The Principles of Free Energy

Module 101:

Molecular Biology and Biochemistry of the Cell

Lecture 6

Dale Sanders

27 January 2010

Aims of the lecture

By the end of this lecture you shouldunderstand…

• How Gibbs Free Energy can be used to determinethe direction of a reaction

• The meaning and significance of the “mass actionratio”

• The meaning of the term “equilibrium constant”

• How Redox Potentials are used to determine thedirection of redox reactions

• How Gibbs Free Energy is related to RedoxPotential

Reading

Any of the big Biochemistry textbooks

More detailed discussion in

Nicholls, DG & Ferguson, SJ (2002)Bioenergetics 3, Chapter 3, AcademicPress

Why study energetics in Biology?

Growth & maintenance of order (homeostasis)depend on energy as well as more obviousfunctions:-

– Generation of heat;

– Movement;

– Transmission of information.

• Energetics underpins the existence of life

What energetics (thermodynamics) tells us:-

“the limits of the possible”.

What thermodynamics cannot tell us:-

1. Whether a given reaction actually occurs.

2. How a reaction occurs (mechanism).

3. Rate at which a reaction occurs.

Predicting the Spontaneity of Reactions:Gibbs Free Energy

The 2nd Law of Thermodynamics (Clausius, 1850):For all changes in a system, the total entropy of thesystem and its surroundings will increase.

SSys + SSurr > 0 (1)

This is the criterion for reaction spontaneity

J W Gibbs (late 19th Century) combined 1st and 2nd Lawsto express spontaneity of reactions in terms of

measurable system parameters.

G = H – TS (2)

H: change in enthalpy (heat content)

T: absolute temp.

G: change in (Gibbs) Free Energy. Units: J/mol

: a measure of the useful work system can perform

: must be – ve for spontaneous reaction

If G is –ve; reaction exergonic; i.e. thermodynamicallydownhill.

If G is +ve, reaction endergonic; proceeds in reversedirection.

If G is 0: equilibrium; no change

Properties of G:

1. Every reaction has a specific standard free

energy (Go)

e.g. the reaction catalysed by hexokinase:

Glucose + ATP Glu-6-P + ADP (3)

Go = - 16.7 kJ/mol

2. Values of Go are additive

What the cell “wants” to do:

Glu +Pi Glu-6-P + H2O Go = + 13.8 kJ/mol (4)

but if Pi from ATP:

ATP + H2O ADP + Pi Go = - 30.5 kJ/mol (5)

Adding the reactions and the Gos

Glu + ATP Glu-6-P + ADP Go = - 16.7 kJ/mol (6)

3. ΔGo is a function of state

ΔGo associated with conversion of specificsubstrate to specific product is independent ofpathway:

e.g.: A B C D Path A

Path B

Thus ΔGoAB + ΔGo

BC + ΔGoCD = ΔGo

AD

Note that reaction A D can occur spontaneouslyeven if ΔGo

AB is positive, so long as

ΔGoAB + ΔGo

BC + ΔGoCD < 0

A B C D

Compound

Sta

ndar

dfr

eeen

ergy

(Go)

(J/m

ol)

Reaction will proceedspontaneously from Ato D, even thoughΔGo

AB is positive

Hydraulic Analogue: The Siphon

Effect of Concentration on Free Energy Change

ΔGo values are derived for standard conditions.

Reactants and products all present at 1 M

Modification of standard Gibbs Free Energy change tonon-standard concentration for the reaction

aA + bB pP + qQ (6)

results in

** ΔG = ΔGo + RT ln { [P]p [Q]q } (7)

{ [A]a [B]b }

mass action ratio

[R is the gas constant = 8.31 J.mol –1 K-1 ]

Other non-standard conditions

ΔGo is also derived at pH 0, 25oC.

For other conditions (eg pH 7, 37oC) symbolize withprime (‘):

ΔG’ , ΔGo’

Reactant and Product Concentrations atEquilibrium

The equilibrium constant (Keq)

At equilibrium, G’ = 0, so Eq. 7 can be rewritten

ΔGo’ = - RT In [P]p [Q]q (8)

[A]a [B]b

where the [ ] terms are specified for the equilibriumconditions.

For this special condition, the mass action ratio isknown as the equilibrium constant (Keq), so

ΔG°’ = -RT In Keq (9)

Oxido-reduction (Redox) Potentials

e.g. NAD+ + H+ + 2e- NADH

Oxidant/reductant together = redox couple

What is capacity of redox couple to donate/accept e-?

Measure Electromotive force (emf): Volts

Red2

V

A B

KCI bridgePt electrode Pt electrode

“Half cell”

pH = O

Ox2Red1 Ox1

e-

Measurement of Standard Redox Potential (EO)

Half Cell A: Standard hydrogen electrode:

Pt electrode, pH = O, H2 bubbled

2H+ + 2e- H2

Half Cell B: Any redox couple:

oxidant and reductant concs =1 Molar.

Strongly REDUCING couples donate e-: Eo very – ve

Strongly OXIDIZING couples accept e-: Eo very + ve.

As with ΔGº, Eo values can be added and subtractedto yield ΔEo for reaction sequence

ΔEo = Eo (oxidizing couple) - Eo (reducing couple)

eg

Reaction: a + bn+ an+ + b

Comprises 2 redox couples: Std. Redox potential

Oxidizing bn+ + ne- b (Eo)b

Reducing an+ + ne- a (Eo)a

Subtracting generates original reaction, with

ΔEo = (Eo)b – (Eo) a

Relationship of ΔGo to ΔEo

Recall (Slide 7): ΔGo defines capacity for useful work (w)

w = - ΔGo (11)

Electrical work done by redox couple:

w = force (Volts) x charge (Coulombs) (12)

Charge carried by 1 “mol” e- in 1 s is the Faraday Constant(F)

F = 96 500 Coulombs/mol

Thus, for reaction in which n electrons participate

w = Eo x nF (13)

Combining Equations 11 and 13 yields

-ΔG° = nFEo (14)

Thus there are 2 ways to describe Free EnergyChange in a Redox System:

1. Difference in Redox potential, ΔE (units, V)

2. Difference in Gibbs free energy, ΔG (units, J/mol)

Whichever we choose is simply a matter of convenience

Modification of Eo for Non-Standard Conditions

A. Concentration:

G0 = - nFEo (14)

G = - nFE : non standard states (15)

Recall: G = Go + RT ln [products] (7)

[reactants]

Substituting Eqs 14 and 15 into Eq 7, for generalisedreaction (oxidized states)n+ +ne- (reduced states)

we can write

nFE = nFEo - RT ln [reduced states] (16)

[oxidized states]

Dividing Eq 16 by nF yields

E = Eo – RT ln _[red]_ (17)

nF [ox]

or E = Eo + RT ln _[ox]_

nF [red] (18)

b. other conditions (e.g. pH 0): signify with ‘ :

E’ = E’o + RT ln [ox]

nF [red]

“mid point potential”

Summary• Gibbs Free Energy can be used to determine the

direction of a reaction

• The “mass action ratio” modifies Gibbs free energies totake account of concentration

• The Equilibrium Constant defines the ratio of productand reactant concentrations for a reaction atequilibrium

• Redox potentials are used to determine the direction ofredox reactions

• Redox potentials can be related to Gibbs free energiesby using the Faraday constant to interconvert Voltsto J/mol