Gibbs Free Energy
 What’s “free” about Gibbs free energy?
 The change in free energy for a process
equals the maximum work that can be done
by the system on the surroundings in a
spontaneous process occurring at constant
temperature and pressure.
DG = wmax
Gibbs Free Energy
Example: What is the maximum work that can be
performed by the combustion of 25.0 g of
methanol (CH3OH)?
Step 1: Write a balanced equation.
Gibbs Free Energy
Step 2: Calculate DGrxn
Step 3: Calculate the DG for the mass used
in the reaction.
Gibbs Free Energy
 On your exam, you must be able to write a
balanced equation for a simple combustion
reaction (including predicting the products).
 You will then be expected to calculate the
maximum work that can be performed using a
given number of grams or moles of a reactant.
Gibbs Free Energy
 You should be able to write a balanced equation
for the combustion of an organic compound or a
metal.
 Organic compounds:
CnHm + O2
CxHYOn + O2
CO2 + H2O
Not bal.
CO2 + H2O
 Metals:
Metal + O2
Metal oxide
Not bal.
Gibbs Free Energy
 You can use the signs (positive or negative) of
DH and DS to predict whether a reaction (or
process) will be:
 Spontaneous at all temperatures
 Spontaneous only at high temperatures
 Spontaneous only at low temperatures
 Non-spontaneous at all temperatures
Gibbs Free Energy
 The sign of DG (and therefore the spontaneity
of the reaction) will depend on
 the sign of DH and DS
 relative magnitude of the enthalpy and the
entropy terms.
 In some cases, the temperature will impact
the spontaneity of a reaction.
DG = DH – TDS
DG =
DH
+
Enthalpy
term
(- TDS)
Entropy
term
Gibbs Free Energy
Effect of Temperature of Spontaneity
DH
-
DS
+
DG
always -
Spontaneity
Spon. all T
+
-
always +
Non-spon. all T
-
-
- at low T
spon. at low T
+
+
- at high T
spon. at high T
Gibbs Free Energy
Example: Predict whether the following reaction
will be spontaneous at low temperature, high
temperature, at all temperatures or always nonspontaneous.
2 PbS(s) + 3 O2 (g)  2 PbO (s) + 2 SO2 (g)
DH = neg.
DS = neg
Gibbs Free Energy
Example: Given the standard heats of formation
below, predict whether the following reaction will
be spontaneous at low temperature, high
temperature, at all temperatures or always nonspontaneous.
CaO (s) + 3 C (graphite)  CaC2 (s) + CO (g)
DHfo (CaO) = - 635.1 kJ/mol
DHfo (CaC2) = - 59.9 kJ/mol
DHfo (CO) = - 110.5 kJ/mol
Gibbs Free Energy
Gibbs Free Energy
 For a system in which the reactants and/or
products are not present in their standard
states, the values of DG and DGo are related:
DG = DGo + RT lnQ
where DG = Gibbs free energy change
DGo = standard Gibbs free energy change
R = 8.314 J/mol.K
T = temp. in Kelvin
Q = reaction quotient
Free Energy and Equilibrium Constants
 For a system at equilibrium,
 DG = 0
Q = K
 and the standard free energy change (DGo) for
the reaction is directly related to the
equilibrium constant for the reaction
DGo = -RT ln K
Free Energy and Equilibrium Constants
 This equation can be used to calculate DGo for
a reaction when the equilibrium constant or the
equilibrium concentrations are known.
 The equation can also be rearranged and used
to find the value of the equilibrium constant if
DGo for the reaction is known:
K =
o
e-DG /RT
Free Energy and Equilibrium Constants
Example: Find DGo for the following reaction at
25oC if Kp = 7.00 x 105.
N2 (g) + 3 H2 (g)
2 NH3 (g)
Free Energy and Equilibrium Constants
Example: Calculate the equilibrium constant at
25oC for the dissolution of barium fluoride if DGo
for this process is +32.9 kJ per mole of barium
fluoride.
Free Energy and Equilibrium Constants
Free Energy and Equilibrium Constants
 Once you find the value for the equilibrium
constant, you can use the equilibrium constant
to :
 Calculate the equilibrium concentrations of
the products and/or reactants.
 How would you calculate the concentrations of
barium ions and fluoride ions present in a
saturated solution of barium fluoride?
Free Energy and Equilibrium Constants