Free Energy, Enthalpy & Entropy
By Curtis Bustos
Equation and key terms:
∆G
= ∆H – T∆S used to determine
whether a chemical-reaction process is spontaneous or not.
Gibbs
free energy (G) = an amount of free energy that is capable of doing work during a
chemical reaction at a constant temperature and pressure.
∆G = change in free energy
(J/mol)
Enthalpy (H) = the heat content of the
reacting system.
∆H = change in enthalpy (heat in
J/mol)
T = temperature in Kelvin (˚C + 273 = Kelvin (K)).
Temperature affects ∆S.
Entropy (S) = a quantitative expression for
the randomness or disorder of a system.
∆S = change in entropy (disorder
or randomness in J/mol)
∆G standard (ΔG°) = the standard free energy change is simply an alternative mathematical calculation used to express its equilibrium constant. ΔG° = -RT ln Keq.
∆G standard (ΔG°) = the standard free energy change is simply an alternative mathematical calculation used to express its equilibrium constant. ΔG° = -RT ln Keq.
Spontaneous = favorable (-∆G)
reaction.
Non-spontaneous = non-favorable (+∆G)
reaction.
Exergonic = -∆G
Endergonic = +∆G
Favorable = ê∆H and é∆S. If ∆H is low
and ∆S is high, then ∆G will be negative or favorable.
Non-favorable = é∆H and ê∆S. If ∆H is high
and ∆S is low, then ∆G will be positive or non-favorable.
Equilibrium = when ∆G = 0. At this point, the rate of the forward reaction equals the rate the the reverse reaction. This is aka
DEATH from a biological perspective.
Reactants = the starting substances of
a chemical reaction.
Products = the substances produced in
a chemical reaction.
Activation Energy (Ea) = the free energy of the highest
transition-state (if more than one) relative to the free energy of the
reactants in a chemical-reaction.
Transition State (TS) = the point of highest free
energy (there may be more than one TS) for a chemical-reaction. Represented by ∆G double-dagger.
SN1 (unimolecular) = rate of reaction depends on one species (substrate). A stepwise
reaction.
SN2 (bimolecular) = rate of reaction depends on two species (substrate &
nucleophile). A concerted reaction.
Rate Determining Step (RDS)
= the transition state of highest free-energy.
Intermediate = a state at which a chemical process undergoes a specific
molecular-conformation in order to reach an end product.
Note - thermodynamics DOES NOT provide a reaction-rate or the speed at which a chemical reaction takes place. Kinetics will provide this information.
Laws of thermodynamics:
First law (biochemist’s version) – in any
physical or chemical change, the total amount of energy in the universe remains
constant, although the form of energy may change.
Second law (biochemist’s version) – in all
natural processes, the entropy of the universe increases (this definition has
several versions). Spontaneous processes are characterized
by the conversion from order to disorder (entropy). From the
illustration below, you can see a spontaneous process and how entropy (disorder or
randomness) will naturally increase with time. Notice how molecules naturally move from a high concentration to a low concentration and achieve a higher level of disorder:
From this, we can also see that chemical reactions tend
toward disorder and equilibrium.
Example of an entropically favorable reaction in the gas phase:
Example of an entropically favorable reaction in the gas phase:
2NH3 à
N2 + 3H2
We can see from the reaction above that we start with one molecule (2NH3) and end with two molecules (N2 + 3H2). Whenever we go from 1 molecule to 2 molecules or more, a higher level of disorder is achieved and is thus entropically favorable. Entropy is therefore a function of concentration!
Furthermore, when describing thermodynamics, words such as system
and surroundings
are used a lot. To avoid confusion, let’s start by defining a system and its surroundings.
A system
can be defined as a specific part of the universe that is of interest. Surroundings can be defined as the universe or
environment that holds or contains these systems of interest. For example, atmospheric pressure of the earth
surrounds different systems of molecules and has an affect on their boiling
points (contingent upon different levels of elevation). The boiling point of a
molecule represents a specific system while the atmospheric pressure represents
the surroundings.
When a system changes, such as by a molecular conformational
change, some of its energy (G) may be used to carry out this chemical process.
Where does this energy come from? It comes from enthalpy, temperature
and entropy
as described below:
Gibbs free energy (G):
G = H – TS or free energy equals enthalpy (heat) minus the
multiplication of temperature (in Kelvin) by entropy (disorder). Change (∆ = change) in G can also be
represented as ∆G. ∆G can be calculated by ∆G = ∆H – T∆S (fundamental equation for all of chemistry).
Thermodynamics is a useful concept that helps determine if a
reaction is spontaneous or non-spontaneous. For example, a change in free energy (G) can
be represented as ∆G. ∆G can tell us whether a reaction is spontaneous or not
by simply referring to + or -∆G. -∆G = spontaneous (a
process that is driven by the output of free energy) and +∆G = non-spontaneous (a process that is driven by the input
of free energy).
∆G = ∆H – T∆S
|
Enthalpy (∆H)
|
Entropy (∆S)
|
Spontaneous (-∆G)
|
ê -
favorable contribution
|
é+
favorable contribution
|
Non-spontaneous (+∆G)
|
é+
unfavorable contribution
|
ê -
unfavorable contribution
|
Contingent upon relative magnitudes of ∆H, ∆S and
temperature. Note – reaction is spontaneous when T
< ∆H/∆S
|
é+
unfavorable contribution
|
é+
favorable contribution
|
Contingent upon relative magnitudes of ∆H, ∆S and
temperature. Note – reaction is spontaneous when T
> ∆H/∆S
|
ê -
favorable contribution
|
ê -
unfavorable contribution
|
By the way, there is a relationship between ∆G standard (ΔG°)
and the equilibrium constant (ΔG° = -RT ln Keq).
and the equilibrium constant (ΔG° = -RT ln Keq).
For example,
When molar concentrations are
greater in the products than they are in the reactants, products will be
favored. A+B ⥂ C+D. These double-arrows imply products are favored at
equilibrium.
When molar concentrations are
greater in the reactants than they are in the products, reactants will be
favored. A+B ⥃ C+D. These double-arrows imply reactants are favored at equilibrium.
Quantitatively:
K ≈ 1 neither
products nor reactants in a chemical process are favored at equilibrium.
K >> 1 the products are favored in a chemical process at
equilibrium. The molar concentration of products (numerator) outweigh the molar
concentration of reactants (denominator).
K << 1 the reactants are favored in a chemical process at
equilibrium. The molar concentration of reactants (denominator) outweigh the
molar concentration of products (numerator).
We now can apply Keq to our equation ΔG° = -RT ln Keq. After a few calculations, it should become apparent that ΔG° is affected by the
concentrations of both the reactants and products of a chemical-reaction.
Keq or K
(units are canceled out)
|
ΔG° (kJ/mol)
|
Products or Reactants are favored at equilibrium
|
10-3
|
17.1
|
Reactants
|
10-2
|
11.4
|
Reactants
|
10-1
|
5.7
|
Reactants
|
1
|
0.0
|
Neutral
|
101
|
-5.7
|
Products
|
102
|
-11.4
|
Products
|
103
|
-17.1
|
Products
|
What does it mean when ΔG or ΔG° = 0?
When ΔG = 0 in a chemical reaction, the net-change in free energy is zero. Therefore, there is no spontaneity as a net result. A graphical representation may help:
The graphical representation above shows I
as a forward reaction (A à
B+C exergonic) and II as a reverse reaction (B+C
à A endergonic). If the forward reaction has a ΔG = -50kJ/mol (spontaneous) and the reverse reaction has a ΔG = +50kJ/mol (non-spontaneous), then
-50kJ/mol and +50kJ/mol will cancel out and result in a net ΔG = 0… this is called equilibrium from a thermodynamic standpoint. Additionally, the ratio of molar
concentrations of products to reactants
and the rate of forward and reverse reactions will remain unchanged over time.
Note - equilibrium does not suggest that molar concentrations of products and reactants are equal to each other (unless K = 1)!
and the rate of forward and reverse reactions will remain unchanged over time.
Note - equilibrium does not suggest that molar concentrations of products and reactants are equal to each other (unless K = 1)!
Moreover, -∆G = spontaneous. Products
will be favored at equilibrium. Whereas +∆G =
non-spontaneous. Reactants will be favored at equilibrium. This makes
sense because chemical reactions are inclined to move toward a lower
energy-state for stability. Products on the -∆G
graph and reactants on the +∆G graph are both
in lower energy-states than their reverse reactions:
Connecting the dots:
a.
First law of thermodynamics states that in any
physical or chemical change, the total amount of energy in the universe remains
constant, although the form of the energy may change.
b.
Second law of thermodynamics states that in all
natural processes, the entropy of the universe increases.
c.
Spontaneous processes are characterized by the
conversion from order to disorder (entropy).
d. Thermodynamic equilibrium is established when ∆G = O (net ∆G from
spontaneous to non-spontaneous).
e.
Equilibrium = death from a biological
perspective.
Is it possible for a living organism to cheat death?
To cheat death would be to cheat spontaneity and entropy. Perhaps the key to
longevity is manipulation of entropy?
Gibbs free-energy diagram explained:
1 = reactants
2 = 1st transition state. This is an extremely
unstable conformation. The bonds are transitioning in a phase where they are
not completely broken nor are they completely formed. Major growing pains! The
1st transition state is also the highest-in-energy transition-state;
therefore, the rate-determining step can be viewed in comparison to the 1st
transition state. The rate of the overall reaction is equal to the rate of the
highest transition state hence the rate determining step).
3 = intermediate. A molecular-conformation is produced between 2 & 4 as part of
a chemical conversion. Reactions with intermediates are considered to be
multistep.
4 = 2nd
transition state. Lowest transition-state; This transition state cannot be the rate-determining
step because the 1st transition state is higher in free energy.
5 =
products
Activation energy or energy barrier is the energy required for
the reactants at 1 to reach the highest transition state (if more than one) at
2. ∆Gdouble-dagger
∆G
can be measured by the free energy difference from 1 to 5 (spontaneous) or 5 to 1 (non-spontaneous). An
additional diagram with one transition-state may prove to be helpful:
In
the spontaneous
reaction, the
products are lower in energy than the reactants; this will result with a -∆G.
In
the non-spontaneous
reaction, the
products are higher in energy than the reactants; this will result with a +∆G.
Relative
stability can also be seen on a Gibbs free energy diagram:
1 is relatively more stable than 2,3,4.
2 is MOST UNSTABLE.
3 is relatively more stable than 2,4.
4 is relatively more stable than 2
5 is relatively more stable than 1,2,3,4 (MOST STABLE).
