My exact concentration when calculated is = 13.8632162661738 The most primitive
ID: 3278627 • Letter: M
Question
My exact concentration when calculated is = 13.8632162661738 The most primitive numerical integration method is Euler's. Here one directly replaces the "d" s in differential equation with deltas: Delta c/Delta c almostequalto -kc^2 or Delta c almostequalto -kc^2 Delta t That can be cast into an algorithm: Start with c_0: then compute c_i+1 from c_i+1 = c_i - kc_i^2, Delta t Integrate the rate law for your set of k, c0, and tmax using Euler's method. Do this using and excel spreadsheet. Report Delta t and similarly to Q2 the concentration at your final time. Say in which digit the first difference from the exact result occurs and whether we should care.Explanation / Answer
for dT = 0.1
k Co T(max) T(step)
0.022 120 2.9 0.1
C t
88.32 0.1
71.15907072 0.2
60.01912136 0.3
52.09407252 0.4
46.12372926 0.5
41.44345277 0.6
37.66482126 0.7
34.54381599 0.8
31.9186105 0.9
29.67725557 1
27.73962867 1.1
26.04675727 1.2
24.55420343 1.3
23.22780384 1.4
22.04083592 1.5
20.97207934 1.6
20.00445749 1.7
19.12406519 1.8
18.31945948 1.9
17.58113377 2
16.90112198 2.1
16.27269655 2.2
15.69013511 2.3
15.14853837 2.4
14.64368629 2.5
14.17192369 2.6
13.73006816 2.7
13.31533566 2.8
12.9252797 2.9
for dT = 0.01
k Co T(max) T(step)
0.022 120 2.9 0.1
T(step)
0.1
0.01 116.832
0.02 86.60390707
0.03 70.04507578
0.04 59.22661648
0.05 51.49703819
0.06 45.65570161
0.07 41.06558962
0.08 37.35272074
0.09 34.28129544
0.1 31.69447501
0.11 29.48349288
0.12 27.57034153
0.13 25.89750189
0.14 24.42156347
0.15 23.10910705
0.16 21.93396026
0.17 20.87531715
0.18 19.91641826
0.19 19.04360462
0.2 18.2456269
0.21 17.51313259
0.22 16.83827944
0.23 16.21444041
0.24 15.63597544
0.25 15.09805316
0.26 14.59651003
0.27 14.12773813
0.28 13.68859491
0.29 13.27633007
0.3 12.88852587
0.31 0
0.32 0
0.33 0
0.34 0
0.35 0
0.36 0
0.37 0
0.38 0
0.39 0
0.4 0
0.41 0
0.42 0
0.43 0
0.44 0
0.45 0
0.46 0
0.47 0
0.48 0
0.49 0
0.5 0
0.51 0
0.52 0
0.53 0
0.54 0
0.55 0
0.56 0
0.57 0
0.58 0
0.59 0
0.6 0
0.61 0
0.62 0
0.63 0
0.64 0
0.65 0
0.66 0
0.67 0
0.68 0
0.69 0
0.7 0
0.71 0
0.72 0
0.73 0
0.74 0
0.75 0
0.76 0
0.77 0
0.78 0
0.79 0
0.8 0
0.81 0
0.82 0
0.83 0
0.84 0
0.85 0
0.86 0
0.87 0
0.88 0
0.89 0
0.9 0
0.91 0
0.92 0
0.93 0
0.94 0
0.95 0
0.96 0
0.97 0
0.98 0
0.99 0
1 0
1.01 0
1.02 0
1.03 0
1.04 0
1.05 0
1.06 0
1.07 0
1.08 0
1.09 0
1.1 0
1.11 0
1.12 0
1.13 0
1.14 0
1.15 0
1.16 0
1.17 0
1.18 0
1.19 0
1.2 0
1.21 0
1.22 0
1.23 0
1.24 0
1.25 0
1.26 0
1.27 0
1.28 0
1.29 0
1.3 0
1.31 0
1.32 0
1.33 0
1.34 0
1.35 0
1.36 0
1.37 0
1.38 0
1.39 0
1.4 0
1.41 0
1.42 0
1.43 0
1.44 0
1.45 0
1.46 0
1.47 0
1.48 0
1.49 0
1.5 0
1.51 0
1.52 0
1.53 0
1.54 0
1.55 0
1.56 0
1.57 0
1.58 0
1.59 0
1.6 0
1.61 0
1.62 0
1.63 0
1.64 0
1.65 0
1.66 0
1.67 0
1.68 0
1.69 0
1.7 0
1.71 0
1.72 0
1.73 0
1.74 0
1.75 0
1.76 0
1.77 0
1.78 0
1.79 0
1.8 0
1.81 0
1.82 0
1.83 0
1.84 0
1.85 0
1.86 0
1.87 0
1.88 0
1.89 0
1.9 0
1.91 0
1.92 0
1.93 0
1.94 0
1.95 0
1.96 0
1.97 0
1.98 0
1.99 0
2 0
2.01 0
2.02 0
2.03 0
2.04 0
2.05 0
2.06 0
2.07 0
2.08 0
2.09 0
2.1 0
2.11 0
2.12 0
2.13 0
2.14 0
2.15 0
2.16 0
2.17 0
2.18 0
2.19 0
2.2 0
2.21 0
2.22 0
2.23 0
2.24 0
2.25 0
2.26 0
2.27 0
2.28 0
2.29 0
2.3 0
2.31 0
2.32 0
2.33 0
2.34 0
2.35 0
2.36 0
2.37 0
2.38 0
2.39 0
2.4 0
2.41 0
2.42 0
2.43 0
2.44 0
2.45 0
2.46 0
2.47 0
2.48 0
2.49 0
2.5 0
2.51 0
2.52 0
2.53 0
2.54 0
2.55 0
2.56 0
2.57 0
2.58 0
2.59 0
2.6 0
2.61 0
2.62 0
2.63 0
2.64 0
2.65 0
2.66 0
2.67 0
2.68 0
2.69 0
2.7 0
2.71 0
2.72 0
2.73 0
2.74 0
2.75 0
2.76 0
2.77 0
2.78 0
2.79 0
2.8 0
2.81 0
2.82 0
2.83 0
2.84 0
2.85 0
2.86 0
2.87 0
2.88 0
2.89 0
2.9 0
so we can see, the final concentration difference in thw two dT values is after the decimal position at the first decimal position, where the difference in the answer from the actual value is there because of the inaccuracies of euler's method of integration
the final answer is C = 12.92 for t = 0.1
the final answer is C = 12.8853 for t = 0.01
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