Exercise 10 Text Reactor for the production of ammonia

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Department of Energy Politecnico di Milano Via Lambruschini 4 – 20156 Milano Exercises of “Fundamentals of Chemical Processes” Prof. Gianpiero Groppi EXERCISE 10 Estimation of the composition at the outlet of a reactor for the production of NH3 Ammonia is produced by reacting H2 and N2 in a catalytic reactor: 3/2 H2 + 1/2 N2 ↔ NH3 The reactor is maintained at 275 atm. At the exit of the reactor, the gas stream is at 500°C. Determine the composition of the outlet stream assuming that the th ermodynamic equilibrium is reached. Assume an ideal mixture of real gases. Data: Stream 2: P = 275 atm T out = 500°C Hypothesis: The thermodynamic equilibrium is reached Ideal mixture of real gases Species Molar fraction (%) NH3 3.53 H2 62.60 N2 20.87 CH4 9.78 Ar 3.22  TTGR  84.27129720 600 < T < 1500 K ∆G0 R(T) = [cal/mol] Solution The composition of the gas stream at the outlet of the reactor is unknown. In order to determine the composition, the material balance is written by applicat ion of the extent of reaction approach. The extent of reaction λ is introduced and 100 mol/s inlet gas is assumed as the basis. The following balances are obtained: Species n IN (mol/s) n OUT (mol/s) NH3 3.53 3.53 +  H2 62.60 62.60 – 1.5*  N2 20.87 20.87 – 0.5* CH4 9.78 9.78 Ar 3.22 3.22 The thermodynamic condition assumed at the outlet requires that:     i yPTaRTTG i NC iR ,,ln 1 0   The activities of the species depend on the compositio n of the outlet gas stream. Thus, one equation in the unknown λ is this obtained. Considering the definition of the activity, one can write:   0ˆ ,,ˆ ,, i G i i f yPTfyPTa   The reference is the ideal gas, at reference pressure of 1 bar, and at the temperature of the outlet current. Assuming ideal mixture, for each specie the activity…