*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*

*1*^{st}Method –

*Average Rate = (10.43 ± Std deviation )*

*Average Rate = (10.43 ± 0.19)*

*2*^{nd}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)**

*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**

*.....................................................................................................................................................*

**Notes for the above post is summarise into slideshare:**

*Thanks to Stephen Taylor for his data table format*
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