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Non-Linear Form of the Integrated Rate Law

Non-Linear Form of the Integrated Rate Law. Edward A. Mottel Integrated, First-Year Curriculum in Science, Engineering and Mathematics. Please Sit with Someone so that there is one computer for two people. Please be sure you or your partner has a copy of the Integrated Rate Law handout.

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Non-Linear Form of the Integrated Rate Law

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  1. Non-Linear Form of the Integrated Rate Law Edward A. Mottel Integrated, First-Year Curriculum in Science, Engineering and Mathematics

  2. Please Sit with Someoneso that there is one computer for two people • Please be sure you or your partner has a copy of the Integrated Rate Law handout. • Turn on your computer and start Excel • You DO NOT have to be on the network.

  3. Is it possible to get the best fit line to look like the original data? NO2 Decomposition at 400 K 500 450 400 350 300 250 PNO2 (torr) 200 150 100 50 0 0 200 400 600 800 1000 Time (s) Take the 1-n root of each side! How can you rewrite the equation so PNO2 is a function of time? (PNO2)t1-n= (n-1) k(t - to) + (PNO2)o1-n

  4. 1 é ù 1-n (PNO2)t= (n-1) k(t - to) + (PNO2)o1-n ë û Plot this function versus time in Excel Non-Linear Integrated Rate Law Method (PNO2)t1-n= (n-1) k(t - to) + (PNO2)o1-n

  5. A B C D E F G 1 Time PNO2 Diff DiffSq 2 0 474 n 3 26 400 Ao 4 88 290 k 5 190 200 SumSq 6 801 70 Using the same procedure name Ao, k and SumSq Set Up the Excel Spreadsheet to Look Like This Fit Click on this cell and from the tool bar select Insert / Name / Define The cell name choice should be listed as n, select OK

  6. A B C D E F G 1 Time PNO2 Diff DiffSq 2 0 474 450 n 2 3 26 400 Ao 450 4 88 290 k 1e-4 5 190 200 SumSq 6 801 70 Click on this cell and enter =((n-1)*k*A2 + (Ao)^(1-n))^(1/(1-n)) If you put into G2, G3 and G4 the numbers 2, 450, 1e-4 the value 450 should appear in cell c2 Set Up the Excel Spreadsheet to Look Like This Fit

  7. A B C D E F G 1 Time PNO2 Diff DiffSq 2 0 474 24 576 n 2 3 26 400 Ao 450 4 88 290 k 1e-4 5 190 200 SumSq 6 801 70 Click on this cell and enter Click on this cell and enter =B2 - C2 =D2 * D2 The value 24 should appear The value 576 should appear Set Up the Excel Spreadsheet to Look Like This Fit 450

  8. A B C D E F G 1 Time PNO2 Diff DiffSq 2 0 474 450 24 576 n 2 3 26 400 Ao 450 207 193 37105 4 88 290 91 199 39710 k 1e-4 5 190 200 SumSq 47 153 23372 6 801 70 12 58 3347 and copy down the columns. Set Up the Excel Spreadsheet to Look Like This Fit Select these three cells (Shift/Click) The indicated values should appear.

  9. A B C D E F G 1 Time PNO2 Diff DiffSq 2 0 474 450 24 576 n 2 3 26 400 Ao 450 207 193 37105 4 88 290 91 199 39710 k 1e-4 5 190 200 SumSq 47 153 23372 104110 6 801 70 12 58 3347 Click on this cell and enter The indicated value should appear. Set Up the Excel Spreadsheet to Look Like This Fit =sum (e2 : e6)

  10. NO2 Decomposition 500 450 400 350 300 250 PNO2 (torr) 200 150 100 50 0 0 100 200 300 400 500 600 700 800 900 Time (s) Click on the lower data set and choose Format Data Series This line should appear Make a graph of the data with two functionsA1:A6,B1:B6,C1:C6 Select Line: Custom Marker: None

  11. Using Solver

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