10. Equilibrium State of a Gas Phase Reaction

1. 10. Equilibrium State of a Gas Phase Reaction • We have started to examine the gas phase reaction: • for which the equilibrium constant is known: • Or • The most convenient standard state for gas phase reactions is that of an ideal gas at a pressure of 1 bar and a temperature equal to the reaction temperature. • When K is derived from this standard state: J.S. Parent

2. Equilibrium State of a Gas Phase Reaction • The equilibrium expression becomes: • The fugacity of each component in the gas mixture is given by: • (i=1,2,3,4) • When substituted into our equilibrium expression, J.S. Parent

3. Equilibrium State of a Gas Phase Reaction • In general, for a gas phase reaction: • 15.23 • Equation 15.23 differs from equilibrium expressions you have seen in previous courses. • No longer are simple partial pressures applicable. • For an accurate representation of the equilibrium condition, mixture fugacity coefficients are required for each component. • From our previous example: J.S. Parent

4. 10. Equilibrium State of a Reactive Liquid Phase • For reactions occurring in a liquid phase, our equilibrium expression holds: • 15.13 • The reference state for which Gio is calculated is the pure component at the reaction temperature, a pressure of 1 bar, in the liquid state. • The activity of each component in the liquid can be expressed in terms of fugacity: • 15.27 • where xi is the mole fraction of i, gi is the activity coefficient, and fil is the pure component liquid fugacity of species i. J.S. Parent

5. Equilibrium State of a Reactive Liquid Phase • If we ignore the effect of pressure on the fugacity of a pure liquid, the expression for the activity of a species simplifies to: • 1 • and our governing equation for the equilibrium state of a liquid phase reaction becomes: • 15.30 • We often use concentrations (mole/litre) in the place of activities. This assumes that the liquid mixture is ideal (all activity coefficients are unity) and the volume of the liquid does not change. This is rarely the case. J.S. Parent

6. Equilibrium State of a Reactive Liquid Phase • Consider the following reaction which we will conduct as a liquid phase: • (MeOH) (IB) (MBTE) • We determine the equilibrium constant, K, from the Gibbs energies of the pure components in the liquid state at the reaction temperature and 1 bar pressure. • This equilibrium constant relates to the liquid phase activities by: J.S. Parent

7. Equilibrium State of a Reactive Liquid Phase • We can relate the mole fractions of the system components to the reaction extent: • 15.5 • where, • In our case, • Substitution of these mole fractions allows us to calculate the reaction extent from the equilibrium constant relation. J.S. Parent

8. Equilibrium State of a Reactive Liquid Phase • Recall, • where gi is a function of xMeOH, xIB, xMBTE and temperature. • Solving the above equation in terms of e can be achieved by successive substitution or trial and error. See example 15.10 for an illustration of the procedure. J.S. Parent