ECHE 311/Fall 08

Problem Set #11

Chemical Reaction Equilibrium

Due Tuesday, December 2nd

  1. A system initially containing 2 mole C2H4 and 3 mole of O2 undergoes the following reactions:

Develop expressions for the mole fractions of the reacting species as function of reaction coordinate for the two reactions.

  1. Consider the water-gas shift reaction:

A high temperatures and low to moderate pressures the reacting species form an ideal- gas mixture. Application of the summability relation to Equation

yields

If the Gibbs energies of the elements in their standard states are set equal to zero,

for each species, and then

(A)

With the understanding that T and P are constant, we may write the equilibrium criterion of Eq. for this reaction system as

or

For the water-gas –shift reaction, . The equilibrium criterion therefore becomes

(B)

Once the are eliminated in favor of , Eq (A) relates to .

a)Determine the equilibrium value of e by application of Eq.(B) at 1,000; 1200 and 1500 K.

b)Plot G vs , indicating the location of the equilibrium value of e determined in (a). Discuss the results.

Hint:

  • Data got for the compounds of interest are given in the example of your textbook (SVNA)
  • For a temperature of 1,000; 1200 and 1500 K (the reaction is unaffected by P) and for a feed of 1 mole H2 and 1 mol CO2.
  • Find and
  • By Eq. 13.5 calculate = and
  • By Eq (A) and data from Example 13.3 at above temperatures write expressions for =
  • Guess value for
  • Given find
  • Plot vs for
  1. For the ammonia synthesis reaction written

with 0.5 mol N2 and 1.5 mol as the initial amounts of reactants and with the assumption that the equilibrium mixture is an ideal gas, show that

  1. I asked Daniel Pittman , Punyawudho Conlayutt and Lee Zachary, members of our thermodynamic class to find equilibrium composition at a particular T and P and for given initial amounts of reactants for the following gas-phase reaction:

(A)

Each solves the problem correctly in a different way. Daniel bases his solution on reaction (A) as written. PC who usually likes “well rounded things” prefers whole numbers and multiplies reaction (A) by 2.

LZ, who usually does things backward, deals with reaction:

Write the chemical-equilibrium equations for the three reactions, indicate how the equilibrium constants are related, and show why, D, P and Lall obtain the same results.

  1. The following reaction reaches equilibrium at 500oC and 2 bar:

If the system initially is an equimolar mixture of nitrogen and acetlylene, what is the composition of the system at equilibrium? Assume ideal gases.

Hint: Use the routine outlined in Example 5.

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