Page 168 - Basic Principles of Textile Coloration

SURFACE ACTIVITY OF DETERGENTS 157

thermodynamic equation, an increase in molecular freedom, corresponding to an
increase in entropy (DS0 positive), implies a process with a higher value for the
equilibrium constant. Therefore, favourable processes involve increases in
molecular freedom.

One of the fundamental principles of thermodynamics is that all favourable
processes increase the overall entropy of the system and its surroundings. DG0 is
the change in the Gibbs free energy for the process. It is a measure of the total
overall change in entropy of the system and surroundings when the process takes
place under standard conditions. A negative value corresponds to a large
equilibrium constant and a favourable change. This is promoted by an increase in
entropy for the process (positive value for DS0) and an exothermic change
(negative value for DH0). In fact, the value of DH0 is a measure of the change in
entropy of the process surroundings. Any released heat from an exothermic
change, increases the temperature of the molecules in the surroundings. The
increased molecular speeds correspond to a gain of molecular freedom and thus
increased entropy. The overall free energy equation above therefore states that the
overall entropy change of the system and surroundings resulting from a given
process (–DG0/T) is the sum of the entropy change for the process (DS0) plus that
of the process surroundings (–DH0/T).

For the evaporation of 1 mole of liquid water, at 1 atm pressure and 25 °C, DH0
= +44 kJ mol–1. The change is strongly endothermic, indicating that the total
bond energy of a mole of water vapour is less than for a mole of the liquid. In the
liquid, water molecules are in close proximity, held together in clusters by
hydrogen bonds. In the vapour, the molecules are widely separated and have little
interaction. The enthalpy of vaporisation is therefore the energy that must be
absorbed (endothermic) to break the hydrogen bonds between the water
molecules in the liquid so that they can pass into the vapour state. Water
vaporisation has DS0 = +119 J mol–1 K–1. This is a significant increase in
entropy interpreted as the large increase in molecular freedom that is possible
when molecules pass from the liquid to the gaseous state. If the above figures are
substituted into the free energy equation:

DG0 = DH0 - TDS0 = 44 000 - 298 ™119 = +8 500 J mol-1 (2)

Thus, water evaporation at 25 °C is not an overly favourable process and the
extent of vaporisation at equilibrium is small.