Biochemistry 304 2014 Student Edition Thermodynamics Lecture

Report
CHEMICAL THERMODYNAMIC
PRINCIPLES
Student Edition
5/23/13
SIGNIFICANCE FOR BIOLOGICAL SYSTEMS
AND PHARMACOLOGY
Dr. Brad Chazotte
213 Maddox Hall
[email protected]
Website:
http://www.campbell.edu/faculty/chazotte
Original material only © Chazotte 2000-14
Pharm. 304
Biochemistry
Fall 2014
Topic: Thermodynamics
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
•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.
Topic: Thermodynamics
THERMODYNAMICS
SOME PHARMACOLOGICAL APPLICATIONS II
•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).
Topic: Thermodynamics
THERMODYNAMICS
SOME BIOLOGICAL APPLICATIONS
•Diffusion
•Osmosis
•Substrate Transport
•Bioenergetics
•Metabolism and Metabolic Pathways
•Membrane Formation and Structure
•Protein Structure
•Receptor Binding (Drug-Receptor Binding, Immunological function
Cell Signaling)
Topic: Thermodynamics
 Versus d
dy
dx
Consider some function
y = f(x)
X
dx
X
Y
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
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
Topic: Thermodynamics
reaction occur.
Some Thermodynamic Constants
and Conversion Factors
1 calorie (cal)
= 4.184 joules (J) = 0.041293 liter atm
1 Joule (J)
= 1 kg m2 s-2 = 1 C V (coulomb volt)
kb (Boltzmann constant)
= 1.3807 x 10-23 J K-1
0 ºC (ice point)
= 273.15 Kelvin (K)
R (gas constant)
= 8. 315 J deg-1 mol-1 =
NA kb
= 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
Relates pressure-volume
product to the number of
moles of gas.
Where:
P= pressure (atm or torr)
V = volume (liters)
n= number of moles (1 mole = 6.023 x 1023 molecules)
R= gas constant
T = absolute temperature º K
Topic: Thermodynamics
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.
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.
Wall 1975
System and Surroundings in Thermodynamics
Heat
Surroundings/Universe
-
+
Adibatic
+
System
Boundary
Closed System
Matter
Open System
Topic: Thermodynamics
Work
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.
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
Wall 1975
THERMODYNAMICS
Definitions: Pressure, Volume and Temperature
Describes physical and chemical phenomena in terms of macroscopic
properties, e.g. temperature, pressure, and volume.
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)
Cramer & Knaff 1990
TEMPERATURE and HEAT FLOW
Heat flow (Q)
60º C
50º C
Topic: Thermodynamics
THERMODYNAMIC PROPERTIES
The state of a system is determined at any given time by the values of
its macroscopic properties:
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
Cramer & Knaff 1990
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
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.
Cramer & Knaff 1990
State Functions and Paths
P2
State 2
P
P1
State 1
V1
V2
V
THERMODYNAMIC PROCESSES
Definitions:
Isothermal:
constant temperature
Isopiestic:
constant pressure
Isochoric:
constant volume
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.
Cramer & Knaff 1990; Wall 1974
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
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.
Cramer & Knaff 1990
THE LAWS OF
THERMODYNAMICS
Topic: Thermodynamics
THERMODYNAMICS
THE ZEROTH LAW
Any two bodies or systems in thermal equilibrium with a third body or
system are in thermal equilibrium with each other.
System A
Q =0
333 º K (60º C)
System B
333 º K (60º C)
Q =0
System C
TA = TB and TB = TC
Then TA = TC
Topic: Thermodynamics
THERMODYNAMICS: 1st 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 dV can be written:
dW = +pdV
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, SpringerVerlag, 1990. Note that they are OPPOSITE)
E = Q + W
dW = -pdV
where dW is positive for work done on the system.
Cramer & Knaff 1990
THERMODYNAMICS: 1st 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
We can write a general expression for the enthalpy change
dH = d(E + PV) = dE + PdV + VdP
= dQ –dW +PdV +VdP
dH = dQ + VdP
Then for system PdV work (VdP=0):
(For such a system undergoing a change at constant P: dH = qp)
The enthalpy is then defined as H  E + pV
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.
Cramer & Knaff 1990
THERMODYNAMICS
pV work
x
vi
x
vi
v
Consider a piston in a cylinder of initial volume vi moving x to
create a final volume vf = vi + v
Topic: Thermodynamics
THERMODYNAMICS
THE SECOND LAW
•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.
Topic: Thermodynamics
THERMODYNAMICS: 2nd Law Definition
THE SECOND LAW OF THERMODYNAMICS
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.
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.
Cramer & Knaff 1990
THERMODYNAMICS: 2nd 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 Sirrev > qirrev/T.
Wrev > Wirrev
S Units: J K-1 mol-1
Cramer & Knaff 1990
THERMODYNAMICS
THE THIRD LAW
The entropy of a perfect crystal at absolute zero is equal to
zero.
lim
T
S = 0
0
Topic: Thermodynamics
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
(S)E,V = 0
or alternatively the internal energy is at a minimum
(E)S,V = 0
Cramer & Knaff 1990
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.
Free Energy G (Gibbs Free Energy) G  H – TS
= E - TS + PV = A + PV
At constant temperature and pressure
Gp,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 :
Greaction = G products -  Greactants
Cramer & Knaff 1990
THERMODYNAMICS
CHEMICAL REACTIONS, EQUILLIBRIUM, AND
FREE ENERGY
Topic: Thermodynamics
THERMODYNAMICS
CHEMICAL REACTIONS: Definitions
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)
Topic: Thermodynamics
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:
[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.
Cramer & Knaff 1990; Lehninger 1977
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
[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 102]
G = -21,456 J mol-1 = -5109.2 cal mol-1
Cramer & Knaff 1990; Lehninger 1977
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)
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.)
Cramer & Knaff 1990; Lehninger 1977
2
Standard States for Free Energies of Reaction (G) :
Free Energy Standard State
Each chemical compound has a characteristic intrinsic free energy by virtue
of its molecular structure.
G = G prod -  G react (also called Gf, free energy of formation)
Thus for the reaction we defined previously:
G = (cG C + dG D) – (aG A + bG B)
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.
Cramer & Knaff 1990; Lehninger 1977
THERMODYNAMICS:Free Energy Rx
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
Thus
K’eq
=
G
=
[A]a [B]b
-2.303RT log K´eq
Lehninger 1977
Keq, G°, and Rx Direction
Products
Keq = Reactant
A reaction with a negative free energy can proceed spontaneously. By coupling
reactions in Bioenergetics a spontaneous reaction can drive a non-spontaneous
reaction.
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
Keq varies with T according to the van’t Hoff isochore.
ln Keq = - (G/RT)
Assuming H is independent of temperature one can write:
H
1
log K = - 2.303R T + constant
If H is constant and we integrate the Gibbs-Helmholtz eq. We can
write:
Keq2 = H 1
ln Keq1
R T1
1
T2
Thermodynamics Dictionary 1976 p233
THERMODYNAMICS
Principles for Coupled Reactions K´eq and G´
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.
The
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.
Segal 1976
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 nonstandardstate G values) depends on the intracellular concentrations (activities) of the
reaction components.
Segal 1976
Coupled Reactions and G Calculation
Lehninger 2000 p498
Topic:Electron Transport
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
H 
E + PV
Enthalpy
G 
A + PV = H – TS = E – TS + PV
Gibbs Free Energy
A 
E -TS
Helmholtz Free Energy
Thermodynamic Dictionary 1976 p113

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