Page 58 - Introduction to chemical reaction engineering and kinetics

40 Chapter 2: Kinetics and Ideal Reactor Models

2.8 PROBLEMS FOR CHAPTER 2

2-1 The half-life (tm) of a reactant is the time required for its concentration to decrease to
one-half its initial value. The rate of hydration of ethylene oxide (A) to ethylene glycol
(Cz&O + Hz0 + C2H602) in dilute aqueous solution is proportional to the concentration
of A, with a proportionality constant k A = 4.11 X 1O-5 s-l at 20°C for a certain catalyst
(HC104) concentration (constant). Determine the half-life (tt&, or equivalent space-time
(rm), in s, of the oxide (A) at 20°C if the reaction is carried out
(a) In a batch reactor,
(b)In a CSTR operating at steady-state.
(c) Explain briefly any difference between the two time quantities in (a) and (b).
2-2 Calculate the mean residence time (t) and space time (7) for reaction in a CSTR for each of
the following cases, and explain any difference between (t) and r:
(a)Homogeneous liquid-phase reaction, volume of CSTR (V) = 100 L, feed flow rate (qo) =
10 L min-‘;
(b)Homogeneous gas-phase reaction, V = 100 L, q. = 200 L min-’ at 300 K (T,); stoichiom-
etry: A(g) = B(g) + C(g); reactor outlet temperature (T) = 350 K; reactor inlet and outlet
pressures essentially the same and relatively low; conversion of A, 40%.
2-3 For the experimental investigation of a homogeneous gas-phase reaction occurring in a CSTR,
explain briefly, but quantitatively, under what circumstances tin > 1. Consider separately each
factor affecting this ratio. Assume steady-state operation, ideal-gas behavior, and equal inlet
and outlet flow areas. 1. Consider each factor affecting this ratio separately. Give an exam-
2-4 For a homogeneous gas-phase reaction occurring in a plug-flow reactor, explain briefly under
v
what circumstances tin <
“OF
0 2-5 The decomposition of phosphine (PHs) to phosphorus vapor (P4) and hydrogen is to take place
ple (chemical reaction + circumstance(s)) for illustration. Assume steady-state operation and
cross-sectional
area.
constant
and the pressure
in a plug-flow reactor at a constant temperature of 925 K. The feed rate of PHs
are constant. For a conversion of 50% of the phosphine, calculate the residence time (t) in the
reactor and the space time (7); briefly explain any difference. Assume the rate of decomposition
is proportional to the concentration of PH3 at any point, with a proportionality constant k =
3.6 x 10v3 s-l at 925 K.
2-6 An aqueous solution of ethyl acetate (A), with a concentration of 0.3 mol L-’ and flowing
at 0.5 L s-l, mixes with an aqueous solution of sodium hydroxide (B), of concentration
0.45 mol L-’ and flowing at 1.0 L s-i, and the combined stream enters a CSTR of volume
500 L. If the reactor operates at steady-state, and the fractional conversion of ethyl acetate in
the exit stream is 0.807, what is the rate of reaction (-IA)?
2-7 An experimental “gradientless” reactor (similar to that in Figure 1.2), which acts as a CSTR
operating adiabatically, was used to measure the rate of oxidation of SO2, to SO3 with a V2Os
catalyst (Thurier, 1977). The catalyst is present as a&ed bed (200 g) of solid particles within
the reactor, with a bulk density (mass of catalyst/volume of bed) of 500 g L-l and a bed voidage
(m3 void space me3 bed) of 0.40; a rotor within the reactor serves to promote BMF of gas.
Based on this information and that given below for a particular run at steady-state, calculate
the following:
(a)The fraction of SO2 converted (fso,) in the exit stream;
(b)The rate of reaction, -rso2, mol SO2 reacted (g cat)-’ s-l; at what T does this apply?
(c) The mean residence time of gas (f) in the catalyst bed, s;
(d)The space time, T, for the gas in the catalyst bed, if the feed temperature T, is 548 K.
Additional information:
Feed rate (total FtO): 1.2 mol t-n&’
Feed composition: 25 mole % SO2,25% 02, 50% N2 (inert)
T (in reactor): 800 K, P (inlet and outlet): 1.013 bar
Concentration of SO3 in exit stream: 10.5 mole %