Reaction kinetics deal with the study of how fast chemical reactions proceed. Researchers derive mathematical models...

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Reaction kinetics deal with the study of how fast chemical reactions proceed. Researchers derive mathematical models to describe the behavior of these reactions as they proceed towards completion. Simply put, reaction kinetics deal with the changes in the concentration of a chemical species with respect to time (i.e., the rate of the reaction). Engineers utilize regression to determine the parameters for this rate of reaction. The procedure is as follows: 1. A mathematical model is proposed. 2. The model is linearized so that linear regression may be done. 3. Experimental data (concentration vs. time) is fitted against the model. 4. If a reasonable fit is obtained, then the proposed model is correct. Otherwise, a new mathematical model is proposed. Consider the system where reactant A decomposes in a batch reactor: A → products The concentration of A (mol/L) in the reactor is measured at various times, and the result is shown in the table below. Time, s Concentration, mol/L 1. Two mathematical models are proposed to describe the kinetics of the reaction: Model 1: CA CAO exp(-kt) 1 1 -- Ca Cao 0 10 Model 2: tr, s CAO, mol/L 20 8 40 6 Model 3: t =kt Linearize these two models so that linear regression is possible. Then, show by linear regression that the two proposed models do not provide a good fit with the experimental data. Recall that a good fit would mean an R² close to 1. 2. For the same decomposition reaction above, the following new data were collected, and a new model was proposed: 18.5 10 60 120 5 3 23 6 180 300 2 1 35 2 0.81-1 k(n-1) Linearize this model and show that it reasonably describes the new data collected. What are the values of k and n? -A0 Reaction kinetics deal with the study of how fast chemical reactions proceed. Researchers derive mathematical models to describe the behavior of these reactions as they proceed towards completion. Simply put, reaction kinetics deal with the changes in the concentration of a chemical species with respect to time (i.e., the rate of the reaction). Engineers utilize regression to determine the parameters for this rate of reaction. The procedure is as follows: 1. A mathematical model is proposed. 2. The model is linearized so that linear regression may be done. 3. Experimental data (concentration vs. time) is fitted against the model. 4. If a reasonable fit is obtained, then the proposed model is correct. Otherwise, a new mathematical model is proposed. Consider the system where reactant A decomposes in a batch reactor: A → products The concentration of A (mol/L) in the reactor is measured at various times, and the result is shown in the table below. Time, s Concentration, mol/L 1. Two mathematical models are proposed to describe the kinetics of the reaction: Model 1: CA CAO exp(-kt) 1 1 -- Ca Cao 0 10 Model 2: tr, s CAO, mol/L 20 8 40 6 Model 3: t =kt Linearize these two models so that linear regression is possible. Then, show by linear regression that the two proposed models do not provide a good fit with the experimental data. Recall that a good fit would mean an R² close to 1. 2. For the same decomposition reaction above, the following new data were collected, and a new model was proposed: 18.5 10 60 120 5 3 23 6 180 300 2 1 35 2 0.81-1 k(n-1) Linearize this model and show that it reasonably describes the new data collected. What are the values of k and n? -A0