Page 143 - Thermodynamics of Biochemical Reactions

Thernwdyanamics of Biochemical Reactions. Robert A. Alberty
Copyright 0 2003 John Wiley & Sons, Inc.
ISBN 0-471-22851-6

8.1 Two-Phase Systems without Chemical
Reactions
8.2 Two-Phase System with a Chemical Reaction
and a Semipermeable Membrane
8.3 Two-Phase System with a Chemical Reaction
and Membrane Permeable by a Single Ion
8.4 Two-Phase System with a Chemical Reaction
and Membrane Permeable by a Single Ion
8.5 Transformed Gibbs Energy of a Two-Phase
System with a Chemical Reaction and a
Membrane Permeable by a Single Ion
8.6 Effects of Electric Potentials on Molar
Properties of Ions
8.7 Equilibrium Distribution of Carbon Dioxide
between the Gas Phase and Aqueous Solution
8.8 Phase Separation in Aqueous Systems
Containing High Polymers

When a system involves two or more phases, there is a single fundamental
equation for the Gibbs energy that is the sum of the fundamental equations for
the separate phases: dG = dG, + dG, + .... The fundamental equation for the
system provides the criterion for spontaneous change and equilibrium. However,
there is a separate Gibbs-Duhem equation for each phase because any intensive
property of a phase is related to the other intensive properties of that phase. In
the treatments here the amount of material in the interface is ignored on the
assumption that the amounts there are negligible compared with the amounts in
the bulk phases. The effects of small pressure differences between the phases are
also ignored. New phases may form spontaneously under certain circumstances,
but phases can also be separated by membranes with specified permeabilities.
Phase equilibrium across semipermeable membranes is of special interest in
biological applications. First, we will consider two-phase aqueous systems with-
out chemical reactions, then introduce reactions, and finally electric potential
differences between phases. The numbers of intensive degrees of freedom F and

141