496
10 The Statistical Basis of Bioenergetics
dependence. In addition, higher temperatures will tend to reduce the clustering
tendencies of oppositely charged ions and of polar molecules because of thermal
diffusion.
Among the complications for biochemical reactions involving ions are:
• Ions of opposite charge will tend to accumulate and also surround other larger
charged molecules;
• Orientation of nearby water molecules near charged ions and molecules due to
the strong electric dipole moments of water molecules;
• Accumulation of water molecules near small ions because of an induced
attractive force on water molecules arising from the strong Coulombic gradients
acting on the water molecule dipoles;
• A tendency for the first layer of water molecules accumulated around a small ion
to ‘crystallize’ into quasi-ordered arrays;
• The electric permittivity of water (about eighty times that of a vacuum because
of the polar nature of the water molecule) will vary with distance from an ion,
dropping nearby because the water molecules are already quasi-oriented and
being so are restricted in their reaction to additional external electric fields;
• Changes in the electric dipole moment of a water molecule in nearby region to
small ions, i.e. distortion of the position of the hydrogens relative to the oxygen;
• At high concentrations of ions, dynamical clusters of oppositely charged ions
may form;
• In an external electric field, ions dissolved in water will move, but with a
dynamical ‘cloud’ of accumulated ions and nearby water, increasing its effective
size and mass;
• When a small ion is dragged, its ‘cloud’ of water and ions changes from quasispherical to quasi-elliptical.
Even with these complications, since the 1920s there have been developed a
number of strategies for finding equilibrium conditions for the concentration of the
molecules involved and reaction rates.
10.9.4 Modeling Reactions Involving Ions in Solution
As with all reactions at constant temperature and pressure, the Gibbs free energy
before and after the reaction can be used to describe reaction rates and, in principle,
determine equilibrium conditions.
In the case of the formation of ions in solution, charge conservation requires
that the reaction occur holding the total charge zero if it started that way. The fact
that the electric force is large between ions and electrons compared to the typical
intermolecular forces between molecules in a solution, the overall total charge in
10 The Statistical Basis of Bioenergetics
dependence. In addition, higher temperatures will tend to reduce the clustering
tendencies of oppositely charged ions and of polar molecules because of thermal
diffusion.
Among the complications for biochemical reactions involving ions are:
• Ions of opposite charge will tend to accumulate and also surround other larger
charged molecules;
• Orientation of nearby water molecules near charged ions and molecules due to
the strong electric dipole moments of water molecules;
• Accumulation of water molecules near small ions because of an induced
attractive force on water molecules arising from the strong Coulombic gradients
acting on the water molecule dipoles;
• A tendency for the first layer of water molecules accumulated around a small ion
to ‘crystallize’ into quasi-ordered arrays;
• The electric permittivity of water (about eighty times that of a vacuum because
of the polar nature of the water molecule) will vary with distance from an ion,
dropping nearby because the water molecules are already quasi-oriented and
being so are restricted in their reaction to additional external electric fields;
• Changes in the electric dipole moment of a water molecule in nearby region to
small ions, i.e. distortion of the position of the hydrogens relative to the oxygen;
• At high concentrations of ions, dynamical clusters of oppositely charged ions
may form;
• In an external electric field, ions dissolved in water will move, but with a
dynamical ‘cloud’ of accumulated ions and nearby water, increasing its effective
size and mass;
• When a small ion is dragged, its ‘cloud’ of water and ions changes from quasispherical to quasi-elliptical.
Even with these complications, since the 1920s there have been developed a
number of strategies for finding equilibrium conditions for the concentration of the
molecules involved and reaction rates.
10.9.4 Modeling Reactions Involving Ions in Solution
As with all reactions at constant temperature and pressure, the Gibbs free energy
before and after the reaction can be used to describe reaction rates and, in principle,
determine equilibrium conditions.
In the case of the formation of ions in solution, charge conservation requires
that the reaction occur holding the total charge zero if it started that way. The fact
that the electric force is large between ions and electrons compared to the typical
intermolecular forces between molecules in a solution, the overall total charge in