The change of chemical concentration C with time t in a reaction can be mathematically modelled...

 

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The change of chemical concentration C with time t in a reaction can be mathematically modelled as dC(t) dt where k is the rate constant, and n (positive integer) is the reaction order. In most cases, concentration is measured in moles per litre (M) and time in seconds (s) or minutes (min). The general solution of (6) is, C(t) = bexp(-kt) for the first order reaction (n = 1), 1 C(t) 1 20² (1) for the second order reaction (n = 2), and for the third order reaction (n = 3). Requirement 1 b + kt n 1 = = + kt 262 1 2 3 ^ 4 1. From the above equations function C(t) has two parameters, namely b and k. These analytical solutions are referred here to as model functions. The table below contains the experimental values of t and C(t) for a certain reaction. r =-kC" 5 6 7 8 9 t model function (7) model function (8) model function (9) 1 2 3 A 4 5 6 7 8 9 C(t) 1.05 0.902 0.801 0.719 0.66 0.6 0.549 0.514 0.473 Fit the three model functions above to the experimental data by means of linear regression and find the best function. Find the two parameters b and k of the three model functions the above set of data points. You must also produce MATLAB code which: 2. Repeats the hand calculations, where the input data are entered into your Matlab program by typing/copying relevant values from the data file. Verify the answers by using the reported results from Requirement 1.4 ENG3104 Engineering Simulations and Computations Semester 2, 2023 3. Loads file converted from the data point table into MATLAB. Verify that the load has been successful by comparing the obtained first and last rows of the numeric data part with those from copy-and-paste. 4. Finds the two parameters b and k of the model function (7) using all data points in the file. Plot the resulting function on the same graph with the data. 5. Finds the two parameters b and k of the model function (8) using all data points in the file. Plot the resulting function on the same graph with the data. 6. Finds the two parameters b and k of the model function (9) using all data points in the file. Plot the resulting function on the same graph with the data. 7. Determines which model function is the best. Demonstrate it numerically and graphically. The change of chemical concentration C with time t in a reaction can be mathematically modelled as dC(t) dt where k is the rate constant, and n (positive integer) is the reaction order. In most cases, concentration is measured in moles per litre (M) and time in seconds (s) or minutes (min). The general solution of (6) is, C(t) = bexp(-kt) for the first order reaction (n = 1), 1 C(t) 1 20² (1) for the second order reaction (n = 2), and for the third order reaction (n = 3). Requirement 1 b + kt n 1 = = + kt 262 1 2 3 ^ 4 1. From the above equations function C(t) has two parameters, namely b and k. These analytical solutions are referred here to as model functions. The table below contains the experimental values of t and C(t) for a certain reaction. r =-kC" 5 6 7 8 9 t model function (7) model function (8) model function (9) 1 2 3 A 4 5 6 7 8 9 C(t) 1.05 0.902 0.801 0.719 0.66 0.6 0.549 0.514 0.473 Fit the three model functions above to the experimental data by means of linear regression and find the best function. Find the two parameters b and k of the three model functions the above set of data points. You must also produce MATLAB code which: 2. Repeats the hand calculations, where the input data are entered into your Matlab program by typing/copying relevant values from the data file. Verify the answers by using the reported results from Requirement 1.4 ENG3104 Engineering Simulations and Computations Semester 2, 2023 3. Loads file converted from the data point table into MATLAB. Verify that the load has been successful by comparing the obtained first and last rows of the numeric data part with those from copy-and-paste. 4. Finds the two parameters b and k of the model function (7) using all data points in the file. Plot the resulting function on the same graph with the data. 5. Finds the two parameters b and k of the model function (8) using all data points in the file. Plot the resulting function on the same graph with the data. 6. Finds the two parameters b and k of the model function (9) using all data points in the file. Plot the resulting function on the same graph with the data. 7. Determines which model function is the best. Demonstrate it numerically and graphically.

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