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La Termodinmica y la Vida
Prof. Mirko Zimic
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La Biologa est basada en lamateria suaveviviente
Auto-ensamblaje
Alta especificidadInformacin
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Los objetos vivientes estn
compuestos por molculas inertesAlbert Lehninger
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El problema es:
Cmo estas molculasconf ieren la admirable
combinacin de
caractersticas que
denominamos vida???
Cmo es que unorganismo vivo aparece
ser ms que la suma de
sus partes inanimadas???
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La Fsica procura entender y reducir la
Biologa en leyes fundamentales
Pero este es un problema muycomplicado !
Son demasiadas las variables y resultaimposible describir un sistema de un
nmero tan grande de partculas
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SOLUCIN:Descripcin estadstica del mundo aleatorio
La ACTIVIDAD COLECTIVA de muchos objetos deMovimiento aleatorio puede ser predicho, aun cuando elmovimiento exacto de un slo objeto es desconocido
Si todo en el nano-mundo de las clulas es aleatorio,cmo podemos realizar predicciones?
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TERMODINMICA
Permite predecir la ACTIVIDADCOLECTIVA de muchos objetos de
movimiento aleatorio, aun cuando elmovimiento exacto de un slo objeto esdesconocido
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Todo en el Universo estacompuesto por Materia y Energa
Materia: - Medida de la inercia
Energa: - Energa cintica (movimiento)- Energa potencial (reposo)
E = M C2
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Trabajo
Trabajo = Fuerza Distancia
W = F Dx
La unidad del trabajo es el Newton-metroconocido tambin como Joule.
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Trabajo mecnico
F
FDx
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Kinetic Energy
Kinetic Energy is the energy of motion.
Kinetic Energy = mass speed2
2mv2
1KE
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Potential Energy
The energy that is stored is calledpotential energy.
Examples:Rubber bands
Springs
Bows
Batteries
Gravitational Potential PE=mgh
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Conversin entre la Energa cintica yla Energa potencial
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Qu es la Bioenergtica?
Es la disciplina que estudia los aspectosenergticos en los sistemas vivos, tanto a
nivel molecular como a nivel celular.Interacciones moleculares
ATP como biomolcula almacenadora de
energaBiocatlisis
Reacciones acopladas
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Interacciones Fundamentales
Interaccin Gravitacional (masa-masa)
Interaccin Electromagntica (carga-dipolo)
Interaccin Nuclear Dbil (electrones-ncleo)
Interaccin Nuclear Fuerte (protones-neutrones)
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Enlace Covalente
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Las interacciones Inicas se dan
entre partculas cargadas
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PUENTE DE
HIDRGENO
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Participacin de los Puentes de Hidrgeno:Replicacin, Transcripcin y Traduccin
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Las interacciones dbiles dirigen elproceso de docking molecular
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El efecto hidrofbico colabora enel plegamiento de las protenas
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Revisin de algunos conceptosTermodinmicos
Sistemas termodinmicos
Equilibrio termodinmico
Temperatura
Calor
Entalpa
Energa Libre
Entropa
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Clasificacin de los sistemastermodinmicos
Sistemas AbiertosIntercambian materia y energa con el exterior
Sistemas CerradosSlo intercambian energa con el exterior
Sistemas AisladosNo tienen ningun tipo de intercambio con el
exterior
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Equilibrio Termodinmico
Un sistema se encuentra en equilibriotermodinmico cuando la distribucin
espacial y temporal de la materia y laenerga es uniforme
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En el equilibrio termodinmico sereducen las gradientes y con ello se
reduce la energa potencial
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Qu esta ms fro?El metal o la madera?
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Temperatura
Es la medida de la energa cinticainterna de un sistema molecular
Ek= N K T /2
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Cool Hot
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Qu es el cero absoluto?
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Escalas de temperatura
Fahrenheit Celsius Kelvin
Boiling Point
of Water
Freezing Point
of Water
Absolute Zero
212F
32F
-459F
100C
0C
-273C
373 K
273 K
0 K
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Los estados de la materia
Slido Lquido
Gas Plasma
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Calor
Es la energa cinticaque se propaga debido a
un gradiente de
temperatura, cuyadireccin es de mayortemperatura a menor
temperatura
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El flujo del calor
T= 100oC
T= 0oC
TemperatureProfile in Rod
HeatVibrating copper atom
Copper rod
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Reversibilidad
Reversibilityis the ability to run a processback and forth infinitely without losses.
Reversible ProcessExample: Perfect Pendulum
Irreversible ProcessExample: Dropping a ball of clay
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Procesos reversibles
Examples:Perfect Pendulum
Mass on a SpringDropping a perfectly elastic ball
Perpetual motion machines
More?
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Procesos irreversibles
Examples:Dropping a ball of clay
Hammering a nail
Applying the brakes to your car
Breaking a glass
More?
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Primera Ley de la Termodinmica
La energa no se crea ni se destruye, slo
se transforma
Q = W + dE
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First Law: Energy conservation
Internal energy (E).-Total energy content of a system. Itcan be changed by exchanging heat or work with thesystem:
EHeat-upthe system
Do work onthe system
ECool-offthe system
Extract work fromthe system
DE = q + ww
-PDV
w
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Entalpa
H=E+PVLa entalpa es la fraccin de la energa
que se puede utilizar para realizar
trabajo en condiciones de presin yvolumen constante
dH0 proceso endotrmico
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Entropa
S = K Ln(W)La entropa es la medida del grado de
desorden de un sistema molecular
S1 > S2
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La entropa es la medida del gradode desorden de un sistema
Di d d Li id
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Ordered Solid
Disordered Liquid
H d h li id
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Hard-sphere crystal
Hard-sphere liquid
Hard-sphere freezing is drivenby entropy !
Higher Entropy
Lower Entropy
S d d l di i
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Segunda Ley de la Termodinmica
En todo sistema
aislado, la entropasiempre aumenta
hasta alcanzar elestado de equilibrio
dS>=0 (dS>=dQ/T)
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Ordering and 2ndlaw of thermodynamics
- Condensation into liquid (more ordered).
-Entropy of subsystem decreased
-Total entropy increased! Gives off heat to room.
System in thermal contact with environment
Equilibration
Initially high Cools to room
Algunos eventos bioqumicos contradicen
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Algunos eventos bioqumicos contradicenla segunda ley de la termodinmica?
Second La of Thermod namics
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Second Law of Thermodynamicsnaturally occurring processes are
directionalthese processes are naturally irreversible
E Lib d Gibb
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Energa Libre de Gibbs
G=H-TSLa energa libre esla fraccin de la
energa que sepuede utilizar pararealizar trabajo en
condiciones depresion, volumen y
temperaturaconstante
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Lo importante es la variacin de la
energa libre
dG0 proceso endergnico
dG
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G= H - T SG+ (exergnico) H +(endotrmico)
G (endergnico) H- (exotrmico)S +(sube entropa)S (baja entropa)
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Table 3.2
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La paradoja del Demonio de Maxwell
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La paradoja del Demonio de Maxwell
Segunda ley: Entropa y desorden
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Las Enzimas o biocatalizadores
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Las Enzimas o biocatalizadores,reducen la Energa de Activacin
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La molcula de ATP
Los seres vivos utilizan lamolcula de ATP comomedio principal para
almacenar energapotencial proveniente dela degradacin de los
alimentos
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La manera de utilizarse la energa en la
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La manera de utilizarse la energa en lamolcula de ATP es mediante la separacin deun grupo fosfato el cual est unido mediante
un enlace covalente de alta energa
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La sntesis deATP ocurredurante la
gliclisis y larespiracincelular en lamitocondria
usualmente
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En las plantas, la sntesis
de ATP ocurre asistida porluz durante la fotosntesis,la cual es luego empleada
en las denominadasreacciones oscuras. Este esun ejemplo de
transformacin de energaradiante en energaqumica.
El ATP participa en una serie de
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El ATP participa en una serie dereacciones acopladas
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Diversas molculasbiolgicas requieren lacapacidad de moverse
para cumplir susfunciones Por lotanto hace falta energa
para realizar estafuncin.
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La fuente de energapara el movimiento
molecular esfundamentalmente el
ATP
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El ATP contribuye a diversos
tipos de reacciones
El ATP suele participar en el
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El ATP suele participar en elcorrecto plegamiento de las
protenas
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Thermodynamics
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First Law: Energy conservation
Internal energy (E).-Total energy content of a system. Itcan be changed by exchanging heat or work with thesystem:
EHeat-upthe system
Do work onthe system
ECool-offthe system
Extract work fromthe system
DE = q + ww
-PDV
w
Thermodynamics
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A more useful concept is: ENTHALPY (H)
H = E + PVAt constant
pressurePVVPwVP-qH p DDDD
DE
00
Only P-V work involved w= 0(as in most biological systems)
So
pqHD
At constant pressure, the enthalpy change in a process isequal to amount of heat exchanged in the process by the
system.
Thermodynamics
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We have
H = E + PV
DH = DE + PDV + VDPDP = 0DV 0
in biologicalsystems
0 0
DH DEat DP = 0 and since DV 0
Q:How is this energy stored in the system?
1) As kinetic energyof the molecules. In isothermal (DT =0) processes this kinetic energy does not change.
2) As energy stored in chemical bonds and interactions. Thispotential energy could be released or increased in chemical
reactions
A:
Thermodynamics
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Second Law: Entropy and Disorder
Energy conservation is nota criterion to decide if a process willoccur or not:
Examples
q
HotT ColdT T T
DE = DH = 0This rxn occurs in onedirection and not in theopposite
these processesoccur because
the final state( with T = T &P = P) are themost probable
states of thesesystems
Let us study a simpler case
tossing 4 coins
Thermodynamics
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All permutations of tossing 4 coins
1way to obtain 4 heads4ways to obtain 3 heads, 1 tail6ways to obtain 2 heads, 2 tails4ways to obtain 1 head, 3 tails
1way to obtain 4 tails
Macroscopic states
HT THH HT TH THTTH HT
T TH HTHTH
2!2!
4!6
Microscopic states
1
4
6
4
14 H, 0 T
3 H, 1 T2 H, 2 T
1 H, 3 T
0 H, 4 T
The most probable
state is also themost disordered
Thermodynamics
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In this case we see that DH = 0,i.e.:
there is not exchange of heat between the system and itssurroundings, (the system is isolated ) yet, there is an
unequivocal answer as to which is the mostprobableresult of the experiment
The most probable state of the system is also the mostdisordered, i.e. ability to predict the microscopic outcomeis the poorest.
Thermodynamics
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A measure of how disordered is the final state is alsoa measure ofhow probable it is:
16
6P 2T2H,
Entropyprovides that measure(Boltzmann)
ln WkS B Number ofmicroscopicways in whicha particularoutcome(macroscopic
state) can beattained
BoltzmannConstant
MolecularEntropy
For Avogadro numbers
of molecules
ln W)k(NS BAvogadroR (gas constant)
Therefore: the most probable
outcome maximizes entropyof isolated systems
DS > 0 (spontaneous)DS < 0 (non-spontaneous)
Criterion for Spontaneity:
Thermodynamics
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The macroscopic (thermodynamic) definitionof entropy:
dS = dqrev/T
i.e., for a system undergoing a change from an initial stateA to a final state B, the change in entropy is calculated
using the heat exchanged by the system between thesetwo states when the process is carried out reversibly.
Thermodynamics
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DS dq
rev
Tinitial
fina l
(Carried through a reversible path)
DS C
P
Tinitial
fina l
dT (If process occurs at contant pressure
DS C
V
Tinitial
fina l
dT (If process occurs at const ant volume
Spontaneity Criteria
In these equat ions, the equal sign applies for reversible
processes. The inequalities apply for irreversible, spontaneous, processes :
DS(system) DS(surroundings) 0
DS(isolatedsystem) 0
Thermodynamics
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Free-energyProvides a way to determine spontaneity whether system is
isolated or not
Combining enthalpic and entropic changes
ST-HG DDD
What are the criteria for spontaneity?
Take the case of DH = 0:
ST-G DD
< 0 > 0 DG > 0DG < 0DG = 0
non-spontaneous processspontaneous process
process at equilibrium
(Gibbs free energy)
Thermodynamics
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Free energy and chemical equilibrium
Consider this rxn:
A + B C + DSuppose we mix arbitrary concentrations of products and reactants
These are not equilibrium concentrations
Reaction will proceed in search of equilibrium
What is the DG is associated with this search and finding?:
[A][B]
[C][D]lnRTGG o DD
is the Standard Free Energyof reactionoGD
i.e. DG when A, B,C, D are mixed intheir standard state:Biochemistry: 1M,25oC, pH = 7.0
11
11lnRTGG oRxn
DD
o
Rxn GG DD
Thermodynamics
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Now Suppose we start with equilibrium concentrations:
Reaction will not proceed forward or backward
0GRxnD
Then
eqeq
eqeqo
[B][A]
[D][C]lnRTG0 D
eqeq
eqeqo
[B][A]
[D][C]lnRT-G D
eq
o KlnRT-G D
RT
oST-oH
eq eK
DD
DD R
oSRT
oH
eeKeq
RT
oG
eq eKD
Rearranging
Thermodynamics
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DD
R
oS
RT
oH
eeKln eq
Graph:
R
S
RT
H-Kln
oo
eq
D
D
1-o KT
1
eqKln
R
SoD
-DHo
R
Slope =
Vant Hoff Plot
Thermodynamics
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1) Change in potentialenergy stored in bondsand interactions
2) Accounts for T-dependenceof Keq
3) Reflects: #, type, andquality of bonds
4) If DHo< 0: T Keq
If DHo> 0: T Keq
1) Measure of disorderS = R ln (# of microscopic ways ofmacroscopic states can be attained)
2) T-independent contributionto Keq
3) Reflects order-disorder inbonding, conformational
flexibility, solvation4) DSoKeq
Rxn is favored
Summary: in chemical processes
DHo DSo
Thermodynamics
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Examples:
A B
Consider the Reaction [A]initial= 1M[B]initial= 10-5MKeq= 1000
eq
o KlnRT-G D
Free energy changewhen products andreactants are present atstandard conditions
1000lnK2981.98-G Kmolca lo
DmolKcalo 4.076-G D Spontaneous rxn
How about DGRxn
[A]
[B]lnRTGG oRxn
D
D
1
10lnK298101.984.076-G
-5
Kmol
Kcal3-
mol
Kcal
Rxn D
molKcal
Rxn 10.9-G D Even more spontaneous
Thermodynamics
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Another question What are [A]eqand [B]eq?
1M101[B]A][
-5
[B]-1A][
1000
[A]
[B]K
eq
eq
eq
eqeq [B]-11000B][
1000B][1001 eq
1M0.999M1001
1000B][ eq
0.001MA][ eq
ThermodynamicsA h E l A i A id Di i i
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Another Example Acetic Acid Dissociation
DHo~ 0
CH3COOH + H2O CH3COO-+ H3O+
5-
3
3
-
3eq 10~
COOH][CH
]O][HCOO[CHK
Creation of charges Requires ion solvationOrganizes H2O around ions
At 1M concentration, this is entropically unfavorable.
Keq~ 10-5
If [CH3COOH]total~ 10-5
50% ionizedPercent ionization is concentration dependent. We can favorthe forward rxn (ionization) by diluting the mixture
If [CH3
COOH]total
~ 10-890% ionized
Thermodynamics
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CH3COOH + H2O CH3COO-+ H3O+
Keq [CH3 COO
-][H 3O
]
[CH3 COOH] =
[CH3
COO-][H3O ]
[CH 3COOH]T2
[CH3 COOH]T [CH3 COO-]
[CH 3COOH]T2
Keq
2[CH3COOH]T
1 with
[CH3 COO-
]
[CH 3COOH]T
and =-Keq K
2eq + 4[CH 3COOH]T Keq
2[CH3
COOH]T
Thermodynamics
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CH3 -COOH total
ThermodynamicsThi d E l A i R ti
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Third Example Amine Reactions
RNH + H2O RNH2+ H3O+
H
H+
DSo0
molKcalo 14H D
-10
eq 10K not favorable
Backbone Conformational FlexibilityR H
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NC
R
HO
N
H
H
C
For the process folded unfolded(native) (denatured)
folded
unfoldedo
conf.backboneW
W
lnRS D
How many ways to form the unfolded state?
Backbone Conformational Flexibility
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degrees of freedom = 2
Assume 2 possible valuesfor each degree of freedom. Then
residueisomersonalconformati4ofTotal
For 100 amino acids4100~ 1060conformations
These results do not take into account excluded volume effects.
When these effects are considered the number of accessibleconfigurations for the chain is quite a bit smaller
Wunfolded~ 1016conformations
Backbone Conformational FlexibilityTh d i id ti
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Thermodynamic considerations
16o
conf.backbone 10lnRS D2.303161.987
Kmolca l73
C25at22-ST-G
o
mol
Kcaloo
conf.backbone DDIn addition other degrees of freedom may be quite important,for example
NC
R
HO
N
H
H
C
We will see thislater in more detail
Ionization of Water
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]][OHO[HK -3w
Water is the silent, most important component in the cell
Its properties influence the behavior and properties of all other
components in the cell.
H2O + H2O H3O++ OH-
Here we concern ourselves with its ionization properties:
O][H
]][OHO[HK
2
-
3eq
Since in the cell, [H2O] ~ 55M, and ionization is very weak, then
[H2O] ~ constant, so se can definethe ionic
product ofwater
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Weak Acids and BasesAll bi l i l id d b b l hi
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All biological acids and bases belong to this category
Consider acetic acid
AH A-+ H+
The Dissociation Constant
AH]
[
]
A
][
[HK
-
a
[AH]][AlogpKpH
-
a rearrange Henderson-Hasselbalchequation
where, pKa= - logKa
F i f d d id i
Weak Acids and Bases
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Fraction of deprotonated acid is
[AH]]A[
][AA
f Also AAH 1 ff
A
Aa
-1
logpKpH
f
f
pH
0.5Af
1.0
0
pKa
i.e. pKais the pH at
which the acid is50% ionized
So, we can re-write theHenderson-Hasselbalch
equation
Weak Acids and BasesB d th i
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Based on the previous page
90%11
10;1pKpH
Aa
f
9%;1pKpHAa
f
etc.0.9%,;2pKpHAa
f
If
Morever the lower the pKa, the stronger the acid
pH
0.5Af
1.0
0
strongeracid
weakeracid
A
Aa
-1logpKpH
f
f
Weak Acids and Bases
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Some useful relationships
fAH AH
A AH
H
Ka H
fA-
Ka
fAH
Ka
fA A
A AH Ka
Ka H
Multiple Acid-Base EquilibriaC id Al i
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Consider Alanine
NH3+
CH3
CH COOH
Titrate a solution of ala, using a gas electrode (pH meter), and aburet to add a strong base of known concentration:
=
2.3
=9.7
pK1 pK2 pH
(fractio
ndeprotonated)
mLo
fbaseadded
Macroscopicexperiment shows2 inflection points(2 pKs)
Please correct in yournotes
Multiple Acid-Base Equilibria
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N+CH3CH COOH
H
HH
N+CH3CH COO
H
HH
NCH3CH COO
H
H
Cation Zwitterion Anion
If we assume that the ionization of a given group is independentof the state of ionization of the others, then
As we vary the pH of the solution from low to high:
So, in fact the two inflection points seen correspond to thedeprotonation of the carboxylic group (at low pH) and thento the deprotonation of the amine group (at high pH).
So, How can we estimate the fraction of these different species in solution?
Multiple Acid-Base Equilibria
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fHAH
fCOOH fNH3
H
Ka1 H
H
Ka2 H
fHA
f
COO f
NH3 K a1
Ka 1H
H
Ka 2H
fAH fCOOH fNH2
H
Ka 1 H
Ka 2
K a 2 H
fA
fCOO
fNH2
Ka1
Ka1 H
Ka 2
Ka 2 H
1AAHHAHAH
ffff
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