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2. This question concerns the following elementary liquid-phase reaction: A B+C (a) Express the net rate of reaction in terms of the initial concentration and conversion of A and the relevant rate constants. [5 marks] (b) Determine the equilibrium conversion for this system. [6 marks] (c) If the reaction is carried out in an isothermal PFR, determine the volume required to achieve 90% of your answer to part (b). Use numerical integration where appropriate. [6 marks]
Data: CAO = 2.5 kmol mr Vo = 3.0 m3n-1 h krwd = 10.7 h- krev = 4.5 [kmol m-31-'n-1 m h
R = 8.3145J/mol K = 1.98 cal/mol K The formulae below are for the following reaction where A is the limiting reactant: aA + bB → CC + dD Excess Ratio: NBo a y = b Nao Kinetics: -Eact/RT (-ra) = KC AC3 k=Ae Conversion: Constant Volume Systems: C; = Cio + VCAOX CA = CAO(1 - x) Variable Volume Systems: E = y208 6-689- )- C d b -+---- ка a a а. = Vi i=1 Cio + viCAOX C = (1 + EX) (1 – X) CA = CAO (1 + EX) Design Equations: 影。 -X NAO Batch Reactor: t= dx JO (-A) V CSTR: V= FAOX (-ra) > T = Vo FAO PFR: V= so dx (مr-)
Numerical Integration: Χη Xnxo Trapezium Rule: ydx = Elyo +2(y, + y2 + y2 + ... + Yo-1) +yn]; n = [h n- n Хо -X2 h Simpson's Rule: = + ; h = X2 - Xo 2 Хо **tx = $ \x + 4%, + ve]n=**** ydx [48 (»-Mlvo , n-* L*ydx = '5lvo + 4y, + 2y2 + 4x +ya] n = *s ** n-- -X3 ydx = 3 8 h[y. + 3y, + 3y2 +y3]; h X3 – XO 3 Хо [4y2 ; h = X4 4