IB Chemistry on Uncertainty calculation for Order and Rate of reaction

1. Using 2nd methodto find order
Determinationorder: Na2S2O3 + 2HCI → NaCI + H2O + S + SO2
Order of Na2S2O3
Conc Na2S2O3 changes, fix [HCI] = 0.1M
Na2S2O3 added
HCI was added
Time taken X fade away
Conc
Na2S2O3
Time/s
Trial 1
±0.01
Time/s
Trial 2
±0.01
Time/s
Trial 3
±0.01
Average
time
Rate
0.05 102.96 103.23 114.80 107.00 0.00046
0.10 45.43 44.08 38.35 42.62 0.0023
0.15 27.36 27.13 26.36 26.95 0.0055
0.20 18.06 18.57 17.53 18.05 0.0111
0.25 15.26 15.44 16.88 15.86 0.0158
Result expt
00046.0
107
05.0
.

timeAve
Conc
Rate
Cal for Conc 0.05M
4 ways for uncertainty rate
1st method
Ave time = (107.00 ± 0.01)
% uncertainty time = 9.34 x 10-3 %
%∆ Rate = % ∆ Time
Rate = 0.00046 ± 9.34 x 10-3 %
= 0.00046 ± 0.000000043
Too small
Poor choice
4th method
Uncertainty rate = (Max – min) for rate
Rate 1 = Conc/time 1 = 0.05 / 102.96 = 0.00049
Rate 2 = Conc/time 2 = 0.05 / 103.23 = 0.00048
Rate 3 = Conc/ time 3 = 0.05 / 114.80 = 0.00043
Max rate = 0.00049
Min rate = 0.00043
Range = (Max – Min)/2
Range = (0.00049 – 0.00043)/2
= 0.00003
Average rate = (R1 + R2 + R3)/3
= 0.00047 ± 0.00003
Consistent
Good choice
3rd method
Uncertainty rate = std deviation (for conc 0.05)
Rate 1 = Conc/time 1 = 0.05 / 102.96 = 0.00049
Rate 2 = Conc/time 2 = 0.05 / 103.23 = 0.00048
Rate 3 = Conc / time 3 = 0.05 / 114.80 = 0.00043
Average rate = (R1 + R2 + R3)/3
= 0.00047 ± std dev
= 0.00047 ± 0.000032
Consistent
Good choice
2nd method
Using Range (Max – Min) for time
Range = (Max – Min) for time/2
Range = (114.80 – 102.96)/2 = 5.92
Ave time = (107.00 ± 5.92)
% uncertainty time = 5.5%
% ∆Rate = % ∆Time
Rate = 0.00046 ± 5.5%
= 0.00046 ± 0.000026
Consistent
Good choice

2. Determinationorder : Na2S2O3 + 2HCI → NaCI + H2O + S + SO2
Order of Na2S2O3
Conc Na2S2O3 changes, fix [HCI] = 0.1M
Na2S2O3 added
HCI was added
Time taken X fade away
Conc
Na2S2O3
Time/s
Trial 1
±0.01
Time/s
Trial 2
±0.01
Time/s
Trial 3
±0.01
Average
time
Rate
0.05 102.96 103.23 114.80 107.00 0.00046
0.10 45.43 44.08 38.35 42.62 0.0023
0.15 27.36 27.13 26.36 26.95 0.0055
0.20 18.06 18.57 17.53 18.05 0.0111
0.25 15.26 15.44 16.88 15.86 0.0158
Result expt
00046.0
00.107
05.0
.

timeAve
Conc
Rate
Cal for Conc 0.05M
2nd method
Using Range (Max – Min) for time
Range = (Max – Min)/2
Range = (114.80 – 102.96)/2 = 5.92
Ave time = (107.00 ± 5.92)
% uncertainty time = 5.5%
% ∆Rate = %∆Time
Rate = 0.00046 ± 5.5%
= 0.00046 ± 0.000026
Consistent
Good choice
Uncertaintyrate for conc 0.05M
Conc
Na2S2O3
Time/s
Trial 1
±0.01
Time/s
Trial 2
±0.01
Time/s
Trial 3
±0.01
Average
time
± Time
Range (Max- Min)/2
% ±Time Rate(±rate)
0.05 102.96 103.23 114.80 107.00 (114.8-102.96)/2= 5.92 5.5% 0.00046±0.000026
0.10 45.43 44.08 38.35 42.62 (45.43 – 38.35)/2 = 3.54 8.3% 0.0023 ±0.00027
0.15 27.36 27.13 26.36 26.95 (27.13 – 26.36)/2 = 0.50 1.8% 0.0055 ±0.00022
0.20 18.06 18.57 17.53 18.05 (18.06 – 17.53)/2 = 0.52 2.8% 0.0111 ±0.0006
0.25 15.26 15.44 16.88 15.86 (16.88 – 15.26)/2 = 0.81 5.1% 0.0158 ±0.0011

3. Determinationorder: Na2S2O3 + 2HCI → NaCI + H2O + S + SO2
Plot of Conc vs Rate
Conc
Na2S2O3
Rate(±rate)
0.05 0.00046±0.0000026
0.10 0.0023 ±0.00027
0.15 0.0055 ±0.00022
0.20 0.0111 ±0.0006
0.25 0.0158 ±0.0011
Order for Na2S2O3 (fix conc HCI)
Let Rate = k[Na2S2O3]x [HCI] y
Rate
Conc Na2S2O3
Uncertainty rate
Conc Na2S2O3
Rate
Best fit
Order = 2.21
Best fit
Order = 2.21
Max fit
Order = 2.29
Min fit
Order = 2.12
Lowest uncertainty (Lowest Conc)
to
Highest uncertainty (Highest Conc)
Highest uncertainty (Lowest Conc)
to
Lowest uncertainty (Highest Conc)
Max order
Min order

4. Determinationorder: Na2S2O3 + 2HCI → NaCI + H2O + S + SO2
Conc
Na2S2O3
Rate(±rate)
0.05 0.00046±0.0000026
0.10 0.0023 ±0.00027
0.15 0.0055 ±0.00022
0.20 0.0111 ±0.0006
0.25 0.0158 ±0.0011
Conc
Na2S2O3
Rate(±rate)
0.05 0.00044
0.10 0.00221
0.15 0.0055
0.20 0.0114
0.25 0.017
Max order
Max fit
Order = 2.29
Max order – Lowest uncertainty (Lowest Conc) to Highest uncertainty (Highest Conc)
Conc
Na2S2O3
Rate(±rate)
0.05 0.00046±0.0000026
0.10 0.0023 ±0.00027
0.15 0.0055 ±0.00022
0.20 0.0111 ±0.0006
0.25 0.0158 ±0.0011
Min order
Conc
Na2S2O3
Rate(±rate)
0.05 0.00048
0.10 0.00248
0.15 0.0055
0.20 0.0108
0.25 0.0147
Conc Na2S2O3
Conc Na2S2O3
Rate
Rate
Min fit
Order = 2.12
Min order – Highest uncertainty (Lowest Conc) to Lowest uncertainty (Highest Conc)
Highest uncertainty
0.0158 + 0.0011
= 0.017
Lowest uncertainty
0.00046 – 0.000026
= 0.00044
Highest uncertainty
0.00046 + 0.000026
= 0.00048
Lowest uncertainty
0.0158 – 0.0011
= 0.0147
Lowest uncertainty
Highest uncertainty
Lowest uncertainty
Highest uncertainty
Max order
Min order

5. % Systematic = (10.7 – 4 )= 6.7%
error
Order respect to Na2S2O3 = 2.21
Theoretical order = 2.00
% Error order = 10.7%
Determinationorder: Na2S2O3 + 2HCI → NaCI + H2O + S + SO2
Conc
Na2S2O3
Rate(±rate)
0.05 0.00046±0.0000026
0.10 0.0023 ±0.00027
0.15 0.0055 ±0.00022
0.20 0.0111 ±0.0006
0.25 0.0158 ±0.0011
Order for Na2S2O3 (fix conc HCI)
Let Rate = k[Na2S2O3]x [HCI] 1
Order x = 2.21
Conc Na2S2O3
Rate
Best fit
Order = 2.21
Max fit
Order = 2.29
Min fit
Order = 2.12
Uncertainty order = (Max order – Min order)/2
%7.10%100
00.2
)00.221.2(


± Uncertaintyfor order = (Max – Min order)/2
Max order = 2.29
Min order = 2.12
± Uncertaintyorder
(Max – Min)/2 = ( 2.29 – 2.12)/2
= 0.09
± Uncertaintyorder = 2.21 ± 0.09
% uncertainty order = (0.09/2.21)x 100 %
= 4%
% Error order = 10.7%
% Uncertainty
(Random Error)
% Uncertainty
(SystematicError)
4%
% Error = % Random + % Systematic
error error
Correct Method !

6. Order respect to Na2S2O3 = 2.21
Theoretical order = 2.00
% Error order = 10.7%
Determinationorder: Na2S2O3 + 2HCI → NaCI + H2O + S + SO2
Conc
Na2S2O3
Rate(±rate)
0.05 0.00046±0.0000026
0.10 0.0023 ±0.00027
0.15 0.0055 ±0.00022
0.20 0.0111 ±0.0006
0.25 0.0158 ±0.0011
Order for Na2S2O3 (fix conc HCI)
Let Rate = k[Na2S2O3]x [HCI] 1
Order x = 2.21
Conc Na2S2O3
Rate
Best fit
Order = 2.21
% Uncertainty rate = % Uncertainty time = 5.5%
%7.10%100
00.2
)00.221.2(


% Error order = 10.7%
% Uncertainty
(Random Error)
% Uncertainty
(SystematicError)
5.5%
Conc
Na2S2O3
Time/s
Trial 1
±0.01
Time/s
Trial 2
±0.01
Time/s
Trial 3
±0.01
Average
time
± Time
Range (Max- Min)/2
% ±Time
0.05 102.96 103.23 114.80 107.00 (114.8-102.96)/2= 5.92 5.5%
0.10 45.43 44.08 38.35 42.62 (45.43 – 38.35)/2 = 3.54 8.3%
0.15 27.36 27.13 26.36 26.95 (27.13 – 26.36)/2 = 0.50 1.8%
0.20 18.06 18.57 17.53 18.05 (18.06 – 17.53)/2 = 0.52 2.8%
0.25 15.26 15.44 16.88 15.86 (16.88 – 15.26)/2 = 0.81 5.1%
Wrong Method !
% Error = % Random + % Systematic
error error
% Systematic = (10.7 – 5.5)= 5.2 %
error