.49) = 3% x ( 1.51 ) M x (1.51 + 1.49) = 3% x ( 1.49 )M = 3% x ( 1.51 )/ ( 1.51 + 1.49 ) M = 3% x ( 1.49 )/ ( 1.51 + 1.49 )M = 1.51% M = 1.49%Max Conc = 1.51% Min Conc = 1.49%

Uncertainty Conc H2O2 = 1.50 ± (1.51%---1.49%)

Uncertainty Calculation for Rate Using Vernier Sensor.

How changing conc of H2O2 affect the rate of decomposition of H2O2 (catalase) measured using pressure sensor?

• Initial Rate for 1.5% = slope or gradient of curve

• Perform 3 trials at 1.5%

•Take Average rate

Average Rate by taking average for 3 trials

Uncertainty for Rate = Standard deviationUse Excel to calculate Std deviationAverage rate = (0.113 ±0.015)kPa/s

Click HERE to view video on how to insert error bar or standard deviation in Excel

Acknowledgements

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Prepared by Lawrence Kok

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