Download 4-Physical Chemistry of SW-Equilibrium-ion

Equilibrium chemistry of
seawater
Governs:
o
o
o
o
o
o
o
Mineral dissolution & precipitation reactions
Metal complexation and reactivity
Redox chemistry
pH and buffering
Adsorption/desorption
Kinetics (rates of reactions)
Gas exchange at sea surface
and more…
It all depends on thermodynamics
Chemical Equilibrium in Aqueous Systems
Most chemical reactions are reversible.
Forward
aA + bB
<=>
cC + dD
Small letters indicate
stoichiometric
coefficients. Large
letters represent
individual chemical
species
Reverse
At equilibrium, the rate of forward reaction (product
formation) is equal to the rate of the reverse reaction
(reactant formation), and the concentrations of all species
is constant with time.
This is not a static condition - rather it is a dynamic equilibrium
- forward and reverse reaction rates balance.
The relative concentrations of products
[C ]c [ D]d
and reactants at equilibrium is given by
K eq 
a
b
[
A
]
[
B
]
the equilibrium constant, Keq:
The value of Keq is fundamentally tied to the thermodynamic stability of
the system – it predicts the most stable allocation of product and reactant
concentrations in a system.
For the chemical reaction
aA + bB <==> cC + dD
The Gibbs free energy change (G) is given by:
Reaction quotient
products
reactants
G = Go + RT ln [(C)c(D)d]/(A)a(B)b]
Where Go is the standard free energy change, R is the gas
constant and T is temperature in Kelvins
At equilibrium, ΔG = 0 and
[(C)c(D)d]/(A)a(B)b] = Keq
0= Go + RT ln Keq
Go = - RT ln Keq
Also
Go = Gfoproducts – Gforeactants
Where Gfo is the
standard free energy
of formation
Chemical Reaction Rates and Chemical Equilibrium
The rate of a chemical reaction, say conversion of A  B
can be written as: d [ A]  k[ A]
dt
which is a first order differential equation.
The k is the first order rate constant and [A] is the
concentration of chemical A.
In other words, the rate of the reaction depends directly on
the concentration of A with the proportionality constant k,
which is the fraction of A reacted per unit time.
Equilibrium constant concept
For reaction: A B at equilibrium
A
A
A
K1 = fraction of A
converted per unit time
B
A
A
B
B
B B
B
A
B
B
B
B
B
A
B
A
A
K2 = fraction of B
converted per unit time
A
B
B
B
B
B
B
B
B
B
BB
B
B
B B
B
A
B
B
B
BB
B
B
B
B
B
B B
B B
BB
B B
B
B
B
B B
B
B
Rate of formation of B = K1 [A]
Rate of formation of A = K2 [B]
At equilibrium the rate in both directions is the same, therefore
K1 [A] = K2 [B], which can be rearranged to: K1/K2 = [B]/[A]. Thus,
the relative amount of product to reactant (B/A) depends upon the ratio
of the forward rate constant to the reverse rate constant. This ratio
(K1/K2) is the equilibrium constant (Keq). The value of Keq predicts
the concentration of the products relative to the reactants.
Equilibrium chemistry depends on the
“effective concentrations” of chemicals
Equilibrium expression for dissolution of a mineral Calcite:
CaCO3 (s) = 1Ca2+ + 1CO32Stoichiometric
coefficients
Keq =
{Ca2+}1 {CO32-}1
{CaCO3 (s)}1
For dissolution of a
mineral, the Keq has
the special name of
Solubility Product
(Ksp)
=
Products
= 3.35 x 10-9
Reactants
The braces { } represent
chemical activities – not total
analytical concentrations
In an almost infinitely dilute solution, say just a few
molecules of Ca2+ and CaCO32- in a liter of pure H2O,
the ions will behave in a nearly ideal manner. That
is, their effective concentrations (activities) will be
equal to their absolute molal concentration.
However, as total solute concentrations increase, the
solution deviates further from ideality, and the
“effective concentration” of solutes is no longer equal
to the absolute molal concentration
(This is because the increasingly crowded ions affect the
solvent, which in turn effects how the ions react)
This is an example of a non-specific interaction
Solvent – ion interactions
Solvent structure
The ion in solution affects
the solvent (water), and this
alters the “effective”
concentration of the ion
Electrostriction
The effective concentration of a solute is called its
activity (ai) and this is not necessarily equal to its molal
concentration (it is usually lower).
The activity of an ion (ai) is equal to its molality (mi)
times an activity coefficient (i), which is the fraction
of the ion that is available to react at any given time
ai =  i * m i
Thus an equilibrium constant should be expressed in
terms of its activities (the effective concentrations):
Keq = {Ca2+}1 {CO32-}1 / {CaCO3}1
or
Keq = (Ca2+ mCa2+)1 (CO32- mCO3-2)1 / (CaCO3 mCaCO3)1
The { } denotes activities, whereas [ ] denotes absolute concentration
Activity coefficients are dependent on T & P, and thus, the conditions of the reaction.
As ionic strength, I, (defined below) increases, the
activity coefficient of an ion deviates from 1.
It usually decreases but the decrease is not always so
dramatic as pictured here - and it sometimes actually
increases! It depends entirely1 on the characteristics of the
solutes and solvent.
1
activity
coefficient
Ac
0
Ionic St rengt h -->
Ionic strength
1
2
I   mi zi
2
where mi is the molal concentration of an ion and zi is the
charge on that ion.
Ionic strength is one half the summation of each ion
concentration times the square of its charge.
A solution of 10-3 molal Na2SO4 dissociates as follows:
Na2SO4 <=> 2Na+ + SO42-
Thus, it has an ionic strength of:
I = 0.5 [( .001 x 2) (1)2 + (.001 x -22)] = .003
= 3 x 10-3
Seawater has an ionic strength of ~0.7
(You should
be able to work this out from major ion concentrations).
At this ionic strength, simple theoretical calculations
of activity coefficients (i.e. the Debye-Huckel
equation) cannot be used.
Seawater is very far from being an ideal solution and this
needs to be taken into account in some circumstances
To predict the solubilities of solids, liquids and gases
in seawater requires knowledge of the activity and
activity coefficients of these solutes in seawater.
Activity coefficients for major species are tabulated.
Ion Pairing – a specific interaction
Single ions with their hydration sphere are termed
free ions - also known as “aquo” ions.
When hydration is relatively weak, the ions can
interact - their primary solvation shells can be
shared momentarily. This is called ion pairing.
Many ions in seawater are significantly paired.
e.g.
Mg2+ + SO42-  MgSO4o
Ion-pairing can occur among groups to form higher order associations ternary, quaternary
etc. i.e. Na+K+SO42- but the concentrations of these associations is low because of the low
probability of collision of all three components.
Ion – ion
interactions
More specific
Ion pair
Less specific
The fraction
The fraction
available to
that is not ionreact based on paired i.e. free.
solvent effects
only (nonspecific effect)
The effective
concentration
as a fraction
of the total
Garrels and Thompson (1962) were the first to surmise the
existence of ion pairs in seawater and they calculated the ion
speciation for major ionic species in seawater.
Major Cation speciation
Major Anion speciation
Major Cations and chloride are mostly free ions, but other
major anions are highly paired in seawater
Non-specific vs. specific interactions in solutions a continuum.
Non-specific
effects
Ion-solvent
interactions affect
activity coefficients
of chemical species
Specific effects
Weak
Ion
Pairing
Strong
Ligand
binding
Coordination
complexes
A stronger specific interaction is when electrons are
shared, held together more strongly than in ion-pairing, (but
not enough for an ionic bond). These can be termed ligand
complexes.
An even stronger specific interaction is called a
coordination complex which has fixed geometry. Most
coordination complexes involve metal cations (Me+) and
multiple ligands (L). Ligands need not be anions. Dipoles
can function as ligands (H2O actually functions as a ligand,
albeit a weak one).
Specific interactions form a continuum from weak ion pairing
to strong coordination complexes. When complexation occurs
on a solid surface or colloid surface the term adsorption or ionexchange is used. Many trace metals are complexed by
surface ligands.
Non-specific vs. specific interactions in solutions a continuum.
Non-specific
effects
Ion-solvent
interactions affect
activity coefficients
of chemical species
Specific effects
Weak
Ion
Pairing
Strong
Ligand
binding
Coordination
complexes
Metals and complexation
We can write an equilibrium constant for the following
equation describing the association of a metal (Me)
with a ligand (L):
aMe+ + bL- <=> MeaLb
{Mea Lb }
K stab 
 a
 b
{Me } {L }
This form of Keq is termed a stability constant - Kstab
A large Stability constant indicates that the
complex is favored over the dissolved ions.
10x molar
X=
Much
higher in
seawater
Metals are extensively complexed by ligands in
seawater - this affects their bioavailability!
Major anionic ligand species include Cl-, SO42-,
HCO3-, CO32- and OH-. These ligands form weak
complexes, but are present at high concentrations.
H2O also can be considered a ligand as hydration of
ions attests.
See Comans and van Dijk (1988) for info on Cd2+ complexation
Chemical species of metals in seawater using iron (Fe) as an example
Operationally
filterable
Dissolved
Colloidal
Particulate
The speciation of
iron is extremely
important in the
biological context
– some forms of Fe
are available to algae
and some are not!
Growth of Raphidophyceae (red tide
microalgae) as measured by change
in fluorescence.
These bioassays were conducted
under conditions of iron limitation
and emendation with
four insoluble iron species [FeO(OH),
Fe2O3, FeS, and FePO4.4H2O],
soluble inorganic iron
(FeCl3.6H2O), and an artificial
organic ion species (Fe-EDTA).
Source: From Naito et al. 2005. Harmful Algae 4,
1021–1032.
In seawater, Ligands affect the chemistry of trace
metals much more than the trace metals affect the
chemistry of the ligands. In most cases [Ligands]
>>>>> [metals]. Exceptions may be the highly specific Zn, Fe and
Cu binding ligands present in ocean water.
Since metals are the limiting reactant, the effects of
metal-metal competition for the ligands is minor and
can be neglected. Thus, speciation calculations can
be done independently as a function of ligand
competition for the metal ion.
Simple case – free metal plus one ligand in solution
The metal can exist in only two forms, free and complexed with the ligand.
The mass balance for the metal is therefore:
[Mtotal] = [Mfree] + [ML]
Kstab = [ML]/[Mfree][L]
Use the equation for Kstab to express [ML] in terms of Mfree
[Mtotal] = [Mfree] + Kstab[Mfree][L]
[Mtotal] = [Mfree] (1+ Kstab[L]
Factor out Mfree on the right side
[Mfree] = [Mtotal]/(1+Kstab[L])
Rearrange to solve for Mfree
Use values for
ΣFe (1 nM) in
seawater and a
major ironspecific ligand
(L1 @ 4 nM)
Calculations
[Mtotal] =
1.00E-09
Molar
[L] =
4.00E-09
Molar
log Kstab =
[Mfree]
25
2.5E-26
0.0000000000000025%
Molar
free
The “strength” of a ligand for a metal is
gauged by its stability constant.
A large stability constant means that the
complex is very stable and
thermodynamically favorable.
But, All things are relative
Ligands compete with each other for metals
The ligand-metal complex with the greater Kstab tends to win the
competition:
If the Kstab of CdL1 is 1 x 102
and the Kstab of CdL2 is 1 x 106
Then L2 forms more stable complexes with Cd2+ than L1.
Thus, Cd is most likely to be found in association with L2. In
fact, if the L1 and L2 are present at equal concentrations, the
concentration ratio of the complexes (CdL2/CdL1) will be
106/102 = 104.
But!
What if L1 is present at a higher concentration than
L2?
How could the solution be modified to achieve
roughly equal distribution of Cd between the two
ligands (i.e. 50% of Cd as CdL1 and 50% as CdL2)?
Increasing the concentration of L1 by a
factor of 104 greater than L2 will result
in equal partitioning of Cd2+ between
L1 and L2 i.e. [ML1] = [ML2]
These calculations assume that only the two
complexes of Cd2+ are possible. In most aquatic
systems many ligand combinations are possible.
Some possible ligands for Cd2+ include Cl-, OH-,
CO32- and some organics like phytochelatins.
Solid phase adsorption
Ligand associations on
particle surfaces
Solid
particle
-O
Cd2+(aq)
(e.g. clay)
Cd2+
-O
-O
(charged surface
groups serve as
ligands for
complexation of
metals)
Dominated by
free Cd+ ion
Dominated by
CdCl+
complexes
Co-dominated
by CdCl+ &
CdCl2
complexes
From Commans & van Dijk, 1988
Cd adsorption onto
suspended particles in
freshwater (0 salinity)
Cd desorption at different
salinities
35.5 ppt
5.9 ppt
2 ppt
0 ppt
Solid lines represent Cd concentration of 1 µg L-1 and dashed lines represent 20 µg L-1
From Commans and van Dijk, 1988
Commans and van Dijk, 1988
0%0
2%0
5.9%0
35.5%0
Corrections for
activity of Cd2+ is
critical for
calculation of
adsorbed amount.
In addition to major ions, dissolved organic matter
(DOM) is an important ligand complexing agent for
metals in seawater.
Most of the ligand binding sites on DOM are occupied
by major ions such as Ca2+ and Mg2+ rather than trace
metals (e.g. Fe3+, Zn2+, Cd2+).
This complexation has little effect on the major ion’s
activities but affects the trace metals ability to
compete for a site. The trace metals may have a
higher affinity for a site (i.e. the trace metal complex is
more stable), but the major ions may be so much
more abundant that they out compete the trace metal.
Binding of metals in a 3-D coordination
complex is called chelation.
Examples of chelators include:
ETDA - Ethylenediamine tetra acetic acid - hexadentate ligand
- strong complexes with di- and trivalent metal ions.
NTA - Nitrilotriacetic acid - tridentate ligand for metals cations
Siderophores - Natural Fe3+ binding ligands - and example is
desferroximine (Desferal; DFOB)
Chlorophyll a - Mg2+ coordination complex
Enzymes and co-factors - many have coordinated metals.
Chelators
Ligand functional
groups
Desferoximine (DFOB)
– a Siderophore (Fe binding chelator)
Fe(III):DFOB Log Kstab = 30.5
EDTA (ethylene diamine tetraacetic acid)
Fe(III):EDTA Log Kstab = 25.1
Log K values for 0.1 M ionic strength and 25 oC
Phytochelatin (Cd2+, Cu2+ and Zn2+ binding chelator)
Siderophores of
biological origin.
Fascinating Fe-binding
ligands!
Some of the
aquachelins and
marinobactins have
conditional stability
constants for Fe3+ of
1024 to 1050!
The complex is greatly
favored over ionic
forms.
See work of Alison Butler for more on
natural marine siderophores
Mineral dissolution and precipitation
The solubility of a particular mineral is predicted by its solubility
product (Ksp), a type of equilibrium constant.
Consider:
CaCO3 (s) <=> Ca2+(aq) + CO32-(aq)
Ksp = {Ca2+} {CO32-}
{CaCO3}
Note that since CaCO3 is a solid, and the activity of solids (or water)
is taken as 1 then the Ksp simplifies to Ksp = {Ca2+} {CO32-}
For calcite, a form of CaCO3, Ksp = 10-8.35 @ 25oC and Ionic strength of 0 (a std
condition).
From the value of this Ksp (about 10-8) it is obvious that the concentrations of Ca2+ and CO32in equilibrium with the solid mineral will be relatively low since when multiplied they have to
equal 10-8.35 M. The Ksp for NaCl is much larger (10+1.5 ), indicating it is a more soluble
mineral.
For:
Ksp = {Ca2+} {CO32-} = 10-8.35
In a complex solution like seawater there are an infinite
number of combinations of the activities (effective
concentrations) for the two ions that can satisfy the
equation.
The right side of the equation is called the Ion Activity
product (IAP).
Consider again, CaCO3 <=> Ca2+ + CO32For a system not necessarily at equilibrium we can measure the
activities of the ions in solution, say Ca2+ and CO32- in the
example above, and calculate the ion product (IAP):
IAP = {Ca2+} {CO32-}
If the IAP is greater than Ksp, then solution is super saturated
and thermodynamics predicts that precipitation should occur
(the rate of the precipitation reaction will be faster than
dissolution reaction).
If the IAP is lower than Ksp, the solution is undersaturated and
more mineral salt should dissolve (dissolution faster than ppt),
until equilibrium is reached when both reaction rates are equal.
It helps to keep in mind the dynamic nature of chemical reactions. There is no static
condition – any steady state is a dynamic one.
From Libes – Web appendices (this is just a
small section from Table 14A)
Acids and bases
Acid: proton donor
Base: proton acceptor
protons exit in the hydrated form, H3O+ or hydronium ion, but
are often abbreviated to H+
Water is a weak acid which can dissociate to a proton and
hydroxyl ion:
H2O <=> H+ + OH-
K
a





{H } {O H }
{ H O}
2
Since the activity of liquid water is considered to be 1, it
drops out and the equilibrium equation becomes
Kw = {H+} {OH-} which has a value of 1 x 10-14 @25 oC
This equilibrium must be satisfied in all cases.
In pure water at 1 atm, 25 oC, the equilibrium activity of H+
is therefore:
{H+} = 1 x 10-7
and
{OH-} is also 1 x 10-7.
That is: {H+} {OH-} = (1 x 10-7) x (1 x 10-7) = 1 x 10-14
Define pH = -log {H+}
In pure water at 25 oC, the pH = -Log (10-7) = 7. Anything that
adds H+ to the solution will increase the concentration of H+, but
the equilibrium for water will be maintained and thus OH- will
decrease (and vice versa).
Thus, at pH = 4 the {H+} = 1 x 10-4 M and {OH-} = 1 x 10-10 M
such that the water equilibrium is still satisfied (10-4 x 10-10 =
10-14)
Acidic vs. Alkaline
pH 7 = neutral
pH > 7 alkaline
pH < 7 acidic
Remember that pH is a
log scale, and a single pH
unit represents a 10-fold
range of {H+} or {OH-}!
The “p” notation is also used with equilibrium
constants in the same fashion. pK = -log K
pH of natural waters
Ocean
Surface
8.0 - 8.2
Deep Sea
7.6 - 8.0
Pore waters
7.0 -8.0
Estuaries
6.5-8.0
Rivers & Lakes
Black water (organic rich)
3.0 - 6.0
Clear water
6.0 -7.0
Natural
5.0 -5.5
Polluted
2.0 - 4.0
Rain
Strong acids
“Completely” dissociated in water i.e. large Ka
Will not accept proton back even at very low pH
Example: HCl  H+ + Cl-
Ka = 108
Weak acids
“Incompletely” dissociated in water i.e., Smaller Ka
May accept proton back at low pH
Example: H2CO3  H+ + HCO3-
Ka = 10-3.6
Mono protic acids:
HCl, HNO3, HF etc. (yield only 1 H+ per mole)
Poly protic acids
H2SO4, H3PO4, H2CO3 (yield more than one H+)
pH dependence of
weak acid dissociation
FIG 5.19 in Libes
Equivalence points – where pH = pK
Consider dissociation of the weak acid:
H2CO3  H+ + HCO3Ka = {H+} {HCO3-}/{H2CO3}
Rearrange to isolate {H+}
Ka {H2CO3} / {HCO3-} = {H+}
Take “p” or negative Log of both sides
pKa {H2CO3} / {HCO3-} = pH
or
{H2CO3} / {HCO3-} = pH/ pKa
At pH = pKa, then {H2CO3} / {HCO3-} = 1
Thus, at pH =pKa, the {H2CO3} and {HCO3-} must be equal, hence
the equivalence point
Less
buffering
O-H+
O-
More
buffering
OH
Silica (SiO2) in
the tests of
diatoms
functions as a
pH buffer
-Si—Si—SiBuffering is critical for function
of carbonic anhydrase
Milligan &
Morel 2002
Time-series of mean
carbonic acid system
measurements within
selected depth layers at
Station ALOHA, 1988–2007
Surface pH
In thermocline
Below
thermocline
Dore J E et al. PNAS 2009;106:12235-12240
©2009 by National Academy of Sciences
Stop!
Apparent equilibrium constants Keq': Often used for
seawater systems
Uses total analytical concentration measured at
equilibrium, rather than activities. Empirical determination of
activity - good only for conditions specified.
*
K app
( CaCO3 )

K sp (CaCO )
3
 Ca  CO
2
2
 [Ca 2 ][CO3 ]
2
3
The Kapp depend on solution conditions.
Fortunately, in oceanic seawater, the major ion composition (which
makes the solution non-ideal) is relatively constant, so once
determined, the apparent activity values can be used reliably.
Weak acids have small Ka values and therefore are not
completely dissociated. They also have the ability to accept
H+, whereas strong acids will not accept protons in aqueous
solution.
For this reason, weak acids (their conjugate bases actually),
can act as buffers, absorbing H+ and minimizing effects on
pH.
Any reaction that involves H+ as a reactant or product,
will be affected by pH.
Complexing of ions in solution affects the total solubility of
a mineral compound.
The influence of ion pairing can be seen in the following example
involving dissolution of calcium carbonate (CaCO3). The amount
of ions in solution at equilibrium is given by the solubility product:
Ksp = {Ca2+}{CO32-} where { } denotes ion activities
the activity of carbonate ion is given by
aCO32- = CO32- * mCO32For carbonate ion in seawater the  is very small due to nonspecific effects at ionic strength of ~=0.7. Therefore, the total
concentration of carbonate (m) needed to satisfy the equilibrium
expression for Ksp is higher than it would be in pure water, where
the the activity coefficient () is close to 1. Thus, much more
CaCO3 will dissolve in seawater than in pure water.
Now for an equilibrium reaction in which A<=> B (something like
H2O(l) <=> H2O(g))
d [ A]
 k a [ A]
The rate of the forward reaction is
dt
whereas the rate of the reverse reaction is d [ B ]
dt
Note that the two rate constants are different.
 kb [ B ]
At equilibrium the forward and reverse reactions rates are equal:
ka[A] = kb[B].
Rearranging we can get:
k a [ B]

kb [ A]
Since both k’s in this case are constants, they can be lumped together to
form a new constant, we’ll call Keq:
[ B]
K eq 
[ A]
The equilibrium constant, then, is really a ratio of the forward
reaction rate constant to the reverse reaction rate constant and its
value predicts the concentration of the products relative to the
reactants.
Rate constants are inverse functions of the Activation energy
(Ea). In other words, a reaction with a large Ea will have a small k
(slow reaction rate constant). The relation between k and Ea is :
k  Ae
 Ea / RT
Arrhenius equation
Where A is and Ea are characteristic reaction constants, R is the gas
constant, and T is temperature in Kelvins. Therefore,
ln k = ln A - EA/RT (rearrange slightly to isolate T as 1/T)
ln k = ln A - EA/R (1/T)
A plot of ln k vs. 1/T yields a straight line with slope -EA/R and
intercept of ln A. Since R is constant, EA can be calculated
Activation energy (Ea) – The energy required to overcome electrostatic
inertial forces that either keep molecules together (as in the case of
complex) or apart (as in the case of two molecules trying to collide and
combine).
The Gibbs free energy per mole of reaction is the difference
between free energy of the products and reactants:
G = Gproducts - Greactants
If products have more free energy than reactants, then G
will be positive (and have a small Keq). Since all reactions
proceed to minimize free energy, this would be an
unfavorable reaction. Products must contain less free
energy for a reaction to proceed spontaneously. The
reaction would proceed in the reverse direction.
What governs whether the reactants will be favored
over products or whether the reaction will proceed as
written?
It depends on thermodynamics. (G= H + TS)
Where G is the Gibbs free energy, H is the enthalpy, T is
absolute temperature, and S is the Entropy
reactants
products
For a given chemical reaction: bB + cC <=> dD + eE
The change in free energy is:
G = Gproducts - Greactants
Absent inputs of external energy, all reactions proceed in the
direction that minimizes free energy - in other words, to
the most stable state. Thus, to proceed, the reaction must
lose free energy and G must be negative.
Every chemical has a standard free energy of formation Gfo
These are measured
under standard
conditions (1 atm
pressure, 25 oC, 1
Molar activities for
each species
Go = Gfoproducts – Gforeactants
For our example reaction
Go = (dGfoD + eGfoE) – (bGfoB + cGfoC)
Standard free energies of formation for
each chemical species times the # moles
of that species in the reaction
Consider the reaction:
CaCO3 (s) <=> Ca2+ + CO32-
How much CaCO3 will dissolve in an aqueous
solution?
The relative concentrations {activities} of products and reactants in
a chemical system at equilibrium is predicted by:
2
K sp (CALCITE )
{Ca 2 }{CO3 }

 3.35 *10 9
{CaCO3}
Many organisms deposit minerals.
Furthermore, dissolution/precipitation reactions are extremely
important with respect to the chemistry of many elements.
Knowledge of the equilibrium constant for a given reaction and
the concentrations of some of the reactants and products we
can predict whether the precipitation is thermodynamically
favored.
Organisms cannot work against thermodynamics !- only
external energy can drive seemingly unfavorable reactions - an
example would be photosynthesis which is the reduction of
CO2 to organic carbon driven by light energy.