Sunday, October 16, 2011

IB Chemistry uncertainty error calculation for rate of reaction and standard deviation

IB Chemistry on error analysis, uncertainty error calculation and standard deviation for rate of reaction.


Research Question - How changing %conc NaCI affect rate of reaction?
Data collected by two students to compute rate and its uncertainty. Which is correct?
Data by student 1-

  • 5 trials for conductivity measurement was done for each conc
  • No average conductivity was taken 
  • 5 different rates obtained for each conc















Graph by student 1 - change of conductivity over time for all trials
For 1% Conc - Rate for first 60s calculated by
  • mesuring slope for 5 trials
  • average rate was taken
  • (Rate 1 + Rate 2 + Rate 3 + Rate 4 + Rate 5)/5
  • ( 10.66±0.02 + 10.41±0.05 + 10.47±0.04 + 10.14±0.05 + 10.50±0.02 ) /5
    Average Rate = (10.43)
    How to calculate uncertainty for rate?



Wrong way to compute rate and its uncertainty
Average Rate = (10.43 ± Average Uncertainty)

NEVER take the average uncertainty
± Uncertainty Rate = (0.02 + 0.05 + 0.04 + 0.05 +0.02)/5 = 0.03
Average Rate = (10.43 ±0.03) WRONG!!!!!

Correct way to compute rate and its uncertainty
1st Method –
Average Rate = (10.43 ± Std deviation )
Average Rate = (10.43 ± 0.19)

2nd Method –
Average Rate =  10.43 ±[ (max rate – min rate)/number of trials]
± Uncertainty rate = (max rate – min rate)/ number of trials
                                  = (10.66 – 10.14)/5 = 0.10
Average Rate = (10.43 ±0.10)
...............................................................................................................................................
Data collected by student 2

Rate = Average Conductivity change/time

  • Average conductivity and std dev was computed for 5 trials
  • For 1% - average conductivity was taken at different time
  • Rate is average conductivity/time
  • For 1% conc - only 1 curve and std deviation is plotted
Graph by student 2 - Average conductivity over time was plotted
Rate = Average conductivity /time
  • Rate for 1% = Average change of conductivity for first 60s
  • Average conductivity at 60s = (0.10±0.07)
Rate for 1% -
  • Measure the slope/gradient for 1st 60s
  • Rate for 1% = 0.10/60 = 0.00167
  • Rate = 0.00167





How to calculate uncertainty for rate?

Calculating uncertainty for rate for first 60s
1st method - using uncertainty from the slope
  • Rate = (0.00167±0.0012) using uncertainty of the slope

Rate = (0.00167 ±0.0012)

2nd method - using Max/Min error method
Conductivity for 1% at 60s = (0.10 +0.07)
  • Rate = Conductivity change /60s = (0.10±0.07)/60
  • Rate = 0.10/60 = 0.00167
Max Conductivity = 0.107            Min Conductivity = 0.03
Max Uncertainty Rate = Max Conductivity/60 = 0.107/60 = 0.00178

Min Uncertainty Rate = Min Conductivity/60 = 0.03/60 = 0.0005
Rate = 0.00167±(0.00178 --0.0005)

3rd Method - % Uncertainty method
Conductivity for 1% at 60s = (0.10±0.07)
  • Rate = Conductivity change/60s 
  • Rate = (0.10±0.07)/60
  • Rate = 0.10/60 = 0.00167
How to calculate uncertainty rate?








Calculating uncertainty rate

  • % Uncertainty rate = % Uncertainty Conductivity
  • % Uncertainty Conductivity = (0.07/0.10) x 100% = 70%
Rate = (0.00167±70%) convert to absolute - (70/100) x 0.00167 = 0.0011
Rate = (0.00167±0.0011)
.......................................................................................................................................................
Difference between student 1 and student 2

Student 1 data :
For 1% conc – 5 rates was obtained
( 10.66±0.02 + 10.41±0.05 + 10.47±0.04 + 10.14±0.05 + 10.50±0.02 )
·         At 1% conc – 5 rates obtained from 5 trials
·         At 1% conc - 5 curves – 5 slopes was obtained
·         Average rate was calculated
·         Uncertainty rate is calculated using std deviation or max/min method
·         NEVER take average for uncertainty!
Student 2 data:
For 1% conc – 1 rate was obtained
·         At 1% conc – average conductivity was taken
·         At 1 % conc – 1 curve – 1 slope was taken
·         Rate was calculated form average change conductivity/time
·         Uncertainty rate is calculated using 3 methods shown above

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Notes for the above post is summarise into slideshare:


Thanks to Stephen Taylor for his data table format

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