Standard State Free Energy Change

• Under "standard state" conditions, all reactants and products have an initial concentration of 1 mol/L (1.0M)
• For any reaction setup using standard state concentrations, the reaction quotient Q = 1.0

A + B ó C + D

Q = [C][D] / [A][B] = 1 * 1 / 1 * 1 = 1.0

• The free energy change for such a reaction as it goes to equilibrium is
DG⁰
• The free energy change for a reaction under non-standard conditions (i.e. starting concentrations of products and reactants are not all equal to 1.0M) can be derived in relationship to the standard state free energy change (
DG⁰) for the same process (i.e. starting concentrations of products and reactants are all 1.0M)

DG = DG⁰ + R*T*lnQ

How does this equation work?

• In a general qualitative sense, this equation tells you whether a reaction will be spontaneous or not, and the the effect of the starting concentrations. For example, if Q is large it means two things: 1) we are starting the reaction with a large concentration of products and a small concentration of reactants, and 2) the value of lnQ will be positive if Q is >1, and so the value of R*T*Q will be positive if Q is big (i.e. >1). Both of these facts are leading to the same conclusion. If we start the reaction with a lot of product and not much reactant then we don't expect the reaction to proceed in the forward direction (i.e. it will not be spontaneous as written). Furthermore, we expect that R*T*lnQ will contribute a positive value to
DG, but DG should be negative for a spontaneous process. The only way that R*T*lnQ can contribute a negative value to DG is if Q<1. In other words, if we start the reaction with an excess of reactants and a dearth (a very groovy word) of products. This should drive the reaction to the right, i.e. spontaneous as written.
• Consider the following: If your initial conditions have all reactants and products present at 1M concentration (i.e. under standard state conditions) the value for Q will be 1.0, and the equation reduces to
DG = DG⁰ (which is correct, the free energy change is equal to DG⁰ when all reactants and products are at 1.0M)
• Consider what happens if you start with concentrations for reactants and products that happen to be an equilibrium condition. At equilibrium the value of
DG = 0, and the above equation will reduce to 0 = DG⁰ + R*T*lnKeq, or:

DG⁰ = -R*T*lnKeq

• The free energy change when a system starts with 1.0M of reactants and products, and then goes to equilibrium is equal to -R*T*lnKeq.

If you know the value of DG⁰ (i.e. the free energy change as the process starts with 1M everything and goes to equilibrium) you can figure out what the equilibrium constant must be, and vice versa.

Physical Significance of Thermodynamic Properties

• Physical processes are best understood when the enthalpy change, entropy change and free energy change are all understood
• As mentioned above, processes that are spontaneous overall (i.e. a negative value for the free energy change) may be enthalpy and/or entropy driven.

Case #1: the transfer of hydrocarbon from a hydrophobic environment to an aqueous environment

Toluene(pure) ó Toluene(aq)

With regard to the enthalpy change for the process:

• We must
input energy to disrupt water-water H-bonds to make a "hole" for the toluene solute. These are strong interactions and a relatively large amount of energy will probably be needed.
• We also have to
input energy to disrupt the van der Waals interactions that keep toluene molecules together. However, these are weak interactions so not much energy will be required
• We will get a
release of energy due to the interactions between solvent and solute (i.e. when we put a separated toluene molecule into a hole we made in the water). However, these are weak interactions since the toluene solute can only participate in van der Waals interactions with the water, so only a small amount of energy will be released due to this interaction

The sum of these energy-related processes suggests that DH° will be positive for the process (i.e. require input of energy, and is not energetically favorable)

With regard to the entropy change for the process:

• Having two liquids separated in a container is a more ordered state than if they are mixed up, so "dissolving" the toluene in water should
increase the entropy
• However, due to the hydrophobic effect, the hydration shell of water molecules will be highly ordered around the toluene solute, this will
decrease the entropy (i.e. increase the order of the water solvent)

Effects on DG°:

DG° = DH° - T*DS°

DH° positive

DS° negative, therefore - T*DS° is positive

DG° will be positive and the process as written is unfavored (will go in reverse direction)

Possible temperature effects:

• The entropic contribution to
DG° is temperature-dependent (-T*DS⁰). It is an unfavorable contribution, and therefore, can be minimized by reducing the temperature (DH° is typically constant over a wide temperature range)

Effect on heat capacity

• Heat capacity measures the amount of internal energy taken up by the molecules of a system as the temperature rises
• The toluene dissolved in water results in a system with a higher heat capacity than when the water and toluene are separated
• There appears to be something about the structure of water in the hydration shell (i.e. the clathrate cage) around the non-polar toluene molecules that results in a higher heat capacity.
• The ordered water molecules in the clathrate cage have a low entropy, but, interactions are somewhat weak and can be disrupted with higher temperature. One equation we saw for heat capacity related the way that the entropy changes with changing temperature. If the ordered clathrate waters are easily disrupted at higher temperature, it means that a large amount of energy can be soaked up with this temperature change, and therefore, the heat capacity is high.

The Importance of Coupled Processes on Living Organisms

Many reactions required for living systems have an unfavorable DG (i.e. positive DG)

• They can be "forced" to proceed if they are coupled with a reaction with an overwhelmingly favorable
DG (i.e. negative DG)

Phosphoenol pyruvate + H₂O ó Pyruvate + Phosphate DG = -78 kJ/mol

ADP + Phosphate ó ATP + H₂O DG = +55 kJ/mol

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Phosphoenol pyruvate + ADP ó Pyruvate + ATP DG = -23 kJ/mol

For more information on the production of energy in the sun, and formation of elements in the sun, see: Nucleosynthesis

• Oxidative, exothermic reactions in chemotrophs exploit the energy stored in complex molecules made by phototrophs, and these energy-releasing spontaneous reactions are coupled to drive energy demanding biosynthetic reactions via reduced coenzymes and high-energy phosphate molecules

Two general properties of such high-energy molecules

1. They are not intended as a means to store energy long-term, but only as a means to transfer energy to drive coupled reactions
2. They are not necessarily "unstable" molecules. The key point is that the energy required to break a high energy bond is less than the energy released when a new, lower-energy bond is formed (and such coupled reactions occur with a net release of energy and therefore represent an process with a -
DG )

Note: DG°' ("prime" symbol indicates standard state pH 7.0) >= -25kJ/mol released during hydrolysis (i.e. splitting) of high-energy phosphate bonds

 ADP/ATP is a very versatile molecule due to its intermediate phosphorylation energy bond(s)

• It can be phosphorylated by some of the higher energy phosphate molecules (which are synthesized in the breakdown of fuel molecules) i.e. it can be loaded up with energy.
• It can subsequently phosphorylate some of the lower energy acceptor molecules that are involved in metabolic reactions. i.e. it can release energy.

"High" or "low" energy phosphate bonds are qualitative descriptions. It is important to be able to quantitatively describe the energy available in such molecular bonds. "Group transfer potential" provides a reference frame to quantitate such energy, using a coupled hydrolysis reaction. This is similar to the way redox reactions are described - something can only be reduced if simultaneously something else is oxidized. Thus, a high energy phosphate bond is broken in a hydrolysis reaction with water.

ATP + H₂O ó ADP + Pi

And

DG⁰ = -RT * ln(K_eq)

K_eq = [ADP] [Pi] / [ATP] [H₂O]

• The
DG⁰' values for the hydrolysis of the various Pi compounds in the above table are the group transfer potentials in water

As you might have guessed by analyzing the above table, there is something energetically important about the linkage between two phosphate groups, as in ATP, ADP, and pyrophosphate. This type of linkage is known as a phosphoric acid anhydride linkage. ATP has two of them, and ADP and pyrophosphate have one each. The key point is that energy is released upon hydrolysis. What are the contributing factors for this?

1. Destabilization of phosphoric acid anhydride bond due to electrostatic repulsion. Each phosphate group in a phosphoric anhydride carries a negative charge. This charge will vary will the pH (pK values for pyrophosphate are 0.8, 2.0, 6.7 and 9.4) and derivatization by functional groups, but at neutral pH values each phosphate will have at least a full negative charge. These adjacent negative charges repel each other (electrostatic repulsion). This repulsion is avoided by hydrolysis, which allows bond breakage and separation of phosphate groups
2. Entropic considerations at neutral pH. The net reaction for the hydrolysis of ATP to ADP was given as:

ATP + H₂O ó ADP + Pi

The highest energy phosphate molecule in the table above is phosphoenol pyruvate (PEP). However, this molecule has only a single phosphate group, and if one compares it to the hydrolysis of AMP, one might expect a much lower release of energy. Why is PEP so energetic?

• Hydrolysis of PEP produces an unstable enol form of pyruvate (releases -29 kJ/mol energy)
• This rapidly tautomerizes to the stable keto form (releases another -34 kJ/mol energy)
• The energy released upon hydrolysis of PEP is the sum of these two contributions

Complex Equilibria Involved in ATP Hydrolysis

• The pK values of phosphate and pyrophosphate are near physiological pH values, and therefore, the ionization state (and therefore energy released upon hydrolysis) can vary. Thus, the associated energy released upon hydrolysis can therefore vary (due to electrostatic repulsion, entropy and resonance stabilization considerations)
• Phosphate ions and phosphate groups in ATP, etc. can bind divalent and monovalent metals. This interaction can reduce electrostatic repulsion between adjacent phosphate groups in ATP, ADP and pyrophosphate, thereby affecting energy released upon hydrolysis

The more basic the solution, the more deprotonated phosphate containing molecules will be.

• The more deprotonated, the greater the electrostatic repulsion between adjacent phosphate anhydrides
• The greater the electrostatic repulsion, the more energy released upon hydrolysis

The higher the concentration of divalent metals (e.g. Mg²⁺) in solution, the lower the energy released upon hydrolysis of ATP, ADP, pyrophosphate, etc.

• Physiological concentration of Mg²⁺ is on the order of 5mM. At this concentration the hydrolysis of ATP yields -30.5 kJ/mol (it is -35.7 kJ/mol in the absence of metal ion)

Calculations above for the energy released upon hydrolysis of ATP are for standard conditions (i.e. 1M all components)

• Actual
DG for the hydrolysis is given by the typical DG equation in relationship to the standard condition DG⁰

DG = DG⁰ + RT ln [ADP][Pi]/[ATP]

• Energy released will be greater with a negative value for {
RT ln [ADP][Pi]/[ATP]}. This will happen when the concentration of ATP is high and that of ADP and Pi are low.

About 65kg(!) of ATP are consumed daily. This is achieved by a much smaller pool of ATP molecules (~50 g) that are recycled.

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