c06 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come
6 The Gibbs Free Energy
Our brief consideration of engines and heat transfer showed that only part of the heat
transferred from a hot reservoir to a cold one by a real process is available to do
work. This is the available or “free” energy that we have been seeking. In the theory
of steam engines, the Helmholtz free energyA=U−TSis central. In chemical
reactions the closely analogous Gibbs free energyG=H−TSis central. We shall
be mainly concerned with the Gibbs free energy.6.1 COMBINING ENTHALPY AND ENTROPY
We seek a combined function that expresses the spontaneous tendency of a chemical
system to undergo a change in enthalpy simultaneously with a change in its entropy.
In other words, we seek a factor that governs chemical reactions. Clearly, the signs
of enthalpy and entropy must be opposite because one function tends to a maximum
and the other tends to a minimum. We might writeX=U−Sfor our unknown
energy function such that matter flows from a point of high potential to one of low
potential in the way that water flows downhill, but we chemists are usually interested
in reactions that are carried out at constant pressure, so we substituteHforUin the
equation. Also we notice that the units are wrong. Enthalpy has the unit J and entropy
has the unit J K−^1. To bring everything into consistent units of energy, we multiply
the entropy byTto get the central equation of chemical thermodynamics:G≡H−TS
Concise Physical Chemistry,by Donald W. Rogers
Copyright©C2011 John Wiley & Sons, Inc.
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