GIBBS FREE ENERGY

1. CCE WORK
PHYSICS
Topic- Gibbs Free Energy
Class- B.Sc. 2nd Sem

2. Derivation
Description

3. G(p,T)=H-TS
Where:
U is the internal energy
P is the pressure (SI unit: joule)
V is the volume (SI unit: m3)
T is the temperature (SI unit: kelvin)
S is the entropy (SI unit: joule per kelvin)
H is the enthalpy (SI unit: joule)

4. The expression for the infinitesimal reversible
change in the Gibbs Free Energy as a
function of its natural variables p and T,
for an open system subjected to the
operation of external forces Xi, which cause
the external parameters of the system ai to
change by an amount dai, can be derived as
follows from the first law of reversible
processes:

5. TdS = dU+pdV-
summation(nu)idNi+summation(Xidai)+….
d(TS)-SdT = dU+d(pV)-Vdp-
summation(nu)idNi+summation(Xidai)+….
d(U-TS+pV) = Vdp-SdT+summation(nu)idNi-
summation(Xidai)+….
dG = Vdp-SdT+summation(nu)idNi-
summation(Xidai)+….

6. where,
(nu)i is the chemical potential of the ith
chemical component (SI unit: joule per
particle or joules per mole)
Ni is the number of particles (or no. of moles)
composing the ith chemical component

7. This is the first form of Gibbs fundamental
equation. In the infinitesimal expression, the
term involving the chemical potential
accounts for changes in Gibbs Free Energy
resulting in from influx or outflux of
particles. In other words, it holds for an
open system. For a closed system, this term
may be dropped.

8. The temperature dependence of the Gibbs energy for an
ideal gas is given by the Gibbs Helmholtz equation and
its pressure dependence is given by:
G/N = Go/N+kT In P/Po
If the volume is known rather than pressure then it
becomes:
G/N = Go/N+kT In Vo/V
Or more conveniently as its chemical potential:
G/N = (nu) = (nu)o+kT In P/Po
In non-ideal systems,fugacity comes into play.

9. The Gibbs Free Energy total differential natural variables may be
derived via legendra transforms of the internal energy.
dU = TdS – pdV + summation(nu)idNi
Because S,V and Ni are extensive variables,Euler’s homogenous
function theorem allows easy integration of dU.
U =TS – pV + summation(nu)iNi
The definition of G from above is
G = U + pV - TS
Taking the total differential,we have
dG =dU + pdV + Vdp – TdS - SdT
Replacing dU with the result from the first law gives,
dG = TdS – pdV +summation(nu)idNi + pdV + Vdp –TdS –SdT
=Vdp – SdT + summation(nu)idNi
The natural variables og G are then p,T and {Ni}

10. “The greatest amount of mechanical work which
can be obtained from a given quantity of a
certain substance in a given initial state,
without increasing its total volume or allowing
heat to pass to or from external bodies except
such as at the close of the processes are left in
their initial condition.”

11. According to second law of thermodynamics,for systems
reacting at STP, there is a general natural tendency to
achieve a minimum of the Gibbs free energy.
A quantitative measure of the favourability of a given
reaction at constant temperature and pressure is the
change del(G) in Gibbs free energy that is effected by
proceeding with the reaction. As a necessary condition
for the reaction to occur at constant temperature and
pressure, del(G)must be smaller than the non-PV work,
which is often equal to zero.

12. In traditional use, the term “free” was included in “Gibbs
free energy” to mean “available in the form of useful
work”. The characterization becomes more precise if we
add the qualification that is the energy available for non-
volume work. However, an increasing no. of books and
journal articles do not include the attachment “free”
referring to G as simply “Gibbs energy”. This is the result
of 1988 IUPAC meeting to set unified terminologies for
the international scientific community, in which the
adjective ‘free’ was supposedly banished. This standard,
however has not yet been universally adopted.

13. Del(G) equals the maximum amount non-PV
work that can be performed as a result of the
chemical reaction. If the analysis indicated a
positive del(G) for the reaction, then energy
in the form of electrical or other non-PV
work would have to be added to the reacting
system for del(G) to be smaller than the non-
PV work and make it possible for the
reaction to occur.

14. THE END