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IB Chemistry on uncertainty error calculation, random and systematic error, precision and accuracy

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IB Chemistry on uncertainty error calculation, random and systematic error, precision and accuracy

IB Chemistry on uncertainty error calculation, random and systematic error, precision and accuracy

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  • 1. Uncertainty Calculation Precision, Accuracy and Uncertainty Calculation.Notes: • No measurement can be made with 100% precision • No measurement is 100% accurate or perfect • Random errors due to limitation of instrument (uncertainty of equipment) • • Must choose equipment with high precision • Significant figs tell us about the degree of precision • More sig fig more precise, more certain we are
  • 2. • Accurate data – low systematic error ( instrument must be calibrated ) • Precise data – low random error ( instrument with high precision ) • Reduce random error, use instrument with high degree of precisionPrecise/ Accurate – Use instrument with high precision + low systematic errorRandom error • sometimes too high or too low due to limitation of instrument • reduce random error by taking replicates and averageSystematic error • Always too high or too low due to instrument not calibrated or procedural error( procedure used always give too low or too high) • Reduce systematic error by calibrating instrument and modifying our experimental procedure • Random Error link to Precision, overcome by using precise instruments and taking replicate samples (average) • Systematic Error link to Accuracy overcome by calibrating the instruments
  • 3. Treatment of Uncertainty Adding or Subtracting measured quantities associated with uncertainty.2 methods can be used1st MethodBy adding up the absolute uncertainty • Initial mass, m = (10.00±0.01)g • Final mass, m = (15.00±0.01)g • Mass difference, m = (15.00 – 10.00) = 5.00g • Absolute uncertainty, ∆m = (0.01 + 0.01)g = 0.02g Answer = (5.00 ± 0.02)g = (4.98 --- 5.02)g2nd MethodMax/min limit error method • Initial mass, m = (10.00±0.01)g • Final mass, m = (15.00±0.01)g • Mass difference, m = (15.00 – 10.00) = 5.00g • Max error = Highest mass difference = (15.01 – 9.99) = 5.02g • Min error = Smallest mass difference = (14.99 – 10.01) = 4.98g Answer = (4.98 ---- 5.02)g Multiplying or dividing measured quantities • Percentage uncertainty is the sum of percentage uncertainty of individual quantitiesMoles, n = Conc x Vol Conc = (2.00±0.02)M , Vol = (2.0±0.1)dm3Moles, n = 2.00 x 2.0 = 4.0% Uncertainty moles, ∆n = % Uncertainty Conc + % Uncertainty Vol% Uncertainty Conc = (0.02/2.00)x100% = 1%% Uncertainty Vol = (0.1/2.0) x 100% = 5%% Uncertainty (Total) = 6%Moles, n = (4.0 ± 6%) convert to absolute uncertainty (6/100) x 4.0 = 0.24Moles, n = (4.0 ± 0.24) or (4.0±0.2)Answer = (3.8 --- 4.2)
  • 4. Uncertainty involving time for rate of reactionRate of reaction = 1/timeAverage time for 3 trials = (5.28 + 4.75 + 4.47)/3 = 4.83sRate of reaction = 1/average time = 1/ 4.83 = 0.207s-1How to find uncertainty for time and rate ?3 ways to find uncertainty for time and rate.1st easy method and not very accurate (% Uncertainty Method)Average time = 4.83sUncertainty for time ∆t = (4.83±0.01) using uncertainty from stopwatch% Uncertainty time ∆t = (0.01/4.83) x 100% = 0.207%Rate = 1/TimeRate = 1/4.83 = 0.207s-1Uncertainty for Rate = (0.207±0.207%) convert to absolute uncertaintyRate = (0.207±0.004)Rate = (0.207 ± 0.004) which range from (0.211 --- 0.203)
  • 5. 2nd method using Max-Min Range (more accurate).Time for 3 trials are 5.28, 4.75, 4.47Average time = 4.83sUncertainty for time = (Max time – Min time)/2 = (5.28 – 4.47)/2 = 0.41sUncertainty for time ∆t = (4.83 ± 0.41)% Uncertainty time ∆t = (0.41/4.83) x 100% = 8.48%Rate = 1/TimeRate = 1/4.83 = 0.207s-1Uncertainty for Rate = (0.207± 8.48%) convert to absolute uncertaintyUncertainty for Rate = (0.207 ± 0.017)s-1Rate = (0.207 ± 0.017) which range from (0.224---0.190)3rd method using Max-Min Error (more accurate)Time for 3 trials are 5.28, 4.75, 4.47Max time = 5.28, Min time = 4.47Average Rate = 1/time = 1/4.83 = 0.207s-1Uncertainty for Rate CalculationMax Rate = 1/min time = 1/4.47 = 0.223s-1Min Rate = 1/max time = 1/5.28 = 0.189s-1Rate with uncertainty = 0.207 ± (0.223—0.189)Rate = 0.207 ± (max 0.223 , min 0.189) which range from (0.223 –0.189)
  • 6. Uncertainty involving Concentration of solution by serial dilutionTwo methods to find uncertainty for concentration1st method using %UncertaintySerial Dilution (3%,1.5%, 0.75%, 0.325%, 0.1875%) of H2O2 using water.M1V1(before dilution)= M2V2(after dilution)Conc M2 = (M1V1)/ V2% Uncertainty M2 = %Uncertainty M1 + %Uncertainty V1+ %Uncertainty V2M1 = (3.000 ±0.00)% H2O2 StandardV1 = (1.500 ±0.012)ml H2O2V2 = (1.500 ±0.012)ml water added%Uncertainty M1 = 0%%Uncertainty V1 = (0.012/1.500)x 100% = 0.8%%Uncertainty V2 = (0.012/1.500)x 100% = 0.8%Total %Uncertainty = 0% + 0.8% + 0.8% = 1.6%Conc M2 = 1.500%Uncertainty conc M2 = (1.500%±1.6%) convert to absolute uncertaintyUncertainty conc M2 = (1.500± 0.024)%Conc M2 = (1.50 ± 0.02)% which ranges from (1.52—1.48)%
  • 7. 2nd method using max/min error methodSerial Dilution (3%,1.5%, 0.75%, 0.325%, 0.1875%) of H2O2 using water.M1V1(before dilution)= M2V2(after dilution)Conc M2 = (M1V1)/ (V1 + V2)= 1.500% * after dilution, total volume = (V1 + V2)M1 = (3.000 ±0.00)% H2O2 StandardV1 = (1.500 ±0.012)ml H2O2V2 = (1.500 ±0.012)ml water addedMax V1 = 1.512ml Max V2 = 1.512mlMin V1 = 1.488ml Min V2 = 1.488mlConc M2 = 1.500%Conc M2 = (M1V1)/ (V1 + V2) * after dilution, total volume = (V1 + V2)Max Conc M2 error happens when Max V1 vol and Min V2 vol usedMax Conc M2 = (M1 x Max V1)/ (Max V1 + Min V2 ) = (3.00 x 1.512)/(1.512 + 1.488) = 1.512%Min Conc M2 error happens when Min V1 vol and Max V2 vol usedMin Conc M2 = (M1 x Min V1)/ (Min V1 + Max V2) = (3.00 x 1.488)/(1.488 +1.512) = 1.488%Uncertainty conc M2 = 1.500 ± (1.512 –1.488 )%Conc M2 = 1.500 ± (1.512 –1.488 )% which ranges from (1.512 –1.488)%Click HERE to view detail uncertainty calculation and standard deviationPrepared by Lawrence Kok