The reaction of hydrogenation of nitrobenzene to aniline can be represented by the following equation: A+B=C+D The reaction is carried out adiabatically in a series of a staged packed-bed reactors with interstage cooling. The lowest temperature to which the reactant stream may be cooled is 27 C. The feed is equimolar in A and B and the catalyst weight in each reactor are sufficient to achieve 99.9% of the equilibrium conversion. If the feed enters at 27 C and four reactors and three coolers are used as indicated in the Figure 2, evaluate the conversion to be achieved from this reaction by plotting equilibrium conversion as a function of temperature. 27 C O 05.000 10-C Jl Figure 2 Schematic diagram of reactor connected with interstage cooling in series Given: AHRX = -30,000 mol.K CPA = CpB = Cpc = Cp = 25 mol. Ke (50 C) = 500,000 (18 marks) CONFIDENTIAL APPENDIX 1(1) ARRHENIUS LAW k = AeE/RT in = J kg E In IDEAL GAS CONSTANT dm.atm m.am R = 0.082 = 0,082 mol. K kmol. cal 1.987 mol-K = 8.314 mol. K ENERGY BALANCE - 1. - Fo ur -T.) Fox{akt: +40 (0 ") = 0 -FR ADIABTIC TEMPERATURE x[-AHpxCr)] + Tie + XACT: TE C + XC. EQUILIBRIUM CONVERSION XER = 2.C:(T-T.) -AHRXTB) + AC (T-T:) NUMERICAL METHODS Trapezoidal rule *FCx) dx = {1FX.) + f(x)] f() Simpson's one-third rule Lax = $1sx) + 45(X.) + F(X2) Simpson's three-eighths rule wax =als(x) + 35(x)+31(x)) +5%)] * r. dX = +3fX) (X:)] CONFIDENTIAL APPENDIX 1(2) Five-point quadrature formula * F(x) dx = $rx.) + 4f(x) + 2F(X.) + 4f(X.) +F(X)] Integrals dx = In: dx (1-x) 1 1 1-X 1-X dx x Site == n1 ) dx 1 + =-In(1 + Ex) *(1 + ex) dx (1 + 2)2x (1-x) = 22(1 + 8) In(1 x) + e*x+ (1-x) Differentiation = deler(x) = cf'(x) a F()g(x)] = f(x)g'(x) + f(x)9(x) g(x)}'(x) f(x)g'(x) 19(x) al caras d f(x) dx 9(x)