CHEMICAL THERMODYNAMIC PRINCIPLES

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CHEMICAL THERMODYNAMIC

PRINCIPLES

Student
Edition
5/23/13

Topic: Thermodynamics


SIGNIFICANCE FOR BIOLOGICAL SYSTEMS

AND PHARMACOLOGY

Dr. Brad Chazotte


213 Maddox Hall

chazotte@campbell.edu

Website:

http://www.campbell.edu/faculty/chazotte

Original material only
© Chazotte
2000
-
13


Pharm. 304
Biochemistry

Fall
2013

What can Thermodynamics Tell Us?

It is concerned with the transfer of heat and the appearance or
disappearance of working attending various chemical and physical
processes.

It may be able to tell that a process will occur, but not how fast it will
occur.

It can often give a quantitative description of an overall change in a
process without giving any indication of the character of the process by
which the change might take place.

It can tell us why certain biological structures are more or less stable

It helps us to understand energy and matter flows in metabolism.


.


GOALS


Realize that understanding some basic thermodynamic concepts helps to understand
why various chemical and biological processes occur.


To understand the basic laws of thermodynamics and such concepts as temperature,
heat, and work.


To understand the basis of energy in systems as described by internal energy (E) ,
enthalpy (H) , and free energy (G) and the concept of entropy (S).


To learn how thermodynamics explains the existence of equilibrium constants and their
variation with temperature.
.



To understand the relationship between free energy and equilibrium constants and to
calculate them. Also to be able to predict the direction of a reaction.


To learn the relationship of thermodynamics to matter and energy flow in the
metabolism of living organisms.


To understand how coupled reactions are important to metabolism.


THERMODYNAMICS


SOME PHARMACOLOGICAL APPLICATIONS I

Topic: Thermodynamics



Predict if a drug will precipitate in solution.


Predict whether a drug can be soluble in a particular solvent
system.


Differentiate between a physical adsorption of a drug on a surface or
absorption is taking place.


Related to a drug’s state of matter, e.g. determining whether the
compound is polymorphic.


Permit a pharmacist to differentiate drugs that are strong or weak
electrolytes e.g., differentiating between HCl and phenobarbital.


Predictions concerning interactions between a drug and a vehicle.

THERMODYNAMICS


SOME PHARMACOLOGICAL APPLICATIONS II

Topic: Thermodynamics



Predicting drug partitioning behavior in the body.


Understanding the transport of Pharmacological Agents


Predicting the feasibility of mixing of Pharmacological Agents


Modeling drug/receptor binding


Likelihood or manner of drug catabolism (pathways).

THERMODYNAMICS


SOME BIOLOGICAL APPLICATIONS

Topic: Thermodynamics



Diffusion


Osmosis


Substrate Transport


Bioenergetics


Metabolism and Metabolic Pathways


Membrane Formation and Structure


Protein Structure


Receptor Binding (Drug
-
Receptor Binding, Immunological function
Cell Signaling)



Versus
d



X

d
x

Consider some function
y = f(x)

dy

dx

Y

X

Equilibrium thermodynamics:

the system changes through small, reversible steps, such
that the system is always at or near equilibrium as it changes.



CHEMICAL
THERMODYNAMICS


BASIC CONCEPTS AND DEFINITIONS

Topic: Thermodynamics


Classical chemical thermodynamics, in essence, looks at the average behavior
of populations of molecules.

Thermodynamics predicts whether or not a reaction occurs spontaneously
and how much energy must be supplied to make a non
-
spontaneous
reaction occur.

Some Thermodynamic Constants
and Conversion Factors

1 calorie (
cal
)



= 4.184 joules (
J
) = 0.041293 liter atm

1 Joule


(
J
)



= 1 kg m
2

s
-
2

= 1

C V (coulomb volt)

k
b

(Boltzmann constant)

= 1.3807 x 10
-
23

J K
-
1

0
º
C (ice point)


= 273.15 Kelvin (
K
)

R

(gas constant)


= 8. 315 J deg
-
1

mol
-
1


=
N
A

k
b





= 1.9872 cal deg
-
1

mol
-
1





=0.082056 liter atm deg
-
1

mol
-
1

1 atm




=760 Torr (mm Hg)

1 Torr




= 1333.2 dyn cm
-
2



Topic: Thermodynamics


Ideal Gas Law

PV = nRT


Where:


P= pressure (atm or torr)

V = volume (liters)

n= number of moles (1 mole = 6.023 x 10
23

molecules)

R= gas constant

T = absolute temperature
º

K

Topic: Thermodynamics


Relates pressure
-
volume
product to the number of
moles of gas.

THERMODYNAMICS


Thermodynamics describes physical and chemical phenomena in terms
of macroscopic properties, e.g
.
temperature, pressure,
and
volume
.

Define the system as the part being studied and the region around the
system

that interacts with it as the
surroundings
.

Wall 1975

System



That portion of the universe delineated by real or imaginary


boundaries. Systems may be closed or open.

Surroundings
The rest of the universe, that which surrounds the



system.

Universe
The whole shootin’ match; everything


Across the boundaries of such a “system” heat will flow, work will appear or
disappear, and matter may even move.

System and Surroundings in Thermodynamics

Topic: Thermodynamics


System

Surroundings/Universe

Heat

Work

Adibatic

Matter

Closed System

+

-

Open System

+

-

Boundary

THERMODYNAMICS

Definitions:

Temperature, Heat, and Work


Temperature

Produces changes in measurable properties of matter, such as:
volume of a liquid, electrical resistance of a metal, the volume of a gas at
constant pressure. Each of these can provide an operational definition of a
temperature scale. Typically the absolute temperature scale in degrees Kelvin
(
°
K
) is used.

Wall 1975

Heat

Heat can be regarded as something (energy) that is transferred between
objects due to a difference in the objects’ temperatures. By convention heat is
positive when it is added to the system.
Units:
J

Work

Simplest representation of work involves the operation of force
through a distance in such a way as to produce an increase in the potential or
kinetic energy of an object. It is easiest to think of pressure operating
through a change in volume. For example, a steam
-
driven piston. Work is by
convention a positive quantity when it appears in the surroundings.
Units:
J


THERMODYNAMICS

Definitions: Pressure, Volume and Temperature


Describes physical and chemical phenomena in terms of macroscopic
properties, e.g.
temperature, pressure,
and
volume
.

Cramer & Knaff 1990

Pressure (P)


is the force exerted by an object on its container



(boundary).


Volume (V)


is the space which an object occupies.

Temperature (T)

is a measure of the amount of heat (energy)





contained in an object (system)


TEMPERATURE and HEAT FLOW

Topic: Thermodynamics


50
º C

60
º C

Heat flow (Q)

THERMODYNAMIC PROPERTIES


The state of a system is determined at any given time by the values of
its macroscopic properties:

Cramer & Knaff 1990

Intensive properties
: e.g. temperature, pressure, density, chemical
potential. These are
independent

of the

size

of the system.

Extensive properties
: e.g. energy, volume, and mass. These
depend

on the
size

of the system.


A gradient in an
intensive

variable leads to a flow in its related
extensive

variable. Temperature & heat flow, pressure & mechanical movement,
chemical potential & matter flow

THERMODYNAMICS: State Functions


The
state of the system

for a single substance may be defined by two
intensive

properties and one
extensive

property, e.g.,
T, P

and
V

Cramer & Knaff 1990

A
State Function:
when the “state” of a system is changed, the change of
any state function or variable, depends only on the value of the function in
the initial and final states; it is independent of the path along which the
change has occurred. We will say later on that these are state functions T,
P,V, S, U (or E), H, G, A, and density.


State Functions and Paths

P

V

State 1

State 2

V
2

V
1

P
1

P
2

THERMODYNAMIC PROCESSES


Definitions:


Isothermal:

constant temperature

Isopiestic:

constant pressure

Isochoric:

constant volume

Cramer & Knaff 1990; Wall 1974

Adiabatic:

process that occurs
without
heat flow across the



boundary separating the system from its surroundings.

Cyclical:

initial and final states of the system are identical.


THERMODYNAMICS

Internal Energy, Work, and Heat

A
state function, e.g.
E

(energy ), has a unique value for a given state and
the value of its change between two states is independent of the path.


Energy is divided into two categories: work (
W
) and heat (
Q
).
Units:
J

Cramer & Knaff 1990

W

is the energy change accomplished by ordered or coherent molecular
movement:



mechanical



pressure/volume


chemical or osmotic


matter movement across gradient


electrochemical

electron moving between two different





oxidation potentials

Q

is the energy change that arises from random molecular motions whose net
flow is directed from matter at higher to that at a lower temperature.


THE LAWS OF
THERMODYNAMICS


Topic: Thermodynamics


THERMODYNAMICS


THE ZEROTH LAW

Topic: Thermodynamics


333
º

K (60
º C)


Q =0

System B

System A


Q =0

System C

T
A

= T
B
and T
B

= T
C

Then T
A

= T
C

333
º

K (60
º C)

Any two bodies or systems in thermal equilibrium with a third body or
system are in thermal equilibrium with each other.

THERMODYNAMICS: 1
st

Law


The First Law of Thermodynamics


(Conservation of Energy):

The total energy of a system and its surroundings does not change
.





E
=

Q

-


W

The pressure
-
volume work due to the expansion or compression of a gas at pressure
P

through volume change
d
V

can be written:




d
W

=
+
p
d
V

where

dW

is
positive

for work done
on

the
surroundings. (This is consistent with other texts
. We will use this convention in this course)


(
The
below
signs

are correct for the convention adopted in the text by Cramer and
Knapff
, Springer
-
Verlag
, 1990. Note that they are OPPOSITE)



E
=

Q

+

W


d
W

=
-
p
d
V

where
dW

is
positive

for work done
on

the system.


Cramer & Knaff 1990

THERMODYNAMICS: 1
st

Law


The First Law of Thermodynamics


(Conservation of Energy):

Enthalpy (
heat content
)
, a state function, can be used to describe the heat content of a
system under constant pressure when only pressure
-
volume work is done. The enthalpy is
derived

If the only work done is by volume change (
pdV
) Then

dE

=
dq


PdV



Cramer & Knaff 1990

The enthalpy is then defined as
H


E

+ p
V



Units:
J mol
-
1

The first law

does

not

provide any definition of equilibrium or make any prediction on the
spontaneity or direction of a reaction.


We can write a general expression for the enthalpy change


dH

= d(E + PV) =
dE

+
PdV

+
VdP




=
dQ


dW

+
PdV

+
VdP

Then for system
PdV

work (
VdP
=0):



dH

=
dQ

+
VdP


(For such a system undergoing a change at constant P:
dH

=
q
p
)

THERMODYNAMICS

p

V work

Topic: Thermodynamics


x


x

Consider a piston in a cylinder of initial volume v
i

moving

x to
create a final volume v
f

= v
i

+

v


v

v
i

v
i

THERMODYNAMICS


THE SECOND LAW

Topic: Thermodynamics



The second law introduces the concept of entropy, indicated by the
symbol,
S
, which is a measure of the randomness or orderliness of the
energy and matter in a system.


The more organized, orderly, constrained or highly structured the system
the lower its entropy.


Only organized nonrandom energy is useful to for work.

THERMODYNAMICS: 2
nd

Law Definition


In all processes the entropy, S, of the system plus the surroundings always
increases until equilibrium is obtained, at which point the entropy is the maximum
possible under the given temperature and pressure
.

Cramer & Knaff 1990

Alternatively, it can be formulated that:

the ultimate driving forces of all chemical and
physical processes is the tendency for randomness in the universe to be maximized.

THE SECOND LAW OF THERMODYNAMICS


THERMODYNAMICS: 2
nd

Law Formula


THE SECOND LAW OF THERMODYNAMICS


Entropy, a state variable, is part of the enthalpy
not

available to do useful work. It can
be regarded as the randomness of a system.





Q

=
T

S or rearranging:

S = Q/T
(T is a constant)


The work done by a reversible process is greater than that that can be done
in an irreversible process since

S
irrev

>

q
irrev
/T.





W
rev


>

W
irrev



S Units:
J K
-
1

mol
-
1

Cramer & Knaff 1990

THERMODYNAMICS


THE THIRD LAW

Topic: Thermodynamics


The entropy of a perfect crystal at absolute zero is equal to
zero.

lim S = 0

T 0



CHEMICAL
THERMODYNAMICS


The CONCEPT OF FREE ENERGY

Topic: Thermodynamics


THERMODYNAMICS

Definitions: Equilibrium


A system is in equilibrium when it has no further tendency to change its
properties.

The fundamental criterion for thermodynamic equilibrium is: in a
system of constant energy and volume, the total entropy is a maximum

Cramer & Knaff 1990

(

S)
E,V

= 0



or alternatively the internal energy is at a minimum

(

E)
S,V

= 0


THERMODYNAMICS


FREE ENERGY

The energy released or utilized in a chemical reaction represents the difference
between the energy contents of the products and reactants. At
constant

temperature

and
pressure
, the energy difference is called the Gibbs free energy.

Cramer & Knaff 1990

Free Energy
G

(Gibbs Free Energy)
G


H


TS

= E
-

TS + PV = A + PV

At constant
temperature

and
pressure






G
p,T

=

H
-
T

S


The free energy change can be defined as that portion of the total energy change
which is available to do work as the system proceeds to equilibrium at constant
temperature and pressure.

One can also state that for a reaction that :





G
reaction

=


G
products

-




G
reactants


THERMODYNAMICS


CHEMICAL REACTIONS, EQUILLIBRIUM, AND
FREE ENERGY

Topic: Thermodynamics


THERMODYNAMICS

CHEMICAL REACTIONS: Definitions

Topic: Thermodynamics


Chemical reaction may be classified as follows:

Exergonic:

those that yield energy, i.e., capable of doing work

Endergonic:

those that utilize (require) energy, i.e. work is used to


make them go

These two types of reaction can be, and are, used biologically to create
the complex molecules and structures necessary for life:

Coupled Reactions:

the use of energy from an exergonic reaction to
drive and endergonic reaction. This is done biologically by trapping the
energy of an exergonic reaction in an “energy
-
rich” compound to be
used later, e.g. ATP (adenosine triphosphate)

THERMODYNAMICS: Free Energy 1


Free Energy Change of Chemical Reactions:

Consider the relationship between a chemical reaction and its equilibrium constant.




reactants


products




aA + bB



cC + dD

Where a,b,c,d, are the number of molecules of A,B,C and D in the reaction. The free
energy change at constant temperature and pressure is given by:

Cramer & Knaff 1990; Lehninger 1977






[C]
c

[D]
d



G

=


G


+ RT ln [A]
a

[B]
b

[ ] = molal concentrations

R = gas constant = 1.98 cal
-
1

mol
-
1
= 8.315 joules mole
-
1

deg
-
1



T = abs. Temp in


K


G


is the standard free energy change of the reaction, here defined as at 298 ºK, at
component concentrations of 1 M and 1.0 atm. pressure.



THERMODYNAMICS: Free Energy Calc.
1
Calculation Free Energy Change at Nonstandard Conditions:

Consider the relationship between a chemical reaction and its equilibrium constant.






[C]
c

[D]
d



G

=


G


+ RT ln [A]
a

[B]
b



where A = 1.6 x 10

3
molar a= 1

; B = 2.6 x 10

4
b= 1



C = 4.8 x 10

2
c= 1

; D = 3.7 x 10

2
d= 2 and

G


=
-
34,000 J mol
-
1

R = gas constant = 1.98 cal
-
1

mol
-
1
= 8.315 joules mole
-
1

deg
-
1
; T = abs. Temp in


K

Cramer &
Knaff

1990;
Lehninger

1977








[4.8 x 10

2
]
1

[3.7 x 10

2
]
2


G =
-
34,000 J mol
-
1

+ 8.315 J mol
-
1

deg
-
1
x

298


K x ln [1.6 x 10

3
]
1

[2.6 x 10

4
]
1












G =
-
34,000 J mol
-
1

+ 2477.9 joules mole
-
1

ln [1.58 x 10
2
]



G

=
-
21,456 J mol
-
1
=
-
5109.2 cal mol
-
1


Free Energy Standard State 1

Standard States for Free Energies of Reaction (


G

)

:


G


is the change in free energy that accompanies the conversion of
reactants in

their standard states to products in their standard states.
Since this is a state

function the terms are additive.

Standard States for Free Energies of Biological Reactions (

G


´
)

:

Biochemists have adopted a modified standard state in which all
substrates or products are in the standard state, i.e. 1 M, except for H
+
.
The H
+

value is taken to be some physiological value, e.g. 10

7

M (pH
7.0)


Cramer & Knaff 1990; Lehninger 1977


G

´

is the change in free energy that accompanies the conversion of
reactants to products in biological systems. (Since this is still a state
function the terms are additive.)

Free Energy Standard State

2

Standard States for Free Energies of Reaction (

G

)

:


Each chemical compound has a characteristic intrinsic free energy by virtue
of its molecular structure.


G


=

G


prod

-



G


react
(also called


G
f

,
free energy of formation)

Cramer & Knaff 1990; Lehninger 1977

It is very important to understand the difference between

G


and

G
.
The latter is the observed free energy change which varies with the
concentrations of reactants
.

Inside cells conditions are rarely if ever
near the standard state.

Thus for the reaction we defined previously:



G


= (
c
G

C

+
d
G

D
)


(
a
G

A

+
b
G

B
)


THERMODYNAMICS:Free Energy R
x


Free Energy Change of Chemical Reactions and K’
eq
:


At equilibrium the free energy is at a minimum, and the free energy change
is zero, thus







[C]
c

[D]
d



0

=


G


+ RT ln [A]
a

[B]
b








[C]
c

[D]
d





G



=


-


RT ln [A]
a

[B]
b

The equilibrium constant for the reaction we defined is:






[C]
c

[D]
d




K’
eq


=





[A]
a

[B]
b

Thus




G



=

-
2.303RT log K
´
eq



Lehninger 1977

A reaction with a negative free energy can proceed
spontaneously
. By coupling
reactions in Bioenergetics

a spontaneous reaction can drive a non
-
spontaneous
reaction.



Products

K
eq

= Reactant


K
eq
,

G
°
, and R
x

Direction

Effect of ∆H and ∆S on

∆G, the Reaction Spontaneity

Voet, Voet & Pratt 2013 Table 1.4

Temperature Dependence of Free Energy

Van’t Hoff Isochore and Equilibrium

K
eq

varies with
T

according to the van’t Hoff isochore.

ln
K
eq

=
-

(

G/RT)

Assuming H is independent of temperature one can write:






H 1



log K =
-

2.303R T


+ constant


Thermodynamics Dictionary 1976 p233


If

H is constant and we integrate the Gibbs
-
Helmholtz eq. We can
write:



K
eq2

=

H 1 1


ln


K
eq1

R T
1

T
2

THERMODYNAMICS

Principles for Coupled Reactions K
´
eq

and

G

´

Segal 1976

1.
The overall
K
´
eq

for any number of consecutive reactions 1, 2, … 3,
etc., is:






K
´
eq1

x

K
´
eq2

x

K
´
eq3

x
… etc

2.
The overall


G

´


for any number of consecutive reactions is







G

´
1

+


G

´
2
+


G

´
3
+
…etc

3.

T
he



G


´

overall

can also be calculated from

K’
eq
overall

:






G


´

overall

=

-
2.303RT log
K
´
eq


4. The
K
´
eq

for a single reaction can be expressed as the product of two or
more consecutive reactions and

G

´

can be expressed as the sum of two or
more consecutive reactions.

THERMODYNAMICS

Coupled Reactions: A General Principle


The

G

´
(or
K
´
eq
) values provide a convenient way to classify and tabulate
various kinds of reactions but they do
not

necessarily indicate the direction in which a
reaction may go in a
living cell
. The spontaneous direction
in vivo
(the nonstandard
-
state

G

values) depends on the
intracellular concentrations

(activities) of the
reaction components.


Segal 1976

Lehninger 2000 p498

Topic:Electron Transport


Coupled Reactions and

G Calculation


Endergonic reaction may be driven toward completion by coupling them to
highly exergonic reactions. The coupling may be so intimate so that the overall
coupled reaction appears as a single step (e.g. the hexokinase or citrate synthase
metabolic reactions), or the coupling my take place in two or more consecutive steps
(e.g., the fumarate


citrate sequence). In sequential reactions, one can think of the
subsequent exergonic reaction removing the product of the preceding endergonic
reaction as it is formed, thereby driving the overall reaction sequence to the right
(final product).

Segal 1976

Hydrophobic Force:

Description

The thermodynamic drive for the system to adopt a conformation in
which the contact between the nonpolar portions of the lipids and
water is

minimized
. The “force” in entropically based and results
from the energetically unfavorable restraints placed on water as it
packs around a nonpolar hydrocarbon.

Water/Phospholipid Thermodynamics

When a nonpolar substance is dissolved in
water , it causes and unfavorable organization
of water around each molecule. Water
molecules orient themselves to maintain
intermolecular hydrogen bonds (5
-
7 kcal/mole
each). However, since the water molecules
adjacent to the nonpolar molecule have fewer
neighboring water molecules there are
substantial configurational constraints on the
system. Hence there is a decrease in the
entropy
of the system.

In addition, there is no large
compensating electrostatic interaction as in the
case of ionic or polar molecules.


Thermodynamic Functions:

Definitions


E



Q


W






Internal Energy

Thermodynamic Dictionary 1976 p113


A



E
-
TS





Helmholtz Free Energy

G



A + PV =
H


TS

=
E


TS + PV

Gibbs Free Energy

H



E + PV





Enthalpy