For the gas-phase reaction
RT lnK = –ΔG
Where G is the Gibbs Free Energy and R is the ideal gas constant.
where ai is the activity of species i
where
fi = fugacity of species i
= fugacity of species i at the standard state. For gases, the standard state is 1 atm.
Kγ = Activity equilibrium constant
KP = Pressure equilibrium constant
KC = Concentration equilibrium constant
where γi is the activity coefficient of species i
Pi = partial pressure of species i, atm, kPa.
Pi = CiRT
Kγ has units of
KP has units of
For ideal gases Kγ = 1.0 atm-δ
KP and KC are related by
then
KP = KC
Example C–1. Water-Gas Shift Reaction
The water-gas shift reaction to produce hydrogen,
is to be carried out at 1000 K and 10 atm. For an equimolar mixture of water and carbon monoxide, calculate the equilibrium conversion and concentration of each species.
Data: At 1000 K and 10 atm, the Gibbs free energies of formation are cal/mol; cal/mol; cal/mol; .
We first calculate the equilibrium constant. The first step in calculating K is to calculate the change in Gibbs free energy for the reaction. Applying Equation (C-10) gives us
then
K = 1.44
Expressing the equilibrium constant first in terms of activities and then finally in terms of concentration, we have
where ai is the activity, fi is the fugacity, γi is the activity coefficient (which we shall take to be 1.0 owing to high temperature and low pressure), and yi is the mole fraction of species i.2 Substituting for the mole fractions in terms of partial pressures gives
In terms of conversion for an equimolar feed, we have
From Figure EC-1.1 on the DVD-ROM we read at 1000 K that log KP = 0.15; therefore, KP = 1.41, which is close to the calculated value. We note that there is no net change in the number of moles for this reaction (i.e., δ = 0); therefore,
K = KP = KC (dimensionless)
Taking the square root of Equation (EC-1.7) yields
Solving for Xe, we obtain
Then
Figure EC-1.1 on the DVD-ROM gives the equilibrium constant as a function of temperature for a number of reactions. Reactions in which the lines increase from left to right are exothermic.
The following links give thermochemical data. (Heats of Formation, CP, etc.)
Also see Chem. Tech., 28 (3) (March), 19 (1998).
3.238.142.134