CHM
1046
General Chemistry II
Dr. Michael Blaber
Chemical
Thermodynamics
Gibbs Free Energy
(Gibbs Energy)
J. Willard Gibbs was the
first person to be awarded a Ph.D. in science from an American University
(Yale, 1863)
Spontaneous
reactions often have:
- A negative enthalpy (release
of heat energy, DH < 0).
- An increase in entropy
(increase in disorder, DS > 0)
The spontaneity of a
reaction appears to involve two thermodynamic properties: enthalpy and
entropy
- Furthermore,
spontaneous reactions are those that go downhill in energetic
terms. In other words, the final state has a lower energy
content than the initial state
Gibbs
came up with an equation, combining both enthalpy and entropy contributions,
that provided a means to describe energy content and therefore a means to
evaluate the spontaneity of a reaction when that energy content changes. The
energy contents of a substance was termed the Gibbs
Energy and it was defined by the Gibbs Energy equation:
G = H - T*S
The Gibbs energy of a
substance = stored heat energy - inherent disorder at a reference temperature
H is
enthalpy, S is entropy and T is the temperature in Kelvin
- If there
is a lot of stored heat energy, then the substance has a lot of Gibbs
energy
- The more
disorder a substance has, the less Gibbs energy it has
Changes
in a substance (as in a chemical reaction or physical phase change):
DG = DH - T*DS
- If the
substance releases heat energy, then the product has a lower value of
stored heat energy and DH <
0. Such a change is downhill energetically (i.e. spontaneous)
- If the
disorder (entropy) increases, this is also a spontaneous process and DS > 0. Since DS > 0 this means that (-T * DS) < 0.
- Therefore,
both the enthalpic (DH) and entropic (-T*DS) terms are negative for
processes that are spontaneous
How to quantify the contribution of the entropic term to the Gibbs
energy?
In
"instant ice packs" a reaction occurs that is spontaneous, and yet is
endothermic (i.e. it is "cold" due to absorption of heat energy). The
absorption of heat energy is unfavorable and therefore must be
"driven" by an increase in entropy (i.e. a large -T*DS term). Therefore, the degree
to which heat can be spontaneously absorbed is actually providing us with
information regarding the magnitude of the entropic increase (i.e.
the entropic increase is what is "driving" the unfavorable heat
absorption).
- Recall that entropy was
defined previously as q/T (i.e. non-mechanical energy transferred
at a constant temperature). This definition is just a way of saying
that if heat is absorbed but the temperature does not change, then the
heat energy is being sucked in due to an entropic increase - and that
entropic increases is energetically equal to the heat energy absorbed
- In such a case DS is positive, entropy increases,
and (-T*DS) is
negative (favoring spontaneous reaction)
- Heat absorbed at a fixed
temperature is essentially an infinite heat capacity, and this is just to
point out that entropy has units of J/molK, like
heat capacity values. A material with a high heat capacity has the ability
to absorb a lot of heat energy with a small temperature change. It can do
this because it is able to increase its internal disorder and
"soak" up the heat energy and thus the temperature won't rise much. If a material cannot increase its internal
disorder, then it will increase temperature in response to even a small
amount of added heat energy.
For a
process occuring at constant temperature, T:
- If DG = 0, it
means that the enthalpy change associated with a reaction is equal in
magnitude (and opposite in sign) to the entropy change. For example, the
process being considered may result in a reduction in entropy (i.e. more
order) but it releases an amount of heat energy that exactly counteracts
the effects of the TDS term. Such a reaction is in equilibrium (i.e. no net
reaction)
- If DG < 0. This
would occur for not only an exothermic reaction (DH = negative) that overwhelms any
unfavorable entropic effect. But potentially also for an endothermic
process that has a significant increase in disorder (i.e. DS is large, and thus, TDS is large and negative). In
either case, the process being considered has a net driving force (release
of energy or increase in entropy) that indicates the reaction is spontaneous
- If DG > 0. This
will happen if the reaction is highly endothermic (DH positive) and the entropic term
is not so great. Or, if the reaction is exothermic (i.e. DH is negative), but the process
results in significant increase in order (i.e. the T*DS term ends up being a negative
number, so that -T*DS is
positive in magnitude). In any case, this is energetically an unfavorable
process being considered. To move in the forward direction, energy must be
supplied. If energy is not supplied, then the
reaction will proceed spontaneously in the reverse direction.
Gibbs energy and chemical reactions at equilibrium.
It
would seem there are 4 possible types of reactions or processes with regard to
the enthalpic and entropic contribution to the Gibbs
energy change:
- DH
= (-), -TDS = (-).
Favorable enthalpic change (exothermic) and
favorable entropic change (disorder increases)
- DH
= (+), -TDS = (+).
Unfavorable enthalpic change (endothermic) and
unfavorable entropic change (disorder decreases)
- DH
= (-), -TDS = (+).
Favorable enthalpic change (exothermic) and
unfavorable entropic change (disorder decreases)
- DH
= (+), -TDS = (-).
Unfavorable enthalpic change (endothermic) and
favorable entropic change (disorder increases)
If
you look at these four types of energy changes, you will notice that 1) and 2)
are considering the same process, just from different directions.
Likewise, with 3) and 4) (i.e. an exothermic process in one direction is
endothermic in the opposite direction). So, in principle, we just have to
understand two types of processes.
- For type 1) above, both
enthalpy and entropy favor the forward direction. There would appear to be
no energetic term favoring the reverse direction. Thus, this type of
process would be expected to go to completion (i.e. no equilibrium
condition because no reverse reaction occurs). Type 2) is the same
situation, but viewed from the opposite direction.
- For type 3) above, enthalpy favors
the forward direction but the energy associated with the entropic change
favors the reverse direction. There are, therefore, energetic forces
driving the process in opposite directions, and it would seem likely that
an equilibrium condition might exist. Type 4) is the same
situation, but viewed from the opposite direction.
Consider
our old friend, the Haber reaction:
- If we start with nothing but
NH3(g) in the sample, the reaction will proceed in the
reverse direction to produce H2(g) and N2(g)
(i.e. DG for the
reaction will be a positive value)
N2(g) + 3H2(g)
¬ 2NH3(g)
Or, DG
is negative for the following reaction (i.e. the following reaction is
spontaneous):
2NH3(g) ® N2(g) + 3H2(g)
- If we start with nothing but
H2(g) and N2(g) in the sample, the reaction
will proceed in the forward direction to produce NH3(g)
(i.e. DG for the
reaction will be a negative value)
N2(g) + 3H2(g)
® 2NH3(g)
- If we start with
concentrations of all components such that Q = Kc,
then the reaction is at equilibrium and DG
= 0.
The reaction wants to be
driven in a direction such that DG goes to 0 (i.e. equilibrium)
At equilibrium the Gibbs
energy of the system is at a minimum. To produce either more product,
or more reactants, requires an increase in Gibbs energy (i.e. some modification
of heat or entropy properties)
Standard
Gibbs Energy Changes
The
Gibbs energy term, G, is a state function, thus values can be
defined for substances at specific conditions of temperature and pressure known
as the standard state. In this case, we will have DG values associated with the formation of compounds from
their elemental constituents, known as the standard Gibbs energy of
formation, DGf0.
Standard
conditions include:
- 1 atm
pressure
- 1M concentration (solutions)
- Pure solid (if a solid) or
pure liquid (if a liquid)
- For elements, the standard
Gibbs energy of formation, DGf0 of an
element in its normal state is 0
- There is no standard state
for temperature. G will vary with temperature. 298K (i.e. 25°C) is a
common temperature chosen for standard reference values of G
Standard
Gibbs energy values can be used to calculate the standard Gibbs energy change
associated with a reaction:
DG0
= S n DGf0(products) - S m DGf0(reactants)
What
information will the calculation of DG0
provide?
- DG0
< 0, the reaction is spontaneous as written (i.e. goes to the
right)
- DG0
> 0, the reaction will proceed to the left as written
- DG0
= 0, the reaction is at equilibrium
Calculate DG0
for the Haber reaction will all components at standard conditions at 298K
H2(g) :
DGf0(298K)
= 0 (note: normal state of element)
N2(g): DGf0(298K)
= 0 (same note)
NH3(g): -16.66 kJ/mol
N2(g) +
3H2(g) ó
2NH3(g)
DG0 = S n DGf0(products)
- S m DGf0(reactants)
DG0 = 2*(-16.66 kJ/mol) - (0 + (3*0))
DG0 = -33.3 kJ/mol
- DG0
is a negative value, which says that if each component were present at 1 atm (standard conditions for gas) at 298K, the
reaction would proceed spontaneously to the right to produce more
product (but we know nothing of the rate)
2002 Dr. Michael Blaber