Styrene can be produced from ethylbenzene by the following reaction: ethylbenzene↔styrene+H2(1)
However, several irreversible side reactions also occur:
ethylbenzene → benzene + ethylene (2) ethylbenzene +H2 → toluene + methane(3)
(J. Snyder and B. Subramaniam, Chem. Eng. Sci., 49, 5585 (1994)). Ethylbenzene is fed at a rate of 0.00344 kmol/s to a 10.0-m³ PFR (PBR), along with inert steam at a total pressure of 2.4 atm. The steam/ethylbenzene molar ratio is initially, that is, parts (a) to (c), 14.5:1 but can be varied.
Given the following data, find the exiting molar flow rates of styrene, benzene, and toluene along with S˜St/BT for the following inlet temperatures when the reactor is operated adiabatically:

(a) T0 = 800 K
(b) T0 = 930 K
(c) T0 = 1100 K
(d) Find the ideal inlet temperature for the production of styrene for a steam/ethylbenzene ratio of 58:1. Hint: Plot the molar flow rate of styrene versus T0. Explain why your curve looks the way it does.
(e) Find the ideal steam/ethylbenzene ratio for the production of styrene at 900 K. Hint: See part (d).
(f) It is proposed to add a countercurrent heat exchanger with U_a = 100 kJ/m³/min/K, where Ta is virtually constant at 1000 K. For an entering stream to ethylbenzene ratio of 20, what would you suggest as an entering temperature? Plot the molar flow rates and S˜St/BT.

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Heat capacities Methane Ethylene Benzene Toluene Styrene 68 J/mol - K 90 J/mol K Steam 201 J/mol - K 249 J/mol K 273 J/mol. K Ethylbenzene 299 J/mol-K Hydrogen 30 J/mol K 40 J/mol K p=2137kg/m3of pelletp=0.4AHRx1EB=118000 kJ/kmol ethylbenzeneAHRX2EB =105200x kJ/kmol ethylbenzeneAHRX3EB=53900 kJ/kmol ethylbenzene KP1= exp{b1+b2T+b3 In(T)+[(b4T+b5)T+b6]Tatm withb1--17.34b4-2.314x10-10K-3b2-1.302x104Kb5-1.302x10-6K-2b3-5.051b6--4.931x10-3K-1 The kinetic rate laws for the formation of styrene (St), benzene (B), and toluene (T), respectively, are as follows (EB = ethylbenzene). r1St-p(1-6)expo(-0.08539-10925 KT)(PEB-PSIPH2Kp1) (kmol/m3 s)r2B-p(1-6)expo (13.2392-25000 KT)(PEB)(kmol/m3 s)r3T-p(1-6)expo (0.2961-1100 0 KT)(PEBPH2) (kmol/m3 s) The temperature Tis in Kelvin and P; is in atm.