For a reaction with the same initial and final temperature, the
changes in enthalpy, entropy, and free energy are related by the
expression
DG = DH
 TDS
This expression says that, at constant temperature, the change
in free energy, DG, is the change
in enthalpy, DH, minus the change in entropy multiplied by the
absolute temperature, TDS. It is
not too difficult to prove that a spontaneous reaction is one in
which the overall free energy decreases, regardless of what happens
to the enthalpy and entropy individually.
Spontaneity is a combined effect of both H and S, and the above
equation is the proper way of combining them. This equation is easier
to understand with the aid of arrow diagrams, as at the right. An
upward pointing arrow represents an increase in free energy, enthalpy,
and order, or a positive value for DG,
DH, and (TDS).
This is the nonspontaneous direction. Conversely, an arrow pointing
downward symbolizes a decrease in free energy or enthalpy, and an
increase in disorder. These correspond to negative values for DG,
DH, and (TDS),
and are in the direction of spontaneity. The DG
arrow is the sum of the DH and the
(TDS) arrows, and if the DG
arrow points downward, the reaction is spontaneous.

