Monday, May 30, 2011

IB Biology, IB Chemistry, Uncertainty, Standard deviation and Error Analysis

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


1) % Uncertainty Method
  • Uncertainty time = Uncertainty stop watch + reaction time, ( 0.01 + 0.09 ) = ( 0.10 )
  • Time  = 4.83 ±( 0.10 )
2) Max-min range Method
  • Uncertainty time = (Max time - Min time)/2, = ( 5.28 - 4.47 )/2 = 0.41
  • Time = 4.83 ±0.41




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


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




1) % 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




2) 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
3) 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 = 0.207
Uncertainty Rate = 0.207 ± ( 0.220 --- 0.190 )



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Uncertainty Cal for Conc, 30ml 0.1M KI (2 Methods used)
1) % Uncertainty Method
Pipette uncertainty  =  ± 0.4 and Total Volume used = 30ml


1) % Uncertainty Method
%Uncertainty Conc = %Uncertainty Vol of KI + %Uncertainty Vol Water
%Uncertainty Vol KI = (0.4/ 30) x100%=1.3%
%Uncertainty Conc = % Uncertainty Vol KI
%Uncertainty Conc = 1.3%








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



.....................................................................................................................................................
2) Max/Minimum Method
Preparing 0.053M from 0.1M KI using pipette.
Pipette uncertainty = ± 0.4
Max 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 = 16.2
Min 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 used
Min Vol KI = 15.8 ± 0.4 = 15.4
Max 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 = 0.051
Min Conc = 0.051
Uncertainty Conc = 0.053 ± ( 0.054 --- 0.051)
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Uncertainty Cal, 2 fold Serial dilution using 3% H2O2
2 Methods using 
1st % 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 xV (conc)
M x (1.5 +1.5) = 3% x 1.5
M = 1.5%

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


Min Conc H2O2 when
Min Vol H2O2 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 Cal 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/ gradient of curve
Perform 3 trials at 1.5% and take Average rate
Average Rate by taking average for 3 trials
Uncertainty for Rate = Standard deviation
Use Excel to calculate Std deviation


















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Video, adding uncertainty, error bar, Std deviation into Excel
Keynotes from video
Video tutorial on how to add standard deviation into our data point in Excel
  • Adding horizontal/vertical error bar/ uncertainty or Std deviation
  • Follow notes provided in powerpoint
Video on adding Std deviation into Excel

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