ProblemSet2 - ChE 101 2012 Problem Set 2 Read Schmidt...

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ChE 101 2012 Problem Set 2 Read Schmidt, Sections 3.1-3.3 1. Consider the following reversible elementary reaction: A 2B The rate coefficient of the forward reaction is k f = 25 hr - 1 , and the rate coefficient of the reverse reaction is k b = 4 M - 1 hr - 1 . The aqueous phase reaction is carried out in a constant volume batch reactor. The reactor is initially charged with 1 mole of pure A and 1 mole of pure B at 1 atm. The reactor volume is 1 L. (a) Write the rates of reaction for A and B. (b) Write r A as a function of the conversion of A. (c) What is the equilibrium conversion of A? (d) Find the conversion of A as a function of time. (e) How long does it take for the system to reach 90% of the equilibrium conversion? 2. Consider the following gas phase reaction, which is performed in a constant volume batch reactor at 500 C at 30-60 MPa: A + 3 B 2 C The standard state thermodynamic data on this reaction are Δ H R, 298 = - 92 . 4 kJ/mol and Δ S R, 298 = - 199 J/(mol · K). ( Note: In reality, this reaction would proceed through a multi-step mechanism since reac- tions involving more than two species are very rare. For now though, just assume power-law kinetics. ). (a) Write the rates of reaction for A, B, and C. Use k f and k b for the forward and backward rate coefficients. (b) Write the rate of reaction of A as a function of conversion of A. Assume a stoichiometric mixture of A and B. (c) What is the equilibrium conversion of a stoichiometric mixture of A and B to C at 298 K at 1 atm? 1
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(d) Assuming that Δ H is independent of temperature, what are K eq and the equilibrium conversion at 30 MPa and 500 C? (e) At what pressure (in MPa) will the equilibrium conversion be 75% at 500 C? (f) What is the relationship between k f and k b at the pressure you found in part (d)?
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