Problem 4.1 Background: The production of biodiesel involves the following reaction of triglycerides (TG) with methanol to produce fatty acid methyl esters (FAME). TG +3MeOH ⇒ 3H₂O + 3FAME The reaction as written is an overall reaction rate and not an elementary reaction. Which is to say, the reaction orders are not inferrable from the stoichiometry. For the purposes of this problem, we will assume that this reaction rate can be described useing a reaction order exponent, r = kC", but that the reaction order n is unknown. The reactant concentration will follow different reaction concentration trajectories (integrated rate laws) depending on the actual reaction order (with respect to TG), where C is the concentration of TG and Co is the concentration of TG at time zero. Zero Order First Order Second Order C = Co - kt C = C₂e-kt 1 C . = 1 Co Со +kt Problem: Analyze the provided experimental data. The reaction order of the transesterification reaction with respect to TG concentration is unknown. The integrated rate law will linearize differently depending on its reaction order. The concentration trajectory observed in samples collected from a transesterification process are provided in the table here. Use this data to determine the most likely reaction order and find the values for k and Co- Linearize each of the integrated rate laws. In the boxes at the top of the table, write in the variables that can be substituted for y=mx+b. This has been filled in for the zero order case to demonstrate. Use the apostrophe symbol (") at the start of a cell to force the contents to be read as text. Transform the provided t and C into linearized x and y for each case. Fit linear trends to each of them, fitting slopes and intercepts. In the provided textbox, provide your explanation for which reaction order best explains the experimental data. Justify your answer using the quality of the regression fit and use any appropriate metrics. • For the best fit reaction order, calculate the corresponding fitted C_0 and k. Time, t (min) 2 5 10 15 20 25 30 35 40 45 TG conc, C (mmol/L) 24 14 8.2 5.8 4.5 3.7 3.1 2.7 2.4 2.1 Best Fit Rxn Order C_0 k Zero Order X y m b X slope intercept R^2 t с -k C_0 y First Order X y m b X slope intercept R^2 V Second Order X y m b X slope intercept R^2 Which reaction order best explains the experimental data? Justify your answer: y The provided experimental data is best explained by a second order reaction. The linearization yields a higher R^2, indicating a better quality fit.

Fig: 1