which equals 6020 J?mol^1. Consequently, the change in entropy of water
molecules going from the solid to the liquid state equals
DH=Te¼22 J?mol^1 ?K^1. This signifies that the molecules gain entropy
on melting, in agreement with the nature of entropy: Eq. (2.1).
It is often tacitly assumed that DH and DS are independent of
conditions like temperature, and this is indeed often true, as long as the
temperature range is small (but not for water: see Section 3.2). Note that the
effect of a change in entropy will be larger at a higher temperature. If the
system does no work, a change in enthalpy can be measured as a change in
heat, i.e., by calorimetry. Changes in entropy mostly cannot be measured
directly.
According to thermodynamic theory, any system will spontaneously
change until it has attained the state of lowest free energy. In an isolated
system (no exchange of energy with the environment) this means that the
entropy will increase until it has attained the highest possible value.
Consequently, a system isstableif it is in a state of lowest free energy. In any
other state the system would thus beunstable. This does not mean that we
observe every unstable system to change. First, the system may be
metastable. This means that it is in a local state of minimum free energy;
at least one other state of still lower free energy does exist, but the system
cannot reach it, because it then has to pass through a state of higher free
energy. An example is the potential energy of a ball laying in a rut on top of
a hill: the ball has to go over the rim of the rut—i.e., go to a state of higher
energy—before it can roll down the hill, reaching its state of lowest potential
energy. Second, the change may be too slow to be observable. In principle,
the rate of change is proportional to the decrease in free energy involved and
inversely proportional to aresistanceto change. Envisage, for example, a
stone lying on a sloping surface. Gravity will try to move it down the slope,
but the frictional resistance between stone and surface may be too large to
allow perceptible movement. Resistance to change can be due to a variety of
causes: for chemical reactions a high activation free energy (Section 4.3.3),
for evening of concentration in a liquid system a high viscosity (Section
5.1.2), etc. For most causes, the resistance tends to be smaller at a higher
temperature, although there are some exceptions.
2.2 SOLUTIONS
Almost all foods are or contain solutions, and solution properties thus are
paramount. In this section we will briefly discuss some properties of simple
solutions of nonelectrolytes.