The following two reactions take place in a gas-phase

Chapter 4, Problem 4.54

(choose chapter or problem)

The following two reactions take place in a gas-phase reactor: 2 COz 2CO + Oz (A) (B) (C) Oz + Nz 2NO (C) (D) (E) If the system comes to equilibrium at 3000 K and 1 atm, the product gas mole fractions satisfy the relations vzy .2 Bo C = 0.1071 YE = 0.01493 YA YcYo (a) Let nAO, . .. ,nEO be the initial number of gram-moles of each species and ~el and ~eZ be the extents of reactions 1 and 2, respectively, at equilibrium (see Equation 4.6-6). Derive expressions for the mole fractions YA, YB, .. ,YE in terms of nAO, nBO, .. ,nEO, ~d, and ~eZ' Then substitute in the equilibrium relations to derive two simultaneous equations for the two extents of reaction. (b) One-third of a gram-mole each of COz, Oz, and Nz are charged into a batch reactor and the reactor contents equilibrate at 3000 K and 1 atm. Without doing any calculations, prove that you have enough information to calculate the component mole fractions ,)f the reactor contents at equilibrium. (c) Perform the calculation of part (b), using either (i) an equationsolving program or (ii) a spreadsheet that implements the Newton-Raphson method outlined in Section A.2i of Appendix A.1f you use the spreadsheet, guess initial values of 0.1 for both ~el and ~eZ and iterate until successive estimates of these values differ by less than 0.1 %. (d) Write a computer program to implement the Newton-Raphson procedure of part (c) for an arbitrary starting composition. The program should take input values of nAO, nBO, nco, nOD, and nEO and calculate the total moles and mole fractions of each species at equilibrium, stopping when the values of ~el and ~eZ each change by less than 0.001 % from one iteration to the next. Run the program for the following feed mixtures: 1/3 o 1/2 1/5 o 1/3 o 1/5 nco 1/3 1/3 o 1/5 nOD 1/3 1/3 o 1/5 o o 1/2 1/5