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CHEMICAL THERMODYNAMICPRINCIPLES
Student Edition 5/23/13
Topic: Thermodynamics
SIGNIFICANCE FOR BIOLOGICAL SYSTEMSAND PHARMACOLOGY
Dr. Brad Chazotte 213 Maddox Hall
Website:
http://www.campbell.edu/faculty/chazotte
Original material only © Chazotte 2000-14
Pharm. 304 Biochemistry
Fall 2014
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
Xdx
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 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
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 KTopic: 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
THERMODYNAMICSDefinitions: 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
THERMODYNAMICSDefinitions: 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
50º C60º CHeat 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
V2V1
P1
P2
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.
THERMODYNAMICSInternal 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 (60º C)Q =0 System BSystem A
Q =0
System C TA = TB and TB = TC
Then TA = TC
333 º K (60º C)
Any two bodies or systems in thermal equilibrium with a third body or system are in thermal equilibrium with each other.
THERMODYNAMICS: 1st Law
The First Law of Thermodynamics (Conservation of Energy):The total energy of a system and its surroundings does not change.
DE = DQ - DW
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, Springer-Verlag, 1990. Note that they are OPPOSITE)
DE = DQ + DW
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
Cramer & Knaff 1990
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.
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 = qp)
THERMODYNAMICSpV work
Topic: Thermodynamics
x
x
Consider a piston in a cylinder of initial volume vi moving x to create a final volume vf = vi + v
v
vi
vi
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: 2nd 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: 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 = TDS or rearranging: DS = 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 DSirrev > Dqirrev/T.
DWrev > DWirrev
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
THERMODYNAMICSDefinitions: 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
THERMODYNAMICSFREE 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
DGp,T = DH -TDS
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 :
DGreaction = DG products - DGreactants
THERMODYNAMICS
CHEMICAL REACTIONS, EQUILLIBRIUM, AND FREE ENERGY
Topic: Thermodynamics
THERMODYNAMICSCHEMICAL 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 1Free 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
DG = DG + 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
DG 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
DG = DG + 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 DG = -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
DG = -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
DG = -34,000 J mol-1 + 2477.9 joules mole-1 ln [1.58 x 102]
DG = -21,456 J mol-1 = -5109.2 cal mol-1
Free Energy Standard State 1Standard 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
DG´ 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 2Standard States for Free Energies of Reaction (DG) :
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)
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 = (cG C + dG D) – (aG A + bG B)
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 = DG + RT ln [A]a [B]b
[C]c [D]d
DG = - 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 DG = -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
Keq = Reactant
Keq, G°, and Rx 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
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
Thermodynamics Dictionary 1976 p233
If H is constant and we integrate the Gibbs-Helmholtz eq. We can write:
Keq2 = H 1 1
ln Keq1 R T1 T2
THERMODYNAMICSPrinciples for Coupled Reactions K´eq and DG´
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 DG´ for any number of consecutive reactions is
DG´1 + DG´2 + DG´3 +…etc
3. The DG ´ overall can also be calculated from K’eq overall :
DG ´ 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 DG´ can be expressed as the sum of two or more consecutive reactions.
THERMODYNAMICSCoupled Reactions: A General Principle
The DG´(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 DG 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
