IB Chemistry, IB Biology on Uncertainty calculation, error analysis and standard deviation on enthalpy change

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Prepared by Lawrence Kok

Video Tutorial on Uncertainty Calculation, standard deviation and Error analysis in Enthalpy Change

IB Chemistry, Uncertainty Calculation, Error analysis, Standard Deviation

Enthalpy change for displacement Zn + CuSO4

2 methods for Uncertainty Calculation• 1st Method using % Uncertainty

Zinc excess, Copper limitingConc CuSO4 = (1M ± 0)Vol = (20.0 ± 0.3) mlMol of Cu ions= M x V= 0.02 mol△t = (68.0±0.2) - (25.1±0.2) = (42.9±0.4)m = 20.0 ± 0.3ml

Q = mc t△Q = 20.00 x 4.184 x  t△Q = 20.00 x 4.184 x 42.9Q = 3589.8J ----------0.02 molQ = 3589.9/0.02------ 1molQ = 179.5kJ/mol

Extrapolation for Temp increase, 68.0 - 25.1= 42.9

%Uncertainty Q = % Uncertainty m + % Uncertainty  t△%Uncertainty m = (0.3/20) x 100% = 1.5%%Uncertainty  t = (0.2+0.2) / 42.9 x 100% = 0.93%△

%Total Uncertainty = (0.93 + 1.5) = 2.43%

Q = (179.5 ± 2.43%)Q = (179.5 ± 4.36) = (180 ± 4)kJ/mol

•2nd Method Using Max/Min

Q = mc t△Q = 20.00 x 4.184 x 42.9Q = 3589.8J ----------0.02 molQ = 3589.9/0.02------1molQ = 179.5kJ/mol

Q = mc t△△t = 42.9 ± (0.2+02) = (42.9±0.4)   Max t = 42.9+ 0.4 = 43.3   Min t = 42.9- 0.4 = 42.5m = 20.0 ± 0.3ml                             Max m = 20.0+ 0.3=20.3     Min m = 20.0- 0.3 = 19.7

Max   Q = Maximum   m and Maximum  t△ △ △Max   Q = m c t = 20.3 x 4.184 x 43.3 = 3677.7J△ △Max Q = 3677.7J -----------0.02molMax Q = 3677.7/0.02-------1molMax Q = 183.3kJ/mol

Min  Q = Minimum   m and Minimum  t△ △ △Min  Q = mc t = 19.7 x 4.184 x 42.5 = 3503.0J△ △Min Q = 3503.0J------------0.02molMin Q = 3503.0J/0.02-------1molMin Q = 175.1kJ/molUsing Max/Min Method                          Using %Uncertainty MethodQ = 179.5 ± ( 183.3--175.1)kJ/mol          Q = (179.5 ± 2.43%) = (180 ± 4)kJ/molQ = (183.3---175.1)                     Q = (184---176)

More Accurate way by taking Uncertainty in Moles Cu1st Method Using %Uncertainty

%Uncertainty moles of Cu usedConc CuSO4 = (1M±0) , Vol = (20.0 ± 0.3) mlMoles of Cu ions = M x V= 0.02 mol

%Uncertainty moles Cu = %Uncertainty in M + %Uncertainty in Vol %Uncertainty Cu = 0% + (0.3/ 20) x 100% = 0% +1.5% = 1.5%

Total %Uncertainty Q = %Uncertainty m + %Uncertainty  t + %Uncertainty mol Cu△Total %Uncertainty Q = 1.5% + 0.93% + 1.5% = 3.93%

Q = (179.5 ± 3.93%)= (179.5 ± 7.05) = (179 ± 7)Q = ( 186 ----172 )kJ/mol

2nd Method Using Max/Min

Conc CuSO4 = (1M±0) , Vol = (20.0 ± 0.3)mlMoles of Cu ions = M x V = 0.02 mol

△t = 42.9 ± (0.2+02) = (42.9±0.4)    Max t= 42.9+0.4 = 43.3     Min t= 42.9- 0.4= 42.5m = 20.0 ± 0.3ml                             Max m= 20.0+ 0.3=20.3    Min m= 20.0- 0.3= 19.7

Max Vol = 20.3ml, Min Vol = 19.7ml        Molarity = (1M±0)

Max moles Cu = Max M x Max Vol = 1 x 20.3 = 0.0203Min moles Cu = Min M x Min Vol = 1 x 19.7 = 0.0197

Uncertainty moles of Cu = 0.020 ± (0.0203--0.0197)

Max Uncertainty Q = mc t = 20.3 x 4.184 x 43.3 = 3677.7J△Min Uncertainty Q = mc t = 19.7 x 4.184 x 42.5 = 3503.0J△

Max Q = 3677.7J----------0.02molMin Q = 3503.0J-----------0.02mol

Uncertainty moles of Cu = 0.02 ± (0.0203--0.0197)Max moles Cu = 0.0203Min moles Cu = 0.0197

Max Q = Max Uncertainty Q + Min Uncertainty mol Cu ( will give greatest error )Min Q = Min Uncertainty Q + Max Uncertainty mol Cu ( will give least error )

Max Q = 3677.7---------------0.0197 mol Cu      Min Q = 3503.0-----------------0.0023mol CuMax Q = 3677.7/0.0197------1 mol                  Min Q = 3503.0/0.023--------1molMax Q = 186.7kJ/mol                                      Min Q = 152.3kJ/mol

Q = 179.5 ± ( 186.7---152.3 )kJ/mol

% Uncertainty Method                                      Max/Min MethodQ = ( 186 ----172 )kJ/mol                                   Q = ( 186.7---152.3 )kJ/mol

IA must be done with minimum 3 trials, for valid conclusion.

Displacement of Zinc + CuSO4

Displacement done with 3 trials.

• Zinc excess, Copper limiting

• Conc CuSO4 = (1M±0)

• Vol = (20.0 ± 0.3) ml

• Mol of Cu ions = M x V = 0.02 mol

Click HERE for Data

Two Methods used1st MethodAverage Q for 3 trials and using Standard deviation as uncertainty

Temp change for 3 trials△t1 =( 26.2 ± 0.2)- (21.7± 0.2)=(4.5± 0.4)

△t2 = (26.1 ± 0.2)- (21.6± 0.2)=(4.5± 0.4)

△t3 = (25.8 ± 0.2)- (21.7± 0.2)=(4.1± 0.4)

Q1 = mc t1 = 20.0 x 4.184 x 4.5 = 376.5△

Q2 = mc t2 = 20.0 x 4.184 x 4.5 = 376.5△

Q3 = mc t3 = 20.0 x 4.184 x 4.1= 343.1△

Average Q = (376.5 + 376.5 + 343.1)/3 = 365.4J    Average Q = 365.4J ----------0.02 mol                      Average Q = 365.4/0.02------1 mol                        Average Q = 18.3kJ/mol                                                  

Uncertainty Q = Standard Deviation Q= (19.28)

Uncertainty Q = 19.28-----------0.02 mol

Uncertainty Q = 19.28/0.02-----1 mol

Uncertainty Q = 0.96kJ/mol

Average Q = (18.3 ± 0.96)kJ/mol     

2nd Method 

Taking average Temp changeClick HERE for data

Average Temp data is taken.Displacement for Zinc + CuSO4

Zinc excess, Copper limiting,Conc CuSO4 = (1M± 0)Vol = 20.0 ± 0.3 mlMol of Cu ions= M x V = 0.02 mol△t = (25.7 ± 0.2) - (21.6 ± 0.2)= (4.1 ± 0.4)

By extrapolation using average temp△t = (25.7 ± 0.2) - (21.6 ± 0.2)= (4.1 ± 0.4)

Q = mc t△Q = 20.0 x 4.184 x  t△Q = 20.0 x 4.184 x 4.1Q = 343.1J ---------0.02 molQ = 343.1/0.02------1 mol

Q = 17.155kJ/mol

More accurate way is to consider Uncertainty for moles Cu

Conc CuSO4 = (1M± 0), Vol = (20.0 ± 0.3) mlMol of Cu ions = M x V

%Uncertainty moles Cu = %Uncertainty in M + %Uncertainty in Vol %Uncertainty Cu = 0% + (0.3/ 20) x 100% = 0% +1.5% = 1.5%

%Total Uncertainty Q = %Uncertainty m + %Uncertainty  t + %Uncertainty mol Cu△

%Total Uncertainty Q = 1.5% + 9.75% + 1.5% = 12.75%

Q = (17.15± 12.75%) = (17.15± 2.18)kJ/mol

Using %Uncertainty Method 

Temp increase = (25.7 ± 0.2) - (21.6 ± 0.2)= (4.1 ± 0.4)%Uncertainty Q = % Uncertainty m + % Uncertainty  t△%Uncertainty m = (0.3/20) x 100% = 1.5%%Uncertainty  t = (0.4 / 4.1) x 100% = 9.75%△

%Total Uncertainty = (1.5 + 9.75)% = 11.25%

Q = (17.155± 11.25%)= (17.15±1.92)kJ/mol

In short, 

• Make sure you perform 3 trials and compute the average or use std deviation

• Use %Uncertainty or Max/min Method of your choice

• Use lots of common sense for error treatment

• The only certainty in life is continual uncertainty

• Have fun with uncertainty

Acknowledgements

Thanks to source of pictures and video used in this presentation

Thanks to Creative Commons for excellent contribution on licenseshttp://creativecommons.org/licenses/

Prepared by Lawrence Kok

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