Page 90 - Modeling of Chemical Kinetics and Reactor Design

60 Modeling of Chemical Kinetics and Reactor Design

reasonable rate (possibly in the presence of any catalyst that may have
been developed for the reactions). Next, the values of the equilibrium
constant, K, in this temperature range must be computed using the
principles of thermodynamics. The equilibrium constant of the reaction
depends only on the temperature and is used to determine the limit
to which the reaction can proceed under the conditions of temperatures,
pressure, and reactant compositions that appear most suitable.

CHEMICAL EQUILIBRIUM

Consider a single homogeneous phase of one component of unchang-
ing composition. If it undergoes an isothermal reversible change and
does work, then from the first law of thermodynamics:

q = dU + pdV or dU = q – pdV (2-1)

From the second law of thermodynamics:

dS = q , reversible change
T

q = TdS (2-2)

Combining the first and second laws (Equations 2-1 and 2-2) gives:

dU = TdS – pdV (2-3)

Now consider a homogeneous phase containing different substances
or components. Its phase contains:

•n moles of component 1
1
•n moles of component i
i
•n moles of component k
k
For a constant composition, it is known that dU = TdS – pdV. For
a variable composition,

U = U(S, V, n , . . . n . . . n ) (2-4)
k
i
1
Performing a partial differentiation on Equation 2-4 yields