1.Tutorial on Random and Systematic errors.Prepared by Lawrence Kok http://lawrencekok.blogspot.com

2. MeasurementEvery measurement associated with an error No measurement is 100% precise or accurate.3 Types of MeasurementNot Precise + Not AccuratePrecise + AccurateAccurate NOT accurate low systematic error NOT precise High systematic High random errorPrecise + Not AccuratePrecise low random errorNot accurate High systematic error 3. MeasurementEvery measurement associated with an error No measurement is 100% precise or accurate.3 Types of MeasurementNot Precise + Not AccuratePrecise + Accurate2 Types of Errors Precise + Not AccurateSystematic ErrorRandom ErrorAffects accuracyAffects precisionhigh systematic errorAccurate NOT accurate low systematic error NOT precise High systematic High random errorPrecise low random errorNot accurate High systematic errorhigh random error 4. MeasurementEvery measurement associated with an error No measurement is 100% precise or accurate.3 Types of MeasurementNot Precise + Not Accurate2 Types of ErrorsPrecise + AccuratePrecise + Not AccurateSystematic ErrorRandom ErrorAffects accuracyAffects precisionhigh systematic errorAccurate NOT accurate low systematic error NOT precise High systematic High random errorPrecise low random errorNot accurate High systematic error2 Types of ErrorsRandom Error Systematic ErrorMeasurement random Instrument imprecise/uncertainty Fluctuation reading burette/pipette Small sample size/trials Statistical fluctuation of measurement/reading by someone/unpredictableVSMeasurement too high/ low Instrument not calibrated Faulty apparatus (zero error) Incorrect measurement Imperfect instrument Procedure/method incorrect/predictable Accurate + Precise Accuracy Measurement value close to correct valueVSPrecise Measurement value close to each otherhigh random error 5. 2 Types of ErrorsSystematic Error Affects accuracy Random Error High systematic errorMeasurement too high/ low Instrument not calibrated Faulty apparatus (zero error) Incorrect measurement Imperfect instrument Procedure/method incorrect PredictableHigh random error Affects precisionMeasurement random Instrument imprecise/uncertainty Fluctuation reading burette/pipette Small sample size/trials Statistical fluctuation of measurement/reading by someone Unpredictable 6. 2 Types of ErrorsSystematic Error Affects accuracy Random Error High systematic errorMeasurement too high/ low Instrument not calibrated Faulty apparatus (zero error) Incorrect measurement Imperfect instrument Procedure/method incorrect PredictablelowerCorrect valuehigherDirection error always one side (higher/lower)High random error Affects precisionMeasurement random Instrument imprecise/uncertainty Fluctuation reading burette/pipette Small sample size/trials Statistical fluctuation of measurement/reading by someone UnpredictablelowerCorrect valuehigherDirection error always random 7. 2 Types of ErrorsSystematic Error Affects accuracy Random Error High random errorHigh systematic errorMeasurement too high/ low Instrument not calibrated Faulty apparatus (zero error) Incorrect measurement Imperfect instrument Procedure/method incorrect PredictablelowerCorrect value Direction error always one side (higher/lower)Calibrating equipment for zero errorCorrect valuehigherDirection error always randomCan be reducedCan be identified/eliminated Improve measuring techniqueMeasurement random Instrument imprecise/uncertainty Fluctuation reading burette/pipette Small sample size/trials Statistical fluctuation of measurement/reading by someone UnpredictablelowerhigherAffects precisionImprove expt designUsing precise instrumentBy repeating more trials/averageCalorimetry expt Prevent heat loss using insulatorHeating expt Cool down before weighing 8. Random and Systematic Error Measuring circumference using a ruler Recording measurement using uncertainty of equipmentRadius, r = (3.0 0.2) cm Treatment of Uncertainty Multiplying or dividing measured quantitiesCircumference = 2p r% uncertainty = sum of % uncertainty of individual quantities Radius, r = (3.0 0.2) %uncertainty radius (%r) = 0.2 x 100 = 6.6% 3.0 % uncertainty C = % uncertainty r % C = % r * Constant, pure/counting number has no uncertainty and sf not takenCircumference = 2p r Circumference = 23.143.0 =18.8495 0.2 100% = 6.6% 3.0 %Dc = %Dr %Dc = 6.6% Circumference = (18.8495 6.7%) %Dr =AbsoluteDC =6.6 18.8495 =1.25 100Circumference = (18.8495 1.25) Circumference = (19 1) 9. Random and Systematic Error Measuring circumference using a ruler Recording measurement using uncertainty of equipmentRadius, r = (3.0 0.2) cm Treatment of Uncertainty Multiplying or dividing measured quantitiesCircumference = 2p r% uncertainty = sum of % uncertainty of individual quantities Radius, r = (3.0 0.2) %uncertainty radius (%r) = 0.2 x 100 = 6.6% 3.0 % uncertainty C = % uncertainty r % C = % r * Constant, pure/counting number has no uncertainty and sf not takenRandom and Systematic Error Correct value = 20.4 Expt value = 19 6.7%Circumference = 2p r Circumference = 23.143.0 =18.8495 0.2 100% = 6.6% 3.0 %Dc = %Dr %Dc = 6.6% Circumference = (18.8495 6.7%) %Dr =AbsoluteDC =6.6 18.8495 =1.25 100Circumference = (18.8495 1.25) Circumference = (19 1) %Percentage Error = 6.7%%Error = (expt - correct )100% correct19 - 20.4 %Error = ( ) 100% = 6.7% 20.4Circumference = (18.8495 6.7%) % Random Error%Random Error 6.6%%Systematic Error 0.1% 10. Random and Systematic Error Measuring circumference using a ruler Recording measurement using uncertainty of equipmentRadius, r = (3.0 0.2) cm Treatment of Uncertainty Multiplying or dividing measured quantitiesCircumference = 2p r% uncertainty = sum of % uncertainty of individual quantities Radius, r = (3.0 0.2) %uncertainty radius (%r) = 0.2 x 100 = 6.6% 3.0 % uncertainty C = % uncertainty r % C = % r * Constant, pure/counting number has no uncertainty and sf not takenRandom and Systematic Error Correct value = 20.4 Expt value = 19 6.7%Circumference = 2p r Circumference = 23.143.0 =18.8495 0.2 100% = 6.6% 3.0 %Dc = %Dr %Dc = 6.6% Circumference = (18.8495 6.7%) %Dr =AbsoluteDC =6.6 18.8495 =1.25 100Circumference = (18.8495 1.25) Circumference = (19 1) %Percentage Error = 6.7%%Error = (expt - correct )100% correct19 - 20.4 %Error = ( ) 100% = 6.7% 20.4Circumference = (18.8495 6.7%) % Random Error%Random Error 6.6%High random error Way reduce random error%Systematic Error 0.1%Small systematic error Step/procedure correct 11. Random and Systematic Error Measuring displacement using a stopwatch Recording measurement using uncertainty of equipmentTime, t = (2.25 0.01) cmTreatment of Uncertainty 1 2 Multiplying or dividing measured quantities Displacement, s = 2 gt % uncertainty = sum of % uncertainty of individual quantities Time, t = (2.25 0.01) %uncertainty time (%t) = 0.01 x 100 = 0.4% 2.25 % uncertainty s = 2 x % uncertainty t % s = 2 x % t * For measurement raised to power of n, multiply % uncertainty by n1 Displacement, s = gt 2 2 1 Displacement, s = 9.8x2.25x2.25 = 24.80 20.01 100% = 0.4% 2.25 Measurement raised to power of 2, %Ds = 2 %Dt multiply % uncertainty by 2 %Ds = 2 0.4% = 0.8% Displacement = (24.80 0.8%) %Dt =AbsoluteDs =0.4 24.80 = 0.198 100Displacement = (24.80 0.198) Displacement = (24.8 0.2) 12. Random and Systematic Error Measuring displacement using a stopwatch Recording measurement using uncertainty of equipmentTime, t = (2.25 0.01) cmTreatment of Uncertainty 1 2 Multiplying or dividing measured quantities Displacement, s = 2 gt % uncertainty = sum of % uncertainty of individual quantities Time, t = (2.25 0.01) %uncertainty time (%t) = 0.01 x 100 = 0.4% 2.25 % uncertainty s = 2 x % uncertainty t % s = 2 x % t * For measurement raised to power of n, multiply % uncertainty by n1 Displacement, s = gt 2 2 1 Displacement, s = 9.8x2.25x2.25 = 24.80 20.01 100% = 0.4% 2.25 Measurement raised to power of 2, %Ds = 2 %Dt multiply % uncertainty by 2 %Ds = 2 0.4% = 0.8% Displacement = (24.80 0.8%) %Dt =AbsoluteDs =0.4 24.80 = 0.198 100Random and Systematic Error Correct value = 23.2 Expt value = 24.8 0.8%expt - correct %Error = ( )100% correct %Error = (24.8 - 23.2 ) 100% = 0.7% 23.2Displacement = (24.80 0.8%) % Random ErrorDisplacement = (24.80 0.198) Displacement = (24.8 0.2) %Percentage Error = 0.7%%Random Error 0.8% 13. Random and Systematic Error Measuring displacement using a stopwatch Recording measurement using uncertainty of equipmentTime, t = (2.25 0.01) cmTreatment of Uncertainty 1 2 Multiplying or dividing measured quantities Displacement, s = 2 gt % uncertainty = sum of % uncertainty of individual quantities Time, t = (2.25 0.01) %uncertainty time (%t) = 0.01 x 100 = 0.4% 2.25 % uncertainty s = 2 x % uncertainty t % s = 2 x % t * For measurement raised to power of n, multiply % uncertainty by n1 Displacement, s = gt 2 2 1 Displacement, s = 9.8x2.25x2.25 = 24.80 20.01 100% = 0.4% 2.25 Measurement raised to power of 2, %Ds = 2 %Dt multiply % uncertainty by 2 %Ds = 2 0.4% = 0.8% Displacement = (24.80 0.8%) %Dt =AbsoluteDs =0.4 24.80 = 0.198 100Random and Systematic Error Correct value = 23.2 Expt value = 24.8 0.8%expt - correct %Error = ( )100% correct %Error = (24.8 - 23.2 ) 100% = 0.7% 23.2Displacement = (24.80 0.8%) % Random ErrorDisplacement = (24.80 0.198) Displacement = (24.8 0.2) %Percentage Error = 0.7%%Random Error 0.8%% error fall within the % uncertainty (%Random error) Little/No systematic error Result is reliable but need to reduce random error 14. Random and Systematic Error Measuring period using a ruler Recording measurement using uncertainty of equipmentLength, I = (1.25 0.05) mTreatment of Uncertainty Multiplying or dividing measured quantitiesT = 2pL g% uncertainty = sum of % uncertainty of individual quantities Length, I = (1.25 0.05) %uncertainty length (%I) = 0.05 x 100 = 4% 1.25 % uncertainty T = x % uncertainty l % T = x % I * For measurement raised to power of n, multiply % uncertainty by nL g 1.25 T = 2p = 2.24 9.8 T = 2p0.05 100% = 4% 1.25 1 power %DT = %Dl Measurement raised to by 1/2 of 1/2, multiply % uncertainty 2 %DT = 2% T = (2.24 2%) %Dl =AbsoluteDT =2 2.24 = 0.044 100T = (2.24 0.044) T = (2.24 0.04) 15. Random and Systematic Error Measuring period using a ruler Recording measurement using uncertainty of equipmentLength, I = (1.25 0.05) mTreatment of Uncertainty Multiplying or dividing measured quantitiesT = 2pL g% uncertainty = sum of % uncertainty of individual quantities Length, I = (1.25 0.05) %uncertainty length (%I) = 0.05 x 100 = 4% 1.25 % uncertainty T = x % uncertainty l % T = x % I * For measurement raised to power of n, multiply % uncertainty by nRandom and Systematic Error Correct value = 2.15 Expt value = 2.24 2%L g 1.25 T = 2p = 2.24 9.8 T = 2p0.05 100% = 4% 1.25 1 power %DT = %Dl Measurement raised to by 1/2 of 1/2, multiply % uncertainty 2 %DT = 2% T = (2.24 2%) %Dl =AbsoluteDT =2 2.24 = 0.044 100T = (2.24 0.044) T = (2.24 0.04) %Percentage Error = 4.2%%Error = (expt - correct )100% correct%Error = (2.24 - 2.15 ) 100% = 4.2% 2.15T = (2.24 2%)% Random Error%Random Error = 2%%Systematic Error = 2.2% 16. Random and Systematic Error Measuring period using a ruler Recording measurement using uncertainty of equipmentLength, I = (1.25 0.05) mTreatment of Uncertainty Multiplying or dividing measured quantitiesT = 2pL g% uncertainty = sum of % uncertainty of individual quantities Length, I = (1.25 0.05) %uncertainty length (%I) = 0.05 x 100 = 4% 1.25 % uncertainty T = x % uncertainty l % T = x % I * For measurement raised to power of n, multiply % uncertainty by nRandom and Systematic Error Correct value = 2.15 Expt value = 2.24 2%L g 1.25 T = 2p = 2.24 9.8 T = 2p0.05 100% = 4% 1.25 1 power %DT = %Dl Measurement raised to by 1/2 of 1/2, multiply % uncertainty 2 %DT = 2% T = (2.24 2%) %Dl =AbsoluteDT =2 2.24 = 0.044 100T = (2.24 0.044) T = (2.24 0.04) %Percentage Error = 4.2%%Error = (expt - correct )100% correct%Error = (2.24 - 2.15 ) 100% = 4.2% 2.15T = (2.24 2%)% Random Error%Random Error = 2%%Systematic Error = 2.2%% error fall outside> than % uncertainty (%Random error) Random error cannot account for % error Systematic error occur way to reduce systematic error 17. Random and Systematic Error Measuring Area using ruler Recording measurement using uncertainty of equipmentLength, I = (4.52 0.02) cm Height, h = (2.0 0.2)cm3 Treatment of Uncertainty Multiplying or dividing measured quantitiesArea, A = Length,l height,h% uncertainty = sum of % uncertainty of individual quantities Length, l = (4.52 0.02) %uncertainty length (%l) = 0.02 x 100 = 0.442% 4.52 Height, h = (2.0 0.2) %uncertainty height (%h) = 0.2 x 100 = 10% 2.0 % uncertainty A = % uncertainty length + % uncertainty height % A = % I + %hArea, A = Length,l height, hArea = 4.52 2.0 = 9.04 0.02 100% = 0.442% 4.52 0.2 %Dh = 100% = 10% 2.0 %DA = %Dl + %Dh %DA = 0.442% +10% = 10.442% Area = (9.04 10%) %Dl =AbsoluteDA =Area = (9.0 0.9)10 9.04 = 0.9 100 18. Random and Systematic Error Measuring Area using ruler Recording measurement using uncertainty of equipmentLength, I = (4.52 0.02) cm Height, h = (2.0 0.2)cm3 Treatment of Uncertainty Multiplying or dividing measured quantitiesArea, A = Length,l height,h% uncertainty = sum of % uncertainty of individual quantities Length, l = (4.52 0.02) %uncertainty length (%l) = 0.02 x 100 = 0.442% 4.52 Height, h = (2.0 0.2) %uncertainty height (%h) = 0.2 x 100 = 10% 2.0 % uncertainty A = % uncertainty length + % uncertainty height % A = % I + %hRandom and Systematic ErrorArea, A = Length,l height, hArea = 4.52 2.0 = 9.04 0.02 100% = 0.442% 4.52 0.2 %Dh = 100% = 10% 2.0 %DA = %Dl + %Dh %DA = 0.442% +10% = 10.442% Area = (9.04 10%) %Dl =AbsoluteDA =Area = (9.0 0.9) %Percentage Error = 9%Correct value = 22.7 Expt value = 24.8 0.87%%Error = (expt - correct )100% correct%Error = (24.8 - 22.7 )100% = 9% 22.7Area = (9.04 10%) % Random Error%Random Error = 10%10 9.04 = 0.9 100 19. Random and Systematic Error Measuring Area using ruler Recording measurement using uncertainty of equipmentLength, I = (4.52 0.02) cm Height, h = (2.0 0.2)cm3 Treatment of Uncertainty Multiplying or dividing measured quantitiesArea, A = Length,l height,h% uncertainty = sum of % uncertainty of individual quantities Length, l = (4.52 0.02) %uncertainty length (%l) = 0.02 x 100 = 0.442% 4.52 Height, h = (2.0 0.2) %uncertainty height (%h) = 0.2 x 100 = 10% 2.0 % uncertainty A = % uncertainty length + % uncertainty height % A = % I + %hRandom and Systematic ErrorArea = 4.52 2.0 = 9.04 0.02 100% = 0.442% 4.52 0.2 %Dh = 100% = 10% 2.0 %DA = %Dl + %Dh %DA = 0.442% +10% = 10.442% Area = (9.04 10%) %Dl =AbsoluteDA =10 9.04 = 0.9 100Area = (9.0 0.9) %Percentage Error = 9%Correct value = 22.7 Expt value = 24.8 0.87%%Error = (Area, A = Length,l height, hexpt - correct )100% correct24.8 - 22.7 %Error = ( )100% = 9% 22.7Area = (9.04 10%) % Random Error%Random Error = 10% % error fall within the % uncertainty (%Random error) Little/No systematic error Result is reliable need to reduce random error Reduce random error HUGE (10%) use precise instrument vernier calipersVernier caliper 20. Random and Systematic Error Measuring moles using dropper and volumetric flask Conc, c = (2.00 0.02) cm Volume, v = (2.0 0.1)dm3Mole, n = Conc, c Volume, v Mole = 2.00 2.0 = 4.00 0.02 100% = 1% 2.00 0.1 %Dv = 100% = 5% 2.0 %Dn = %Dc + %Dv %Dn = 1% + 5% = 6% Mole = (4.00 6%) %Dc =Treatment of Uncertainty Mole, n = Conc Vol Multiplying or dividing measured quantities % uncertainty = sum of % uncertainty of individual quantity Conc, c = (2.00 0.02) %uncertainty conc (%c) = 0.02 x 100 = 1% 2.00 Volume, v = (2.0 0.1) %uncertainty volume (%v) = 0.1 x 100 = 5% 2.0 % uncertainty n = % uncertainty conc + % uncertainty volume % n = % c + %vAbsoluteDn =Mole = (4.00 0.24) Mole = (4.0 0.2)Dropper, volumetri c flask6 4.00 = 0.24 100 21. Random and Systematic Error Measuring moles using dropper and volumetric flask Conc, c = (2.00 0.02) cm Volume, v = (2.0 0.1)dm3Mole, n = Conc, c Volume, v Mole = 2.00 2.0 = 4.00 0.02 100% = 1% 2.00 0.1 %Dv = 100% = 5% 2.0 %Dn = %Dc + %Dv %Dn = 1% + 5% = 6% Mole = (4.00 6%) %Dc =Treatment of Uncertainty Mole, n = Conc Vol Multiplying or dividing measured quantities % uncertainty = sum of % uncertainty of individual quantity Conc, c = (2.00 0.02) %uncertainty conc (%c) = 0.02 x 100 = 1% 2.00 Volume, v = (2.0 0.1) %uncertainty volume (%v) = 0.1 x 100 = 5% 2.0 % uncertainty n = % uncertainty conc + % uncertainty volume % n = % c + %vAbsoluteDn =Mole = (4.00 0.24) Mole = (4.0 0.2)Dropper, volumetri c flask6 4.00 = 0.24 100%Percentage Error = 10%Random and Systematic Error Correct value = 3.63 Expt value = 4.00 6%expt - correct %Error = ( )100% correct %Error = (4 - 3.63 )100% =10% 3.63 Mole = (4.00 6%) % Random Error%Random Error = 6%%Systematic Error = 4% 22. Random and Systematic Error Measuring moles using dropper and volumetric flask Conc, c = (2.00 0.02) cm Volume, v = (2.0 0.1)dm3Mole, n = Conc, c Volume, v Mole = 2.00 2.0 = 4.00 0.02 100% = 1% 2.00 0.1 %Dv = 100% = 5% 2.0 %Dn = %Dc + %Dv %Dn = 1% + 5% = 6% Mole = (4.00 6%) %Dc =Treatment of Uncertainty Mole, n = Conc Vol Multiplying or dividing measured quantities % uncertainty = sum of % uncertainty of individual quantity Conc, c = (2.00 0.02) %uncertainty conc (%c) = 0.02 x 100 = 1% 2.00 Volume, v = (2.0 0.1) %uncertainty volume (%v) = 0.1 x 100 = 5% 2.0 % uncertainty n = % uncertainty conc + % uncertainty volume % n = % c + %vAbsoluteDn =Mole = (4.00 0.24) Mole = (4.0 0.2)Dropper, volumetri c flask6 4.00 = 0.24 100%Percentage Error = 10%Random and Systematic Error Correct value = 3.63 Expt value = 4.00 6%expt - correct %Error = ( )100% correct %Error = (4 - 3.63 )100% =10% 3.63 Mole = (4.00 6%) % Random Error%Random Error = 6%%Systematic Error = 4%% error fall outside> than % uncertainty (%Random error) Random error cannot account for % error Systematic error occur improve on method/steps used. Ways to reduce errorRandom error (6%) More precise instrument -pipetteSystematic error (4%) Calibration of instrument 23. Random and Systematic Error Measuring density using mass and measuring cylinderMass, m = (482.63 1)g Volume, v = (258 5)cm3Density, D = Density, D =Mass Volume482.63 =1.870658 2581 100% = 0.21% 482.63 5 %DV = 100% = 1.93% 258 %DD = %Dm + %DV %DD = 0.21% +1.93% = 2.1% Density = (1.87 2.1%) %Dm =Treatment of Uncertainty Mass Multiplying or dividing measured quantities Density, D = Volume % uncertainty = sum of % uncertainty of individual quantities Mass, m = (482.63 1) %uncertainty mass (%m) = 1 x 100 = 0.21% 482.63 Volume, V = (258 5) %uncertainty vol (%V) = 5 x 100 = 1.93% 258 % uncertainty density = % uncertainty mass + % uncertainty volume % D = % m + %VAbsoluteDD =2.1 1.87 = 0.04 100Density = (1.87 0.04) 24. Random and Systematic Error Measuring density using mass and measuring cylinderMass, m = (482.63 1)g Volume, v = (258 5)cm3Density, D = Density, D =Mass Volume482.63 =1.870658 2581 100% = 0.21% 482.63 5 %DV = 100% = 1.93% 258 %DD = %Dm + %DV %DD = 0.21% +1.93% = 2.1% Density = (1.87 2.1%) %Dm =Treatment of Uncertainty Mass Multiplying or dividing measured quantities Density, D = Volume % uncertainty = sum of % uncertainty of individual quantities Mass, m = (482.63 1) %uncertainty mass (%m) = 1 x 100 = 0.21% 482.63 Volume, V = (258 5) %uncertainty vol (%V) = 5 x 100 = 1.93% 258 % uncertainty density = % uncertainty mass + % uncertainty volume % D = % m + %VAbsoluteDD =2.1 1.87 = 0.04 100Density = (1.87 0.04) %Percentage Error = 5%Random and Systematic Error Correct value = 1.78 Expt value = 1.87 2.1%expt - correct %Error = ( )100% correct 1.87 -1.78 %Error = ( )100% = 5% 1.78Density = (1.87 2.1%) % Random Error%Random Error = 2.1%%Systematic Error = 2.9% 25. Random and Systematic Error Measuring density using mass and measuring cylinderMass, m = (482.63 1)g Volume, v = (258 5)cm3Density, D = Density, D =Mass Volume482.63 =1.870658 2581 100% = 0.21% 482.63 5 %DV = 100% = 1.93% 258 %DD = %Dm + %DV %DD = 0.21% +1.93% = 2.1% Density = (1.87 2.1%) %Dm =Treatment of Uncertainty Mass Multiplying or dividing measured quantities Density, D = Volume % uncertainty = sum of % uncertainty of individual quantities Mass, m = (482.63 1) %uncertainty mass (%m) = 1 x 100 = 0.21% 482.63 Volume, V = (258 5) %uncertainty vol (%V) = 5 x 100 = 1.93% 258 % uncertainty density = % uncertainty mass + % uncertainty volume % D = % m + %VAbsoluteDD =2.1 1.87 = 0.04 100Density = (1.87 0.04) %Percentage Error = 5%Random and Systematic Error Correct value = 1.78 Expt value = 1.87 2.1% %Random Error = 2.1%expt - correct %Error = ( )100% correct%Systematic Error = 2.9%% error fall outside> than % uncertainty (%Random error) Random error cannot account for % error Systematic error occurs1.87 -1.78 %Error = ( )100% = 5% 1.78Ways to reduce errorDensity = (1.87 2.1%) Random error (6%) Precise instrument mass balance% Random Error Precise balanceSystematic error (4%) Use different method like displacement can Displacement can 26. Random and Systematic Error Measuring Enthalpy change using calorimeter/thermometer Recording measurement using uncertainty of equipmentMass water = (2.00 0.02)g Temp = (2.0 0.4) C Treatment of Uncertainty Multiplying or dividing measured quantities Enthalpy, H % uncertainty = sum of % uncertainty of individual quantities Mass, m = (2.00 0.02) %uncertainty mass (%m) = 0.02 x 100 = 1% 2.00 Temp = (2.0 0.4) %uncertainty temp (%T) = 0.4 x 100 = 20% 2.0 % uncertainty H = % uncertainty mass + % uncertainty temp % H = % m + %T= m c DTEnthalpy, H = m c DT Enthalpy, H = 2.00 4.18 2.0 =16.72 0.02 100% = 1% 2.00 0.4 %DT = 100% = 20% 2.0 %DH = %Dm + %DT %DH = 1% + 20% = 21% Enthalpy = (16.72 21%) %Dm =AbsoluteDH =21 16.72 = 3.51 100Enthalpy = (16.72 3.51) Enthalpy = (17 4) 27. Random and Systematic Error Measuring Enthalpy change using calorimeter/thermometer Recording measurement using uncertainty of equipmentMass water = (2.00 0.02)g Temp = (2.0 0.4) C Treatment of Uncertainty Multiplying or dividing measured quantities Enthalpy, H % uncertainty = sum of % uncertainty of individual quantities Mass, m = (2.00 0.02) %uncertainty mass (%m) = 0.02 x 100 = 1% 2.00 Temp = (2.0 0.4) %uncertainty temp (%T) = 0.4 x 100 = 20% 2.0 % uncertainty H = % uncertainty mass + % uncertainty temp % H = % m + %T Random and Systematic ErrorCorrect value = 33.44 Expt value = 16.72 21%%Error = (expt - correct )100% correct16.72 - 33.44 %Error = ( )100% = 50% 33.44 Enthalpy = (16.72 21%) % Random Error= m c DTEnthalpy, H = m c DT Enthalpy, H = 2.00 4.18 2.0 =16.72 0.02 100% = 1% 2.00 0.4 %DT = 100% = 20% 2.0 %DH = %Dm + %DT %DH = 1% + 20% = 21% Enthalpy = (16.72 21%) %Dm =AbsoluteDH =21 16.72 = 3.51 100Enthalpy = (16.72 3.51) Enthalpy = (17 4) %Percentage Error = 50%%Random Error =21%%Systematic Error = 29% 28. Random and Systematic Error Measuring Enthalpy change using calorimeter/thermometer Recording measurement using uncertainty of equipmentMass water = (2.00 0.02)g Temp = (2.0 0.4) C Treatment of Uncertainty Multiplying or dividing measured quantities Enthalpy, H % uncertainty = sum of % uncertainty of individual quantities Mass, m = (2.00 0.02) %uncertainty mass (%m) = 0.02 x 100 = 1% 2.00 Temp = (2.0 0.4) %uncertainty temp (%T) = 0.4 x 100 = 20% 2.0 % uncertainty H = % uncertainty mass + % uncertainty temp % H = % m + %T= m c DTEnthalpy, H = 2.00 4.18 2.0 =16.72 0.02 100% = 1% 2.00 0.4 %DT = 100% = 20% 2.0 %DH = %Dm + %DT %DH = 1% + 20% = 21% Enthalpy = (16.72 21%) %Dm =AbsoluteDH =21 16.72 = 3.51 100Enthalpy = (16.72 3.51) Enthalpy = (17 4)Random and Systematic Error%Percentage Error = 50%Correct value = 33.44 Expt value = 16.72 21%%Error = (Enthalpy, H = m c DTexpt - correct )100% correct%Random Error =21%16.72 - 33.44 %Error = ( )100% = 50% 33.44 Enthalpy = (16.72 21%)%Systematic Error = 29%% error fall outside> than % uncertainty (%Random error) Random error cannot account for % error Systematic error occurs reduce this error Ways to reduce errorRandom error (21%) Precise Temp sensor% Random ErrorTemp sensorSystematic error (29%) Reduce heat loss using styrofoam cup 29. Random and Systematic Error Measuring speed change using stopwatch Recording measurement using uncertainty of equipment G = (20 0.5) H = (16 0.5) Z = (106 1.0) Treatment of Uncertainty Multiplying or dividing measured quantitiesSpeed, s =Addition add absolute uncertainty(G + H ) Z% uncertainty = sum of % uncertainty of individual quantities (G + H) = (36 1) %uncertainty (G+H) (%G+H) = 1 x 100 = 2.77% 36 Z = (106 1.0) %uncertainty Z (%z) = 1.0 x 100 = 0.94% 106 %uncertainty s = %uncertainty(G+H) + %uncertainty(Z) % s = % (G+H) + %z *Adding or subtracting- Max absolute uncertainty is the SUM of individual uncertaintiesSpeed, s =G+H = (36 1) Z = (106 1.0)(G + H ) Z(20 +16) = 0.339 106 1.0 %D(G + H ) = 100% = 2.77% 36 1.0 %DZ = 100% = 0.94% 106 Speed, s =%DS = %D(G + H) +%DZ %DS = 2.77%+ 0.94% = 3.7%Speed, s = (0.339 3.7%) AbsoluteDS =3.7 0.339 = 0.012 100Speed, s = (0.339 0.012) 30. Random and Systematic Error Measuring speed change using stopwatch Recording measurement using uncertainty of equipment G = (20 0.5) H = (16 0.5) Z = (106 1.0) Treatment of Uncertainty Multiplying or dividing measured quantitiesSpeed, s =Addition add absolute uncertainty(G + H ) Z% uncertainty = sum of % uncertainty of individual quantities (G + H) = (36 1) %uncertainty (G+H) (%G+H) = 1 x 100 = 2.77% 36 Z = (106 1.0) %uncertainty Z (%z) = 1.0 x 100 = 0.94% 106 %uncertainty s = %uncertainty(G+H) + %uncertainty(Z) % s = % (G+H) + %z *Adding or subtracting- Max absolute uncertainty is the SUM of individual uncertaintiesRandom and Systematic ErrorSpeed, s =G+H = (36 1) Z = (106 1.0)(G + H ) Z(20 +16) = 0.339 106 1.0 %D(G + H ) = 100% = 2.77% 36 1.0 %DZ = 100% = 0.94% 106 Speed, s =%DS = %D(G + H) +%DZ %DS = 2.77%+ 0.94% = 3.7%Speed, s = (0.339 3.7%) AbsoluteDS =Speed, s = (0.339 0.012) %Percentage Error = 3%Correct value = 0.330 Expt value = 0.339 3.7%%Error = ( %Error = (expt - correct )100% correct0.339 - 0.330 )100% = 3% 0.330Speed = (0.339 3.7%) % Random Error3.7 0.339 = 0.012 100%Random Error = 3.7% 31. Random and Systematic Error Measuring speed change using stopwatch Recording measurement using uncertainty of equipment G = (20 0.5) H = (16 0.5) Z = (106 1.0) Treatment of Uncertainty Multiplying or dividing measured quantitiesSpeed, s =Addition add absolute uncertaintySpeed, s =G+H = (36 1) Z = (106 1.0)(G + H ) Z% uncertainty = sum of % uncertainty of individual quantities (G + H) = (36 1) %uncertainty (G+H) (%G+H) = 1 x 100 = 2.77% 36 Z = (106 1.0) %uncertainty Z (%z) = 1.0 x 100 = 0.94% 106 %uncertainty s = %uncertainty(G+H) + %uncertainty(Z) % s = % (G+H) + %z(G + H ) Z(20 +16) = 0.339 106 1.0 %D(G + H ) = 100% = 2.77% 36 1.0 %DZ = 100% = 0.94% 106 Speed, s =%DS = %D(G + H) +%DZ %DS = 2.77%+ 0.94% = 3.7%Speed, s = (0.339 3.7%) AbsoluteDS =*Adding or subtracting- Max absolute uncertainty is the SUM of individual uncertaintiesRandom and Systematic Error3.7 0.339 = 0.012 100Speed, s = (0.339 0.012) %Percentage Error = 3%Correct value = 0.330 Expt value = 0.339 3.7%%Error = ( %Error = (expt - correct )100% correct%Random Error = 3.7%% error fall within the % uncertainty (%Random error) Little/No systematic error Result is reliable need to reduce random error0.339 - 0.330 )100% = 3% 0.330Ways to reduce errorSpeed = (0.339 3.7%) Random error (3.7%) Precise time sensor % Random Errorprecise time sensorNo systematic error Steps/method are reliable. 32. Random and Systematic Error Recording measurement using uncertainty of equipment Volt, v = (2.0 0.2) Current, I = ( 3.0 0.6) Temp, t = (4.52 0.02)Treatment of Uncertainty Multiplying or dividing measured quantitiesEnergy, E =% uncertainty = sum of % uncertainty of individual quantity Time, t = (4.52 0.02) %uncertainty temp (%t) = 0.02 x 100 = 0.442% 4.52 Current, I = (3.0 0.6) %uncertainty current (%I) = 0.6 x 100 = 20% 3.0 Volt, v = (2.00.2) %uncertainty volt (%v) = 0.2 x 100 = 10% 2.0 % E = %t + 2 x %I + x %Vt I2 v1/2%DE = (Energy, E =t I2 v1/24.52(3.0)2 Energy, E = = 28.638 2.01/2 0.02 %Dt = 100% = 0.442% 4.52 0.6 %DI = 100% = 20% 3.0 0.2 %Dv = 100% = 10% 2.0 1 %DE = %Dt + 2 %I + %Dv 2 0.02 0.6 1 0.2 100% ) + ( 2 100% ) + ( 100% ) = 45% 4.52 3.0 2 2.0Energy, E = (28.638 45%) AbsoluteDE =Energy, E = (29 13)45 28.638 =13 100 33. Random and Systematic Error Recording measurement using uncertainty of equipment Volt, v = (2.0 0.2) Current, I = ( 3.0 0.6) Temp, t = (4.52 0.02)Treatment of Uncertainty Multiplying or dividing measured quantitiesEnergy, E =t I2 v1/2% uncertainty = sum of % uncertainty of individual quantity Time, t = (4.52 0.02) %uncertainty temp (%t) = 0.02 x 100 = 0.442% 4.52 Current, I = (3.0 0.6) %uncertainty current (%I) = 0.6 x 100 = 20% 3.0 Volt, v = (2.00.2) %uncertainty volt (%v) = 0.2 x 100 = 10% 2.0 % E = %t + 2 x %I + x %V%DE = (Energy, E =t I2 v1/24.52(3.0)2 Energy, E = = 28.638 2.01/2 0.02 %Dt = 100% = 0.442% 4.52 0.6 %DI = 100% = 20% 3.0 0.2 %Dv = 100% = 10% 2.0 1 %DE = %Dt + 2 %I + %Dv 2 0.02 0.6 1 0.2 100% ) + ( 2 100% ) + ( 100% ) = 45% 4.52 3.0 2 2.0Energy, E = (28.638 45%) AbsoluteDE =Energy, E = (29 13)45 28.638 =13 100Random and Systematic Error %Percentage Error = 50%Correct value = 19.092 Expt value = 28.638 45%%Error = ( %Error = (expt - correct )100% correct28.638 -19.092 )100% = 50% 19.092Energy, E = (28.638 45%) % Random Error%Random Error = 45%%Systematic Error = 5% 34. Random and Systematic Error Recording measurement using uncertainty of equipmentEnergy, E =t I2 v1/2% uncertainty = sum of % uncertainty of individual quantity Time, t = (4.52 0.02) %uncertainty temp (%t) = 0.02 x 100 = 0.442% 4.52 Current, I = (3.0 0.6) %uncertainty current (%I) = 0.6 x 100 = 20% 3.0 Volt, v = (2.00.2) %uncertainty volt (%v) = 0.2 x 100 = 10% 2.0 % E = %t + 2 x %I + x %V%DE = (t I2 v1/24.52(3.0)2 Energy, E = = 28.638 2.01/2 0.02 %Dt = 100% = 0.442% 4.52 0.6 %DI = 100% = 20% 3.0 0.2 %Dv = 100% = 10% 2.0Volt, v = (2.0 0.2) Current, I = ( 3.0 0.6) Temp, t = (4.52 0.02)Treatment of Uncertainty Multiplying or dividing measured quantitiesEnergy, E =1 %DE = %Dt + 2 %I + %Dv 2 0.02 0.6 1 0.2 100% ) + ( 2 100% ) + ( 100% ) = 45% 4.52 3.0 2 2.0Energy, E = (28.638 45%) AbsoluteDE =Energy, E = (29 13)45 28.638 =13 100Random and Systematic Error %Percentage Error = 50%Correct value = 19.092 Expt value = 28.638 45%%Error = (expt - correct )100% correct%Random Error = 45%% error fall outside> than % uncertainty (%Random error) Random error cannot account for % error Systematic error occur small compared to random error28.638 -19.092 %Error = ( )100% = 50% 19.092Energy, E = (28.638 45%) % Random Error%Systematic Error = 5%Reduce random error HUGE (45%) Precise instrument. Temp sensor 35. Expt on enthalpy change of displacement between Zinc and copper sulphate 25 ml (1M) (0.025mole) CuSO4 solution added to cup. Initial Temp, T1 taken. Excess zinc powder was added. Final Temp T2 was taken. Calculate H for reaction.Treatment of uncertaintyAdding or subtracting Max absolute uncertainty is the SUM of individual uncertaintiesInitial mass beaker, M1 = (20.00 0.01) g Final mass beaker + CuSO4 M2 = (45.00 0.01)gInitial Temp, T1 = (20.0 0.2)C Final Temp, T2 = (70.6 0.2)CMass CuSO4 m = (M2 M1) Absolute uncertainty, m = (0.01 + 0.01) = 0.02Diff Temp T = (T2 T1) Absolute uncertainty, T = (0.2 + 0.2) = 0.4Mass CuSO4 m = (45.00 20.00) = 25.00 Absolute uncertainty, m = (0.01 + 0.01) = 0.02 Mass CuSO4 m = (25.00 0.02)gDiff Temp T = (70.6 20.0) = 50.6 Absolute uncertainty, T = (0.2 + 0.2) = 0.4 Diff Temp, T = (50.6 0.4)Mass CuSO4 m = (25.00 0.02)gTemp = (50.6 0.4) C 36. Expt on enthalpy change of displacement between Zinc and copper sulphate 25 ml (1M) (0.025mole) CuSO4 solution added to cup. Initial Temp, T1 taken. Excess zinc powder was added. Final Temp T2 was taken. Calculate H for reaction.Treatment of uncertaintyAdding or subtracting Max absolute uncertainty is the SUM of individual uncertaintiesAddition/Subtraction/Multiply/DivideMultiplying or dividing Max %uncertainty is the SUM of individual %uncertainties Addition/Subtraction Add absolute uncertaintyInitial mass beaker, M1 = (20.00 0.01) g Final mass beaker + CuSO4 M2 = (45.00 0.01)gInitial Temp, T1 = (20.0 0.2)C Final Temp, T2 = (70.6 0.2)CMass CuSO4 m = (M2 M1) Absolute uncertainty, m = (0.01 + 0.01) = 0.02Diff Temp T = (T2 T1) Absolute uncertainty, T = (0.2 + 0.2) = 0.4Mass CuSO4 m = (45.00 20.00) = 25.00 Absolute uncertainty, m = (0.01 + 0.01) = 0.02 Mass CuSO4 m = (25.00 0.02)gDiff Temp T = (70.6 20.0) = 50.6 Absolute uncertainty, T = (0.2 + 0.2) = 0.4 Diff Temp, T = (50.6 0.4)Mass CuSO4 m = (25.00 0.02)gTemp = (50.6 0.4) CEnthalpy, H = (M2-M1) x c x (T2-T1) Multiplication Add % uncertainty 37. Expt on enthalpy change of displacement between Zinc and copper sulphate 25 ml (1M) (0.025mole) CuSO4 solution added to cup. Initial Temp, T1 taken. Excess zinc powder was added. Final Temp T2 was taken. Calculate H for reaction.Treatment of uncertaintyAdding or subtracting Max absolute uncertainty is the SUM of individual uncertaintiesAddition/Subtraction/Multiply/DivideMultiplying or dividing Max %uncertainty is the SUM of individual %uncertainties Addition/Subtraction Add absolute uncertaintyInitial mass beaker, M1 = (20.00 0.01) g Final mass beaker + CuSO4 M2 = (45.00 0.01)g Mass CuSO4 m = (M2 M1) Absolute uncertainty, m = (0.01 + 0.01) = 0.02Initial Temp, T1 = (20.0 0.2)C Final Temp, T2 = (70.6 0.2)C Diff Temp T = (T2 T1) Absolute uncertainty, T = (0.2 + 0.2) = 0.4Enthalpy, H = (M2-M1) x c x (T2-T1) Enthalpy, H = m c DTMultiplication Add % uncertaintyEnthalpy, H = 25.00 4.18 50.6 = 5.29 Mass CuSO4 m = (45.00 20.00) = 25.00 Absolute uncertainty, m = (0.01 + 0.01) = 0.02 Mass CuSO4 m = (25.00 0.02)g Mass CuSO4 m = (25.00 0.02)gDiff Temp T = (70.6 20.0) = 50.6 Absolute uncertainty, T = (0.2 + 0.2) = 0.4 Diff Temp, T = (50.6 0.4)Temp = (50.6 0.4) CTreatment of Uncertainty Multiplying or dividing measured quantities Enthalpy, H = m c DT % uncertainty = sum of % uncertainty of individual quantities Mass, m = (25.00 0.02) %uncertainty mass (%m) = 0.02 x 100 = 0.08% 25.00 Temp = (50.6 0.4) %uncertainty temp (%T) = 0.4 x 100 = 0.8% 50.6 % uncertainty H = % uncertainty mass + % uncertainty temp % H = % m + %T0.025moleCuSO4 = 5.291moleCuSO4 = 5.29 1 = 212 0.0250.02 100% = 0.08% 25.00 0.4 %DT = 100% = 0.8% 50.6 %DH = %Dm + %DT %DH = 0.08% + 0.8% = 0.88% Enthalpy = (212 0.88%) %Dm =AbsoluteDH =Enthalpy = (212 1.8) Enthalpy = (212 2)0.88 212 =1.86 100 Continue next slide 38. Random and Systematic Error Measuring Enthalpy change using calorimeter/thermometer Recording measurement using uncertainty of equipmentMass CuSO4 = (25.00 0.02)g Temp = (50.6 0.4) CEnthalpy = (212 0.88%)%Percentage Error = 15%Random and Systematic ErrorCorrect value = 250 Expt value = 212 0.8% %Random Error =0.88%%Error = ( %Error = (expt - correct )100% correct212 - 250 )100% =15% 250Enthalpy = (212 0.88%) % Random Error%Systematic Error = 14.1% 39. Random and Systematic Error Measuring Enthalpy change using calorimeter/thermometer Recording measurement using uncertainty of equipmentMass CuSO4 = (25.00 0.02)g Temp = (50.6 0.4) CEnthalpy = (212 0.88%)%Percentage Error = 15%Random and Systematic ErrorCorrect value = 250 Expt value = 212 0.8% %Random Error =0.88%%Error = ( %Error = (expt - correct )100% correct212 - 250 )100% =15% 250%Systematic Error = 14.1%% error fall outside> than % uncertainty (%Random error) Small random error cannot account for % error Systematic error occurs reduce this error Ways to reduce errorEnthalpy = (212 0.88%) % Random ErrorSystematic error (14.2%)Small random error Equipments OK 40. Random and Systematic Error Measuring Enthalpy change using calorimeter/thermometer Recording measurement using uncertainty of equipmentMass CuSO4 = (25.00 0.02)g Temp = (50.6 0.4) CEnthalpy = (212 0.88%)%Percentage Error = 15%Random and Systematic ErrorCorrect value = 250 Expt value = 212 0.8% %Random Error =0.88%%Error = ( %Error = (expt - correct )100% correct%Systematic Error = 14.1%% error fall outside> than % uncertainty (%Random error) Small random error cannot account for % error Systematic error occurs reduce this error212 - 250 )100% =15% 250Ways to reduce errorEnthalpy = (212 0.88%) % Random ErrorReduce heat loss use styrofoam cupSmall random error Equipments OKSystematic error (14.2%)Extrapolate to higher temp (Temp correction)Stir the solution to distribute heatstirrer Assumption wrong Heat capacity cup is significant Specific heat capacity CuSO4 is not 4.18 Thermometer has measurable heat capacity Density solution not 1.00g/dm3 41. Acknowledgements Thanks to source of pictures and video used in this presentation http://crescentok.com/staff/jaskew/isr/tigerchem/econfig/electron4.htm http://pureinfotech.com/wp-content/uploads/2012/09/periodicTable_20120926101018.png http://www.wikihow.com/Find-the-Circumference-and-Area-of-a-CircleThanks to Creative Commons for excellent contribution on licenses http://creativecommons.org/licenses/Prepared by Lawrence Kok Check out more video tutorials from my site and hope you enjoy this tutorial http://lawrencekok.blogspot.com