Reaction Equilibrium and Chemical Potential

1
Reaction Equilibrium and Chemical Potential

• We have developed a criterion for chemical
  equilibrium in terms the chemical potentials of
  components.
• 13.8
• While this criterion is complete, it is not in a
  useable form.
• Recall our definition of fugacity which applies
  to any species in any phase (vapour, liquid,
  solid)
• In dealing with reaction equilibria, we need to
  pay particular attention to the reference state,
  Gi(T). We can assign a standard state, Gio, as

2
Standard States

• For our purposes, the Gibbs energy at standard
  conditions is of greatest interest.
• This is the molar Gibbs energy of
• pure component i
• at the reaction temperature
• in a user-defined phase
• at a user-defined pressure (often 1 bar)
• A great deal of thermodynamic data are published
  as the standard properties of formation at STP
  (Table C.4 of the text)
• DGfo is standard Gibbs energy of formation per
  mole of the compound when formed from its
  elements in its standard state at 25oC.
• Gases pure, ideal gas at 1 bar
• Liquids pure substance at 1 bar

3
Chemical Potential and Activity

• Substituting our standard Gibbs energy (Gio) in
  the place of Gi(T), the chemical potential of
  component i in our system becomes
• 13.9
• We define a new parameter, activity, to simplify
  this expression
• where,
• The activity of a component is the ratio of its
  mixture fugacity to its pure component fugacity
  at the standard state.

4
Reaction Equilibrium and Activity

• When a reactive system reaches an equilibrium
  state, we know that the equilibrium criterion is
  satisfied. Recall that chemical reaction
  equilibrium requires
• where ni is the stoichiometric coefficient of
  component i and mi is the chemical potential of
  component i at the given P,T, and composition.
• Substituting our expression for chemical
  equilibrium into the above equation gives us
• Or,

5
The Equilibrium Constant

• Our equilibrium expression for reactive systems
  can be expressed concisely in the form
• 13.10
• where P signifies the product over all species.
• The right hand side of equation 15.12 is a
  function of pure component properties alone, and
  is therefore constant at a given temperature.
• The equilibrium constant, K, for the reaction is
  defined as
• 13.11
• K is calculated from the standard Gibbs energies
  of the pure components and the stoichiometric
  coefficients of the reaction.

6
Standard Gibbs Energy Change of Reaction

• The conventional means of representing the
  equilibrium constant uses DGo, the standard Gibbs
  energy change the reaction.
• Using this notation, our equilibrium constant
  assumes the familiar form
• 13.11
• When calculating an equilibrium constant (or
  interpreting a literature value), pay attention
  to standard state conditions.
• Each Gio must represent the pure component at the
  temperature of interest
• The state of the component and the pressure are
  arbitrary, but they must correspond with fio used
  to calculate the activity of the component in the
  mixture.

7
Temp. Dependence of Reaction Equilibrium

• Defined by the following relationship,
• the equilibrium constant is a function of
  temperature.
• Recall that DGo represents the standard Gibbs
  energy of reaction at the specified temperature.
• We know that
• From which we can derive the temperature
  dependence of K
• 13.14
• If we assume that DHo is independent of
  temperature, we can integrate 15.16 directly to
  yield
• 13.15

8
K vs Temperature

• Equation 12.15 predicts that ln K
• versus 1/T is linear. This is based on
• the assumption that DHo is a weak
• function of temperature over the
• range of interest.
• This is true for a number of
• reactions, including those
• depicted by Figure13.2.
• A rigorous development of
• temperature dependence
• of K may be found in the text

9
Equilibrium State of a Reactive System

• Given that an equilibrium constant for a reaction
  can be derived from the standard state Gibbs
  energies of the pure components, we can define
  the composition of the system at equilibrium.
• Consider the gas phase reaction
• The equilibrium constant gives us
• Or