Gibb’s Free Energy
Chapter 19
G
• Gibbs free energy describes the greatest
amount of mechanical work which can be
obtained from a given quantity of a
reactants in a given initial state
• Also referred to as the chemical potential of
a system
Gibbs Free Energy
• TSuniverse is defined as the Gibbs free
energy, G.
• When Suniverse is positive, G is negative.
• Therefore, when G is negative, a process
is spontaneous.
Gibbs Free Energy
1. If G is negative, the forward
reaction is spontaneous
(products are favored at
equilibrium, K>1).
2. If G is 0, the system is at
equilibrium.
3. If G is positive, the reaction
is spontaneous in the reverse
direction but
thermodynamically not
favored in forward direction.
Spontaneous
• Means reaction will occur but has no
specification as to how long it will take to
occur
– Spontaneous does not mean quick or that it will
occur at a measurable rate, just that it is
thermodynamically favored without something
outside the system to cause it
Standard Free Energy Changes
Analogous to standard enthalpies of
formation are standard free energies of
formation, G.f
G = SnG(products)
 SmG(reactants)
f
f
where n and m are the stoichiometric
coefficients.
G is for a substance at standard state which is
P =1 atm and concentrations of reactants and
products that equal 1 M
Practice Problem
• Use the data from Appendix C to calculate the
standard free energy change for the following
reaction at 298 K:
P4(g) + 6 Cl2(g)  4
PCl3
G = SnG(products)  SmG(reactants)
= 4G(PCl3)
- G(P4 ) - 6G(Cl2 )
= 4*(-269.6) – 1(24.4) – 0
= -1102.8 KJ
Free Energy Changes
At temperatures other than 25°C,
G° = H  TS
If H = -196.6 KJ and S = -189.6 J/K, is the
reaction spontaneous at a temperature of
298 K?
G° = -196.6 – 298(-189.6* 1kJ/1000J)
= -120.8 kJ (spontaneous)
Free Energy and Temperature
• There are two parts to the free energy
equation:
– H— the enthalpy (internal energy) term
– TS — the entropy (disorder) term
• The temperature dependence of free
energy, then comes from the entropy term.
Free Energy and Temperature
• Any process that has both H < 0 (exothermic) and S > 0 will always be
spontaneous (G < 0) and thermodynamically favored and favors products (K > 1)
• Any process that has both H > 0 (endothermic) and S < 0 will always be
nonspontaneous (G > 0) and favors the reactants (K < 1)
• Just because a reaction is exothermic, does
not mean that it decreases in entropy
– Each different type of reaction will have to be
looked at individually and both the values for
enthalpy and entropy must be considered to
determine if the reaction is thermodynamically
favored (G < 0)
Conditions that can cause
nonspontaneous reactions to occur
• Electricity
– Charging a battery
– Electrolysis
• Light
– Photosynthesis in plants (converting sunlight into food)
– Photoionization of an atom (removing additional electrons from
an atom)
• Coupling favorable reactions with unfavorable reactions
– Conversion of ATP to ADP releases energy in living things
– Series of reactions with common intermediates are grouped
together with an overall G < 0
Thermodynamically Favored but not
at a measurable rate
• Processes that are thermodynamically
favorable but do not occur at measurable
rates are said to be under kinetic control
– Common reason is High activation energy
– Note: Just because a thermodynamically favored
reaction does not occur at a measurable rate does
not mean that it is at equilibrium
Free Energy and Equilibrium
Under any conditions, standard or
nonstandard, the free energy change can
be found this way:
G = G + RT lnQ
(Under standard conditions, all concentrations are 1 M, so Q
= 1 and lnQ = 0; the last term drops out.)
Free Energy and Equilibrium
• At equilibrium, Q = K, and G = 0.
• The equation becomes
0 = G + RT lnK
• Rearranging, this becomes
G = RT lnK
or,
K = eG/RT
• K = eG/RT
• This means the equilibrium constant is related
to free energy
– When G is large compared to the thermal
energy (RT), then K deviates strongly from 1 (away
from equilibrium)
– When a reaction is at equilibrium G is 0 (since
there is no change between reactants and
products) so K = 1
• G < 0, the reaction favors products so K > 1
– Reaction is classified as “exergonic”
• Spontaneous
• G > 0, the reaction favors products so K < 1
– Reaction is classified as “endergonic”
• nonspontaneous
Practice Problem
• Use data from Appendix C to calculate the
standard free energy change, G°and the
equilibrium constant, K, at 298 K for the
reaction
H2(g) + Br2(l) 2HBr(g)
G°= -106.4 kJ/mol
K = 4 x 1018
Spontaneous, since K > 1 products are favored