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INTRODUCING THE GIBBS FUNCTION 145

solvent rises up the interior passage of the condenser from the flask, cools and thence
condenses (Equation (4.20)) as it touches the inner surface of the condenser. Con-
densed liquid then trickles back into the flask beneath.

solvent (g) −−→ solvent (l) + energy (4.20)

The energy is transferred to the glass inner surface of the condenser. We maintain
a cool temperature inside the condenser by running a constant flow of water through
the condenser’s jacketed sleeve. The solvent releases a large amount of heat energy
as it converts back to liquid, which passes to the water circulating within the jacket,
and is then swept away.
Addition of heat energy to the flask causes several physicochemi-
cal changes. Firstly, energy allows the chemical reaction to proceed, The ‘Gibbs function’ G
but energy is also consumed in order to convert the liquid solvent is named after Josiah
into gas. An ‘audit’ of this energy is difficult, because so much of Willard Gibbs (1839–
the energy is lost to the escaping solvent and thence to the sur- 1903), a humble Amer-
ican who contributed
rounding water. It would be totally impossible to account for all
to most areas of phys-
the energy changes without also including the surroundings as well
ical chemistry. He also
as the system.
had a delightful sense
So we see how the heater beneath the flask needs to provide
of humour: ‘A math-
energy to enable the reaction to proceed (which is what we want to ematician may say
happen) in addition to providing the energy to change the surround- anything he pleases,
ings, causing the evaporation of the solvent, the extent of which but a physicist must be
we do not usually want to quantify, even if we could. In short, at least partially sane’.
we need a simple means of taking account of all the surroundings
without, for example, having to assess their spatial extent. From
the second law of thermodynamics, we write

As well as calling G
G (system) = H (system) − T S (system) (4.21)
the Gibbs function, it is
often called the ‘Gibbs
(see Justification Box 4.2) where the H, T and S terms have their energy’ or (incorrectly)
usual definitions, as above, and G is the ‘Gibbs function’. G is ‘free energy’.
important because its value depends only on the system and not on
the surroundings. By convention, a positive value of H denotes
an enthalpy absorbed by the system.
H here is simply the energy given out by the system, i.e. by the
reaction, or taken into it during endothermic reactions. This energy The Gibbs function is
transfer affects the energy of the surroundings, which respectively the energy available for
absorb or receive energy from the reaction. And the change in the reaction after adjusting
energy of the surroundings causes changes in the entropy of the for the entropy changes
surroundings. In effect, we can devise a ‘words-only’ definition of the surroundings.
of the Gibbs function, saying it represents ‘The energy available
for reaction (i.e. the net energy), after adjusting for the entropy
changes of the surroundings’.