Advanced Chem Lecture #16
Gibbs Free Energy
Enthalpy – thermodynamic quantity used to describe heat changes at constant pressure.
Enthalpy of reaction is difference between enthalpy of products and
enthalpy of reactants.
Entropy – A direct measure of the randomness or disorder of the system. Absolute
entropy is the difference between entropy at given temperature and
entropy at 0K (S = 0).
Free Energy – The energy available to do useful work.
For a spontaneous process: ΔSuniv = ΔSsys + ΔSsurr > 0
For an equilibrium process: ΔSuniv = ΔSsys + ΔSsurr = 0
Entropy Changes in Surroundings
ΔSsurr α – ΔHsys
That is, an exothermic process (-ΔHsys) adds energy to the system, and will thus
increase entropy. An endothermic process (+ΔHsys) draws energy away from the system,
cooling surrounding molecules and slowing them, thus decreasing entropy.
Change in entropy also dependent upon temperature. If temperature of
surroundings is already very high, a small exothermic reaction will have little change in
entropy. If temperatures are low, the addition of a small amount of heat will cause a
drastic increase in entropy. By analogy, someone coughing in a crowded restaurant will
not disturb anyone, but someone coughing in a library certainly will.
From the inverse relationship between ΔSsurr and T, we can write:
ΔSsurr = - ΔHsys / T
Gibbs Free Energy
ΔSuniv = ΔSsys + ΔSsurr > 0
ΔSuniv = ΔSsys - ΔHsys / T > 0
T ΔSuniv = - ΔHsys + ΔSsysT > 0
-T ΔSuniv = ΔHsys - ΔSsysT < 0
ΔG = ΔHsys - TΔSsys
or
G = H – TS
In this context, free energy is the energy available to do work. That is, if ΔG is
negative, this fact alone guarantees that the reaction is spontaneous.
ΔG < 0 reaction is spontaneous
ΔG > 0 reaction is non-spontaneous. Spontaneous in other direction
ΔG = 0 reaction is at equilibrium
The standard free energy of reaction (ΔG˚rxn) is the free energy change for a
reaction when it occurs under standard conditions. The standard free energy of formation
(ΔG˚f) is the free energy change when one mole of a compound is synthesized from its
elements in their standard states. The ΔG˚f of elements is arbitrarily set at zero.
ΔG˚rxn = ΔG˚f (products) - ΔG˚f (reactants)
Calculate:
CH4 + 2O2  CO2 + 2H2O
2MgO  2Mg + O2
Predicting Sign of ΔG
If both ΔH and ΔS are positive, than ΔG will be negative only when TΔS is
greater than ΔH. This is met when T is large.
Rxn spontaneous at high temps, at low temps, reverse is spontaneous
If ΔH is positive and ΔS is negative, ΔG will always be positive, regardless of T
Spontaneous in reverse direction at all temps
If ΔH is negative and ΔS is positive, ΔG will always be negative, regardless of T
Spontaneous in forward direction at all temps
If ΔH is negative and ΔS is negative, then ΔG will be negative only when TΔS is
smaller than ΔH. This is met when T is small.
Rxn spontaneous at low temps, at high temps, reverse is spontaneous
Consider:
CaCO3  CaO + CO2 (reaction is reversible)
First calculate ΔH˚ and ΔS˚ (at 25˚C).
ΔH˚ = ΔH˚ (products) – ΔH˚ (reactants)
ΔH˚ = 177.8 kJ/mol
ΔS˚ = ΔS˚ (products) – ΔS˚ (reactants)
ΔS˚ = 160.5 J/K·mol
ΔG˚ = ΔHsys - TΔSsys
ΔG˚ = 177.8 kJ/mol – (298K)(0.160kJ/K·mol)
ΔG˚ = 130.0 kJ/mol
Because ΔG˚ is a large positive quantity, the reaction is not favored at 25˚C. In
order to make ΔG˚, we need to increase the temperature (increase value of TΔS). Try
new calculation with T = 1108K. Some CO2 is made at lower temperatures, but this is
the temp at which an appreciable amount begins to be made spontaneously. Also, STP
not maintained, but this temp gives a “ballpark” estimate
Phase Transitions
At the temperature of a phase change, system is at equilibrium, that is:
ΔG = ΔH – TΔS
0 = ΔH – TΔS
ΔS = ΔH / T
Consider:
The phase transition of water from solid to liquid. ΔH is the molar heat of
fusion (6.010kJ/mol) and T is the melting point (273K). So,
ΔS = ΔH / T
ΔS = (6010 J/mol) / 273 K
ΔS = 22.0 J / K·mol
This number also corresponds to the increase in the number of possible
microstates in the liquid form. Also consider the phase change from liquid to solid. The
molar heat of freezing is the reverse of the molar heat of fusion (-6.010 kJ/mol). This
yields a negative value for entropy, signifying a decrease in the number of possible
microstates.
Coupled Biological Reactions
Many biological processes have a positive ΔG value, and yet they are essential to
metabolism and biosynthesis. In living systems, these processes are coupled to other
reactions that have large negative ΔG values, to produce a net equation with a negative
change in free energy.
Consider:
The extraction of zinc from the ore sphalerite (ZnS)
ZnS  Zn + S
(ΔG˚ = 198.3 kJ/mol)
But the combustion of sulfur to a favorable reaction
S + O2  SO2
(ΔG˚ = -300.1 kJ/mol)
Coupling the two processes means that the tendency of S to form SO2 will
promote the decomposition of ZnS.
ZnS  Zn + S
S + O2  SO2
(ΔG˚ = 198.3 kJ/mol)
(ΔG˚ = -300.1 kJ/mol)
ZnS + O2  Zn + SO2
(ΔG˚ = -101.8 kJ /mol)
Also can consider a mechanical model as an analogy. You can make a small a
smaller weight move upwards (non-spontaneous) by attaching it to a larger weight
through a pulley.
In a biological system, the synthesis of ATP is coupled with the decomposition of
glucose. Connected by electron transfer in NADH and FADH2
Consider:
C6H12O6 + 6O2  6CO2 + 6H2O
(ΔG˚ = -2880 kJ/mol)
ADP + H3PO4  ATP + H2O
(ΔG˚ = +31 kJ/mol)
Conversely, the release of a free phosphate from ATP gives -31 kJ/mol of energy,
which can then be harnessed by the organism to drive energetically unfavorable
reactions.