Question

Problem 4.2 Background: Reaction rate parameters can be fitted to experimental data for simple reaction systems where only one reaction is occurring at a time (as in problem 4.1). Consider a system where a conversion A → B occurs by two parallel reactions occurring at the same time. Both reactions are first order reactions. n = k₁C r₂ = K₂C mol lem³-s Where r is the rate of reaction and C is the reactant concentration reactions, the ,k is the reaction rate coefficient [s-¹], mol Làm Because both are first order r = (k₁ + k₂)C The reaction rate coefficients, k, are temperature-dependent, following the Arrhenius equation. k₁ = A₁ exp k₂ = A₂ exp . EA₁ RT EA₂ RT Where A is the Arrhenius prefactor [s], EA is activation energy temperature [K], and R is the ideal gas constant mol-K] Tis Problem: Consider the two competing reactions. Suppose that Reaction 1 has a prefactor of 1.106 s- and activation energy of 25,000 J/mol and Reaction 2 has a prefactor of 1.108 s- and activation energy of 50,000 J/mol. Use the Arrhenius rate law to calculate the values for k1 and k2 at the various temperatures listed. Graph the reaction rate constants k1 and k2 against temperature. Include appropriate axis labels and plot formatting. Use a log scale y-axis and show the axis labels in scientific notation. Add columns to the table to calculate these values. Add together k1 and k2 to get a total k representing the total reaction rate constant. Make a column to show when temperatures have a total rate constant greater than 10,000 1/s, as a Boolean output. Make a column that shows "Reaction 1" or "Reaction 2" for which reaction contributes more to the overall reaction rate. Make a column that shows when the overall reaction rate is a mix of the two, with both reactions accounting for at least 20% of the whole. A EA M T 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000 1050 1100 rxn 1 k1 rxn2 k2 k1+k2 k>10000 dominant mixed

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