The University of Texas at Austin
College of Engineering

Reaction Equilibria

For ideal gas phase reactions one computes the equilibrium composition using

The equilibrium composition is dependent on the temperature, pressure, initial composition, and reaction stoichiometry. When is known at only one temperature,

(1)

can be used to calculate the equilibrium constant at other temperatures. When integrating Equation 1 you need to decide if the heat of reaction, , can justifiably be assumed constant over the temperature range of the integration.

THE PROBLEM STATEMENT

Butene isomerization reactions are shown below.

The thermodynamic data are

Components

(kcal/mole)

(kcal/mole)

A

B
(x 102)

C
(x 105)

D
(x 109)

1-butene

17.04

 -0.03 -0.7156 8.442 -4.756 10.67

Cis-2-butene

15.74

 -1.67 0.1051 7.058 -2.433 -0.1472

Trans-2-butene

 15.05 -2.67 4.379 6.128 -1.676 -2.148

isobutene

 13.88 -4.04 3.865 6.702 -2.608 2.174

where the component heat capacities in cal/gmole-K can be calculated using

THE QUESTIONS

1. How would you determine the minimum number of reactions needed to calculate the equilibrium composition? Run the program to check your answer. The minimum number is 3, and one linearly independent set is

2. At 298 K, K1 = 8.984, K2 = 28.81, and K3 = 207.8. Develop the set of equations needed to compute the equilibrium composition if 1 mole of 1-butene is present initially and the total pressure is 1 atm. Use the reaction set provided in Question 1. Develop these equations using the variable extent that was presented in lecture and in the book to describe the moles of each component. Next write an equation for each reaction that describes the equilibrium constant in terms of activities and simply these relations to ones that contain only mole fractions because the pressure is 1 atm and the gases are ideal. You will see that the three equations are linear and can be sorted into

    where:

    Generate the matrix B and compute the values at 298 K. Check your answer against the program. How would you solve this set of linear equation?

3.Use the program to examine the effect of changing the temperature on the heats of reactions r1, r2, and r3. Why do the heats of reaction change? What do the changes suggest about how you should integrate Equation 1?

4. Use the program to examine the effect of changing the temperature on the equilibrium constants and the equilibrium composition. Explore several temperatures. Are the values reasonable and why? What thermodynamic principle permits you to predict this change?