The Richard Stockton College of New Jersey
Chemistry Program, School of Natural Sciences and Mathematics
PO Box 195, Pomoma, NJ
CHEM 3410: Physical Chemistry I — Fall 2008
October 1, 2006
Lecture 13: Gibbs Free Energy & Equilibrium
References
1. Brady, Physical Chemistry, Sections 4.1–4.5
Key Concepts
•Last time we developed a new function, the Gibbs Free Energy (G(T, P )), a new thermodynamic energy
function that was minimized at equilibrium under constant pressure and temperature conditions.
G=U−T S +P V
•Using our definition of enthalpy (H=U+PV ) we can write G=H−T S. If we look a small changes in
Gat constant temperature, this reduces to dG =dH −T dS. For macroscopic changes we can integrate
this to give us an expression that looks very familiar:
∆G= ∆H−T∆S
•A similar derivation is possible under conditions of constant Vand T, which yields the Helmholtz Free
Energy (A(V, T ) in our book):
A=U−T S
dA =−T dS −P dV
•From these new functions, we can develop additional expression by comparing the forms derived above
with the expressions we used for a function that was an exact differential (state function):
dG =∂G
∂T P
dT +∂G
∂P T
dP
Comparing this with dG =−SdT +V dP we arrive at the following:
∂G
∂T P
=−Sand ∂G
∂P T
=V
and the following Maxwell relations (the derivative of Gwith respect to first Tand then Pmust be
equal to taking the derivative of Gwith respect to Pfirst and then T).
−∂S
∂V T
=∂V
∂T P
Experimental Key Fundamental At Spontaneous At
Conditions Parameter Equilibrium Process Equilibrium
Isolated Smaximized ∆S > 0dS = 0
Constant T & P Gminimized ∆G < 0dG = 0
Constant T & V Aminimized ∆A < 0dA = 0
•We can apply condition that the Gibbs Free energy is a minimum at equilibrium for systems at constant
Pand Tto situations where other forms of work are important, such as where surfaces (or interfaces)
are being created and destroyed.
dG =−SdT +V dP +γdA
