L1 Thermodynamics

Exam 1

Living Systems

1. Complicated & highly organized

2. Require biological structures that serve functional purposes

3. Living systems are engaged in energy transformations

4. Living systems have capacity for self-replication

STRUCTURE DETERMINES FXN- important to understand the composition of biological structures & how that facilitates appropriate fxn

Introduction to Thermodynamics

Thermodynamics- allows us to understand the free energy of the system 

• It’s really all about energy

  • The word ”thermodynamics” comes from Greek roots meaning thermo (heat) and energy, or power (dynamics)

  • So thermodynamics is really just the study of heat and energy, and how it relates to the matter in our universe

  • Used by biochemists to understand processes and chemical reactions that occur in living organisms

Thermodynamics

Thermodynamics: The study of energy and its effects on matter

Life obeys the laws of thermodynamics → Used to describe and quantify a particular process, Used to predict if a process can occur

• 1st Law: Energy is conserved. For any process, the energy of the system and its surroundings is constant

  • Energy is neither created nor destroyed 

  • Energy is only converted from one form to another 

• 2nd Law: The disorder of the universe is constantly increasing 

  • Spontaneous processes are characterized by the conversion of order to disorder 

  • The tendency in nature is toward increasing disorder 

Thermodynamics 2

• Living organisms require ENERGY 

• Thermodynamics or bioenergetics gives us a way to describe or characterize the energy changes in any biochemical reaction 

Life Obeys the Laws of Thermodynamics

• Living organisms are open systems that exchange both energy and matter with their surroundings (ex: humans… also consume food to make body fxn)

• Open systems take up nutrients and release waste products are never at equilibrium 

• Living systems are characterized as being in a steady state- existing with a constant flow so that the system does not change with time 

  • Formation and degradation of individual components are balanced

•  Living systems utilize biological catalysts called enzymes to accelerate biochemical processes by physically interacting with substrates to provide a more favorable pathway 

• Isolated system: no exchange of matter, energy, heat, or mass 

• Closed system: energy exchange may occur 

Thermodynamics 3

1. Enthalpy (H) → HEAT

• Reflects the number and kinds of chemical bonds or non-covalent interactions made or broken 

• State of molecular complexity 

• More complex => more enthalpy… delta H will be (-) b/c energy has to be added for this bond to be formed 

• Smaller => weaker… delta H is positive (+), not great

2. Entropy (S) → DISORDER

• Randomness or disorder of the components of a chemical system 

• If delta S is (+)/inc… the entropy of the system is inc. 

3. Free Energy (G) → AVAILABLE ENERGY 

Describes the relationship between enthalpy, entropy, and temperature 

Connect enthalpy and entropy w/ impact of temp. we end up defining Gibbs Free Energy

Enthalpy (H)

• 1st Law: For any process, the energy (E) of the system and its surroundings is constant

  • We can not make NEW energy 

  • We can only convert energy from one type to another 

  • Energy can only change its structure 

  • Energy can be conserved in mass & chemical bonds… so if mass is changing, energy will change as well

internal energy of a system (E)= the heat absorbed by the system from the surrounding (q) + the work done on the system by the surroundings (w)

E= q + w

w= work = P△V (insignificant in biological systems)

• Under constant temp. & pressure conditions, the total energy change of a biological system (△E) can be approximated by the heat evolved or absorbed (△H)

△E = q =△H

Enthalpic Reactions

• During a chemical reaction 

  • Old bonds break 

  • New bonds form 

  • Energy is either consumed or released 

• Endothermic reactions: △H > 0

  • Heat is absorbed by the system 

  • New bonds are less stable 

  • Requires heat, not enthalpicaly favorable 

• Exothermic Reactions: △H < 0

  • Heat is evolved by the system 

  • New bonds are more stable 

  • Gives off heat, enthalpically favorable 

Entropy (S)

• A measure of the degree of randomness or disorder 

  • An ordered state has low entropy 

  • A disordered state has high entropy

• 2nd Law: For any process, the entropy (S) of the system and its surroundings always increases, the disorder of the universe increases 

△S < 0

• When the final state is more ordered than the initial state 

• Products are more complex and more ordered 

△S > 0

• When the final state is less ordered than the initial state 

• Products are less complex and more disordered 

Free energy (G)

Defined in terms of H, S, and T

1. Enthalpy (H)- heat 

2. Entropy (S)- disorder 

3. Temperature (T)- kelvin 

G = H - TS

Notice signs are opposite for H and S… why? A more stable product is formed during a biochemical reaction. What happens to H & S?

Enthalpy (heat release) is increased upon formation of more stable bonds 

Entropy (disorder) is decreased upon formation of more stable bonds

Enthalpy/Entropy Compensation

Spontaneous vs. Non-spontaneous Reactions 

• A spontaneous process: one that takes place with no outside intervention 

  • reactions proceed from a state of high energy to low energy 

  • exergonic reaction (energy released)

• A non-spontaneous process: one that takes place with outside intervention 

  • reactions proceed from a state of low energy to high energy

  • endergonic reaction (energy absorbed)

Free Energy Change (△G)

• At constant temp. (T) and pressure- as in the body- it is important to look at the change in free energy (△G)… G = H - TS → △G = △H - T△S

• Neither △H nor △S alone is sufficient to determine whether a reaction is a spontaneous process or a non-spontaneous process 

• Gibbs free energy change (△G) is a measure of spontaneity of a chemical process 

  • △G = △H = T△S < 0     Spontaneous 

  • △G = △H - T△S > 0     Non-Spontaneous 

Free Energy

A + B →← C + D

△G is used to determine the spontaneity of a process 

△G = △H - T△S

• △G < 0 exergonic, spontaneous: energy released

• △G = 0 the system is at equilibrium 

• △G > 0 endergonic, non-spontaneous: energy required 

• Signs for enthalpy and entropy are opposite- indicating that free energy is based on enthalpy/entropy compensation. Any favorable reaction will either be enthalpically or entropically driven 

Spontaneity is defined by the change in free energy of the process (△G)

Free energy- the amount of energy available to do work 

Free Energy & Concentration

• Entropy (disorder) increases with volume 

• Entropy is a function of concentration 

• Thus, free energy depends on concentration 

Free Energy 2

A + B →← C + D

• Free energy change (△G) is based on two things:

1. A function of the standard free-energy change (△G°)

2. The initial concentrations of products and reactants [Ai], [Bi], [Ci], [Di]

• Following equation describes these relationships: 

△G= △G° + RT ln [Ci]^c [Di]^d/[Ai]^a [Bi]^b 

R, gas constant: 8.315 J*mol^-1 * k^-1

T, Temperature in K 

Free Energy 3

△G = △G° + RT ln

• △G°: Constant Term: Standard Free Energy Change 

[Ci]^c [Di]^d/[Ai]^a [Bi]^b 

• Variable Term: Initial [R] and [P]

• Reactants & their concentration of products will change 

The free energy change (△G) of a chemical reaction depends on two parts: 

1. A constant term dependent on the reaction taking place

• a characteristic for each specific reaction

2. A variable term based on the concentration of both the reactants and products, the stoichiometry of the reaction, and the temp.

Standard States

1. Constant term △G°

• In order to compare thermodynamic parameters of different reactions, it is convenient to define a reference or standard state 

△G° is knows as the Standard Free Energy change 

• Standard states apply to only ONE defined set of conditions 

1M reactants and products 

a specific temp. (usually 298 K)

a specific pressure (usually 1 atm) 

• Standard state conditions are denoted by a degree sign- ie: △H° or △G°

• Standard conditions do not normally occur in cells 

  • Do not use △G° for cellular conditions- Biochem defined standard-state conditions △G°’

△G°’

1. Constant Term △G° → △G°’

Standard free energy change, △G°, assumes a concentration of 1 M for hydrogen ions 

• if [H+] = 1 M, then pH = 0

• but the pH in most cells is near the neutral range (pH =7)

Biochemists’ Standard-State Conditions 

1. Biochemical reactions are buffered so that the [H+] concentration does not vary 

• use a value of 1 for [H+], (pH = 7)

2. Additionally in biochemical reactions the concentration of water is very high (55.5 M)

• use a value of 1 for water 

3. Since we modified the standard state to reflect these changes it is given the symbol △G°’

△G= △G°’ + RT ln [Ci]^c [Di]^d/[Ai]^a [Bi]^b 

△G°’ 2

An added annoyance:

• In biochem the △G° and △G°’ symbols are used interchangeably 

• SO, look at the context of the problem

• If it pertains to biochem, assume △G° is △G°’

2. Variable Term [Ri] and [Pi]

A variable term based on:

1. The concentration of both the reactants and products 

• ie [Ai] where “i” designates the initial or starting concentrations 

2. The stoichiometry of the reaction 

• ie [Ai]^a where “a” the number of each species in a balanced equation 

3. The temp 

• “T” units Kelvin 

The composition of a reacting system will continue to change until equilibrium is reached 

• The mixture of reactants and products changes, affecting the free energy of the reaction until equilibrium is reached

Equilibrium

aA + bB →← cC + dD

• State in which forward and reverse reactions occur at the same rate

  • Concentration of reactants and products remain constant over time 

• All chemical reactions proceed until they reach equilibrium

• The equilibrium level for a reaction in intrinsic to that specific reaction 

  • Equilibrium may favor higher reactant concentration, or favor product formation 

Concentration of products and reactants will be the same over time… don’t expect a change in free energy 

Equilibrium Constant

• The concentration of products and reactants does not change with time

  • Use the “eq” subscript to denote concentrations of products and reactants at equilibrium 

• Therefore, at equilibrium:

 [Ceq]c [Deq]d / [Aeq]a [Beq]b = Keq

• How does Keq relate to the change in free energy?

  • When a reaction reaches equilibrium (△G=0), no driving force remains 

Keq and △G°

An equilibrium expression can be written for any reaction at constant temp

Keq= [Ceq]^c [Deq]^d / [Aeq]^a [Beq]^b = [P]eq / [R]eq

• Keq is a ratio of [P]eq and [R]eq

Keq » 1: Favors product formation so △G° is large and negative →

Keq « 1: Favors reactant formation so △G° is large and positive ← 

Change the temp., change Keq

Chemical Equilibrium 

For the reaction: aA + bB →← cC + dD

△G = △G° + RT ln [Ci]^c [Di]^d / [Ai]^a [Bi]^b

When the reaction reaches equilibrium, △G = 0: 

0 = △G° + RT ln [Ceq]^c [Deq]^d / [Aeq]^a [Beq]^b

△G° = -RT ln [Ceq]^c [Deq]^d / [Aeq]^a [Beq]^b 

[Ceq]^c [Deq]^d / [Aeq]^a [Beq]^b = Keq

△G° = -RT ln Keq or Keq = e-^△G°/RT

Chemical Equilibrium 2

The driving force for the reaction, the free energy change equals: 

△G = △G° + RT ln [Ci]^c [Di]^d / [Ai]^a [Bi]^b

R, gas constant: 8.315 J*mol^-1 * K-1

T, temp in K 

• △G° known as the Standard Free Energy change, when all reactant and product concentration is 1 M, and at constant pressure (1 atm) and temp. (298 K)

• △G°’ in biochem: the concentration of pure water is assumed to be 1, and the concentration of H+ is assumed to be 1 at pH = 7

• At equilibrium: △G = 0, [Peq] / [Req] = Keq, is given by:

△G° = -RT ln [Ceq]^c [Deq]^d / [Aeq]^a [Beq]^b

The relationship between △G° and Keq

• By definition, the relationship between Keq and △G° is temp. dependent

△G° = -RT lnKeq

T = △G° / (-R lnKeq)

^ Assume T= 298 K unless otherwise indicated 

• Keq varies as a function of temp.

• When no temp. is given, it is assumed that Keq and △G° were determined at 25°C or 298 K

• It is valid to determine Keq at a different temp. (ie: not 298 K) and △G° is valid at that temp

Sample Problem

Glucose 1-phosphate →← Glucose 6-phosphate

• The concentration of G 1-P is 1 mM and G 6-P is 19 mM at equilibrium 

1. Calculate Keq

Keq = G 6-P / G 1-P = 19 mM / 1 mM = 19

2. Calculate the standard free energy change 

△G°’ = =RT lnKeq = -(8.315×10^-3 kJ/mol*K) (298K) (ln 19) = -7.3 kJ/mol 

Thermodynamic State Functions are ADDITIVE

• This applies to the standard and non-standard state (△G° or △G)

• The total free energy change (△GTotal) for two consecutive reactions (or metabolic pathways) are additive!

• △G1 + △G2 = △GTotal

△G1: Glucose + Pi → Glucose-6-P, △G°=14 kJ/mol

△G2: ATP → ADP + Pi, △G°=-30 kJ/mol

△G3: Glucose + ATP → Glucose-6-P + ADP, △GTotal=-16 kJ/mol

How to “Drive” an Unfavorable Reaction Forward

1. Increased concentrations of reactants

• Compartmentation: an enclosed system can maintain high local concentrations of components that would otherwise diffuse away (stated differently- it promotes unequal distribution of molecules/metabolites)… more reactions probable 

2. Coupling of reactions 

• Favorable reaction couple with unfavorable reaction 

When do I use these equations?

1. △G = △H - T△S

Equation 1 is used when you are given or need info about entropy or enthalpy

2. △G = G° + RT ln([P]/[R])

Equation 2 is used for NON equilibrium conditions

3. △G° = -RT lnKeq

Equation 3 is used ONLY for equilibrium conditions