The equilibrium constant for the ethane dehydrogenation reaction,
is defined as
where P(atm)is the total pressure and y1is the mole fraction of the ith substance in an equilibrium mixture. The equilibrium constant has been found experimentally to vary with temperature according to the formula
The heat of reaction at 1273 K is +145.6 kJ, and the heat capacities of the reactive species may be approximated by the formulas
Suppose pure ethane is fed to a continuous constant-pressure adiabatic reactor at 1273 K and pressure P(atm), the products emerge at Tf(K)and P(atm), and the residence time of the reaction mixture in the reactor is large enough for the outlet stream to be considered an equilibrium mixture of ethane, ethylene, and hydrogen.
- Prove that the fractional conversion of ethane in the reactor is
(2)
(3)
where
(4)
Finally, substitute for
We now have two expressions for the fractional conversion f: Equation 2 and Equation 3. If these expressions are equated, Kpis replaced by the expression of equation 1 and
- is replace by the expression derived in Part(b), the result is one equation in one unknown, Tf.Derive this equation, and transpose the right side to obtain an expression of the form
(5)
Prepare a spreadsheet to take P as input, solve equation 5 for Tf(use Goal Seek or Solver), and determine the final fractional conversion, f.(suggestion: Set up columns for P, Tf,f,Kp,
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Chapter 9 Solutions
EBK ELEMENTARY PRINCIPLES OF CHEMICAL P
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