Wednesday, June 1, 2011

IB Chemistry, IB Biology, Enthalpy, Uncertainty, Error, Standard Deviation

IB Chemistry, Enthalpy, Uncertainty Calculation, Error analysis, Standard Deviation

Enthalpy change for displacement Zn + CuSO4

2 methods for Uncertainty Cal
1) % Uncertainty Method
Zinc excess, Copper limiting,
Conc CuSO4 = (1M± 0)
Vol = (20.0 ± 0.3) ml
Mol 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 42.9
Q = 3589.8J ----------0.02 mol
Q = 3589.9/0.02------ 1mol
Q = 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




2) Using Max/Min Method
Q = mc△t
Q = 20.00 x 4.184 x 42.9
Q = 3589.8J ----------0.02 mol
Q = 3589.9/0.02------ 1mol
Q = 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=42.5
m = 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 -----------0.02mol
Max Q = 3677.7/0.02-------1 mol
Max 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------------0.02mol
Min Q = 3503.0J/0.02-------1 mol
Min Q = 175.1kJ/mol
Using Max/Min Method                           Using %Uncertainty Method
Q = 179.5 ± ( 183.3--175.1)kJ/mol          Q = (179.5 ± 2.43%) = (180 ± 4)kJ/mol
Q = (183.3---175.1)                    Q = (184---176)

..................................................................................................................................................

Accurate way taking Uncertainty Moles Cu

1) Using %Uncertainty Method.
%Uncertainty moles of Cu used
Conc CuSO4 = (1M±0) , Vol = (20.0 ± 0.3) ml
Moles 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

2) Using Max/Min Method

Conc CuSO4 = (1M±0) , Vol = (20.0 ± 0.3) ml
Moles 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=42.5
m = 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 = 0.0203
Min moles Cu = Min M x Min Vol = 1 x 19.7 = 0.0197
Uncertainty moles of Cu 0.020 ± (0.023--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 ----------0.02mol
Min Q = 3503.0J-----------0.02mol
Uncertainty moles of Cu 0.02 ± (0.023--0.0197)
Max moles Cu = 0.023
Min 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---------------0.023mol Cu
Max Q = 3677.7/0.0197-------1 mol                   Min Q = 3503.0/0.023--------1mol
Max Q = 186.7kJ/mol                                        Min Q = 152.3kJ/mol
Q = 179.5 ± ( 186.7---152.3 )kJ/mol


%Uncertainty Method                                       Max/Min Method
Q = ( 186 ----172 )kJ/mol                                   Q = ( 186.7---152.3 )kJ/mol
..................................................................................................................................................
IA must be done with minimum 3 trials, for valid conclusion.
Displacement done with 3 trials.
Click HERE for Data

Displacement of Zinc + CuSO4
Zinc excess, Copper limiting,
Conc CuSO4 = (1M±0)
Vol = (20.0 ± 0.3) ml
Mol of Cu ions= M x V = 0.02 mol





Two Methods used
1st Method
Average 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    Uncertainty Q = Standard Deviation Q= (19.28)
Average Q = 365.4J----------0.02 mol                      Uncertainty Q = 19.28-----------0.02 mol
Average Q = 365.4/0.02------1 mol                        Uncertainty Q = 19.28/0.02-----1 mol
Average Q = 18.3kJ/mol                                       Uncertainty Q = 0.96kJ/mol
Average Q = (18.3 ± 0.96)kJ/mol                           


2nd Method 
Taking average Temp change
Click 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 ml
Mol 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 4.1
Q = 343.1J ---------0.02 mol
Q = 343.1/0.02------1 mol
Q = 17.155kJ/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

More accurate way is to consider Uncertainty for moles Cu
Conc CuSO4 = (1M± 0), Vol = (20.0 ± 0.3) ml
Mol 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

You can also use Max/min Method as shown above.
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


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