Thermodynamics I

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Thermodynamics I

• Dr Una Fairbrother

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General Biochemistry 2006-07

• Module Convenor Dr Chris Bax,
  c.bax_at_londonmet.ac.uk
• Lecture 1 Water (Dr Una Fairbrother).
• Lecture 2 Thermodynamics I (Dr Una Fairbrother).

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THERMODYNAMICS

• Relationship between heat and movement 
• BUT better in biology to consider the
  relationship between energy and work
• For example - can thermodynamics be used to
  predict whether any useful work can be achieved
  in a chemical reaction?
• Does a reaction occur spontaneously or does
  energy need to be provided?

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DEFINTIONS

• SYSTEM
• matter within a defined region of the universe
• SURROUNDINGS
• matter outside that defined region
• BOUNDARY
• A separator, real or imaginary between system
  and surrounding

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First Law of Thermodynamics

• The total energy of a system and its surroundings
  is a constant_at_ ie energy is conserved.
• DE EB - EA Q-W 
• DE - energy change
• EB - energy of system at end of process
• EA - energy of system at beginning
• Q - heat absorbed by system
• W - work done

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NOTE about enthalpy

• "enthalpy is the amount of energy in a system
  capable of doing mechanical work"
• Heat content, total heat, enthalpy, H
• a thermodynamic quantity equal to the internal
  energy of a system plus the product of its volume
  and pressure
• DH DE PDV
• H is ENTHALPY, P is pressure, V is volume change

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THERMODYNAMICS

• Unfortunately measuring DE (or DH) does not
  predict spontaneity of a reaction.
•  
• The next step is to consider another function of
  thermodynamics called ENTROPY (denoted by S) -
  this is the measure of randomness or disorder of
  system

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Second Law of Thermodynamics

• A process can occur spontaneously only if the sum
  of the entropies of a system and its surroundings
  increases_at_
• DS system DS surroundings gt 0 (for a
  spontaneous reaction)

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Entropy

• the entropy of the universe increases during any
  spontaneous process
• universe just means the system youre looking
  at PLUS its surroundings, i.e., everything thats
  close around it. System plus surroundings.
• Energy spontaneously disperses from being
  localized to becoming spread out if it is not
  hindered from doing so.
• A rock will fall if you lift it up and then let
  go.
• Hot frying pans cool down when taken off the
  stove.
• Iron rusts (oxidszes) in the air.
• Air in a high-pressure tire shoots out from even
  a small hole in its side to the lower pressure
  atmosphere.
• Ice cubes melt in a warm room.
• Whats happening in each of those processes?
• Energy of some kind is changing from being
  localized ("concentrated" in the rock or the pan,
  etc.) to becoming more spread out

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Iron doesnt have to be hot to have localized
energy

• Iron atoms plus oxygen molecules have more energy
  localized within their BONDS than iron rust (iron
  oxide).
• Iron reacts with oxygen releasing energy from
  higher energy bonds and form the lower energy
  bonds in iron oxide
• The difference in energy is dispersed to the
  surroundings as heat i.e., the reaction is
  exothermic and makes molecules in the
  surroundings move faster .
• Iron spontaneously, but slowly, reacts with
  oxygen and each spreads out some of its bond
  energy to the surroundings when the iron and
  oxygen form iron oxide.
• System iron and oxygen, iron oxide.
• Surroundings the nearby air and any moisture or
  salt in the air plus any object in contact with
  the rusting iron

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Motional energy and bond energy

• In chemistry the energy that entropy measures as
  dispersing is motional energy, the
  translational and vibrational and rotational
  energy of molecules
• and the DH of phase change energy both motional
  or phase change energy being designated either as
  "q" or DH in many equations.
• Bond energy, the potential energy associated
  with chemical bonds that we talked about in the
  iron oxidation example,
• measured by the potential energy of bond
  formation
• and this is measured by entropy change in
  connection with a chemical reaction

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FREE ENERGY

• Because entropy changes are difficult to measure
  a third thermodynamic parameter is introduced.
  This is called FREE ENERGY
• DG DH - TDS
•  
• DG - free energy change
• DH -enthalpy change
• DS -entropy change
• T -temperature in Kelvin

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Gibbs free energy

• The Gibbs free energy was developed in the 1870s
  by the American mathematical physicist Willard
  Gibbs.
• A thermodynamic potential which measures the
  "useful" work obtainable from an isothermal,
  isobaric thermodynamic system.
• When a system evolves from a well-defined initial
  state to a well-defined final state, the Gibbs
  free energy DG equals the work exchanged by the
  system with its surroundings, less the work of
  the pressure forces, during a reversible
  transformation of the system from the same
  initial state to the same final state.

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How do you use DG?

• A reaction can only occur spontaneously if DG is
  negative .
•   If DG is 0 then the reaction is at equilibrium.
• A reaction cannot normally occur if DG is
  positive ( an input of free energy from another
  reaction is required to drive it).

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Consider the first step of glycolysis

• Glucose Pi Glucose 6-phosphate DG
  13.8 kJ mol-1
• Not spontaneous

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If the reaction is COUPLED to the hydrolysis of
ATP

• ATP H2O ADP Pi DG -30.5 kJ
  mol-1
• and
• Glucose Pi Glucose 6-phosphate DG13.8 kJ
  mol-1 
• Glucose Pi ATP H2O Glucose 6-phosphate
  ADP Pi DG -16.7 kJ
  mol-1
•  The net reaction is spontaneous and therefore
  permits the phosphorylation of glucose

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Relationship between free energy (G) and the
equilibrium constant (Keq)

• A B C D 
• DG DGo RT ln CD
• AB 
• NOTE ln loge
• DG0 standard free energy change ie change
  under standard conditions - A,B,C,D present at
  1.0M, 298.15 K, atmospheric pressure of 101,235
  Pa
• R gas constant 8.314 JK-1mol-1
• T temperature in K

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DG0 and DG0

• At equilibrium DG 0, Keq CD
• 
  AB
• So DG DGo RT ln CD
• AB
• Becomes 0 DGo RT ln Keq
• Therefore DGo -RT ln Keq
• In biochemistry there is a further standard free
  energy change which occurs at pH7 - this is
  given the symbol DGo

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Reducing agents

• A reducing agent is defined as a substance that
  will donate an electron and become oxidised
• eg Fe2 Fe3 e-
• An oxidising agent is able to accept an electron
  and becomes reduced
• eg Fe3 e- Fe2

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HALF-REACTIONS

• Reactions showing the electrons being accepted
  (or donated) but where the electron donor (or
  acceptor) is not shown are called HALF-REACTIONS
• eg H e- H (sometimes written as 1/2 H2 )
• Eo of -0.42 V
• E0 , which is the reduction potential,
• a measure of the tendency of H to accept
  electrons

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• Half reaction (written as a reduction) E0 (at
  pH 7.0), V
• Fe3 e- Fe2 0.77
• Dehydroascorbic acid 2H 2 e-
  0.06
• ascorbic acid
• Ethanal 2H 2 e- ethanol
  -0.16
• NAD 2H 2 e- NADH H -0.32

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Two half reactions can be added together to
obtain the full reaction

• When any two half reactions are coupled the half
  reaction with the more positive reduction
  potential will proceed as written (ie as a
  reduction) driving the other half reaction
  backwards (ie as an oxidation)

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 Free energy is related to reduction potential
as follows

• DG0 - n F DE0
• n number of electrons transferred
• F Faradays constant (96,496 JV-1)
• DE0 E0of half reaction containing the
  oxidising
• agent - E0of half reaction containing reducing
  agent
• Ethanal 2H 2 e- ethanol -NAD 2H 2
  e- NADH H

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NOTE overall the reaction is

• Ethanal NADH H ethanol NAD
• DE0 -0.16 -(-0.32) V
• 0.16V
• Therefore
• substituting in DG0 - n FDE0
• DG0 -(2)(96,496)(0.16) joules (per mole)
• -30 kJmol-1

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Summary

• 1st Law of Thermodynamics enthalpy
• 2nd Law of Thermodynamics entropy
• FREE ENERGY, DG
• Relationship between free energy and the
  equilibrium constant (Keq)
• DG0 and DG0
• Reducing agents
• HALF-REACTIONSTwo half reactions can be added
  together to obtain the full reaction
• Free energy is related to reduction potential

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Reading list

• Stryer, 5th edition Principles of Biochemistry
• http//www.entropysite.com/students_approach.html