Transcript to 1

Physical Chemistry
Reference: Physical Chemistry
Principles and Applications in Biological Sciences
Tinoco and others
Fourth Edition-2002
By
Dr. Gehan Abdel Raouf
1
Principles of Physical Chemistry
• Physical chemistry has been especially powerful in
understanding fundamental biological processes.
• Its principles are basic to the methods used to
determine the sequence of the human genome,
obtain atomic resolution structures of proteins and
nucleic acids, and learn how biochemicals react and
interact to make a cell function.
2
Course Portfolio
• Thermodynamics
• Intermolecular forces
• Quantum mechanics and its biological
application
• Chemistry of radiation
• Pharmacokinetics
3
Principles of thermodynamics
• Thermodynamics deals with interchanges
among different forms of energy {energy
conversion and conservation}.
• It is the change in energy in which we are
interested.
• The three laws of thermodynamics have been
summarized as:
You can’t win, you can’t break even, and you
can’t get out of the game.
4
Thermodynamics
• Thermodynamics originated as the study of
the relationship between mechanical and
thermal energy- the energy associated with
the disordered motions of the atoms and
molecules within a substance
• It is important whenever temperature play a
role.
5
Applications
• How do you calculate the work done when
muscle contract or stretches?
• How can chemical reactions be used to do
work or to produce heat?
• How much heat can be generated by burning
1 g of sugar or from heating and digesting 1 g
of sugar?
6
Systems
• System
• Surroundings
• Boundaries
• Systems:
-Closed system ex. Water in a beaker plus
evaporated water.
-Open system ex. Water in a beaker only.
7
Work and Heat
• A system can do work on the surroundings, or
the surroundings can do work on the system.
• Work: is defined as the product of force times
a distance.
W= F.dX , F is the force in newtons (N)
X is the distance in meter (m)
W is the work done in joules(J)
also 1 erg=10-7J , 1cal= 4.184J
8
Work and Heat
• Work is positive if the surroundings are doing
work on the system.
• Work is negative if the system is doing work
on the surroundings.
• Work of extending spring(Hooke’s law)
Ex. DNA, muscle fiber
• W= F(X2-X1) , F= - k.dx
9
• Work in gravitational field
• Work in an electric field
• Radiation energy= hγ
W=mg(h2-h1)
W=vIt
10
Work of increasing or decreasing volume
• P=F/A , F=PA
• W= F.dX
= PA.dX ,A.dX= dV
=- P.dV
Compression a decrease in volume or a –ve dV, means
the surroundings have done work on the system and
W is +ve.
Expansion an increase in volume or a +ve dV, means
the system dose work on the surroundings and W is
–ve.
11
Ex. 2.2 P 22
• Calculate the PV work done when a system
containing a gas expands from 1.0L to 2.0L
against a constant external pressure of 10
atm.{1L.1atm.= 101.325J}
• W = -P(V2-V1)
=-10(2-1) = -10 L.atm
W =-10x101.325 = -1013 J
the system dose work; W is negative.
12
Heat
• When two bodies are in contact with each
other, their temperatures tend to become
equal.
• Energy is being exchanged. The hot body will
lose energy and cool down; the cold body will
gain energy and warm up. {heat transfer}
• Heat is +ve if it flows into the system
• Heat is -ve if it flows out of the system
13
•
•
For closed system, the transfer of a small quantity of heat dq will result in a change dT in
its temperature.
The ratio dq/dT is called heat capacity C
C = dq/dT → q= C(T2-T1)
Heat capacity of every material: is a quantity that characterizes how much heat is necessary
to raise its temperature by 1oC or 1 K.
It is usually determined by measuring the changes in temperature when known amounts of
electrical energy are dissipated in this material.
Its units are
JK-1mol-1
or
cal K-1mol-1
, K = oC + 273.15
- C is different for different materials, and for a given material, C will vary with temperature.
- For a hot body in contact with cold body, the heat capacity C of each body must be known
and the equation
q= C(T2-T1) must be applied separately.
- C is increasing with the amount of materials in the body.
- For a pure chemical substance
-
C= nC¯ , n is the number of moles
C¯ is the molar heat capacity
14
• Ex. 2.5 p 26
• Calculate the heat, in joules, necessary to change the
temperature of 100 g of liquid water by 50oC at
constant pressure. The heat capacity of liquid water
at constant pressure is 1 cal g-1 deg-1 and is nearly
independent of temperature.
(1cal= 4.184J)
• The heat absorbed by the system
• q=C(T2-T1)
• = 100g (1 cal g-1 deg-1 )x(50 deg)x4.184
•
=20.9 KJ
15
First law of thermodynamics
• It states that energy is conserved; it can be transferred
between the system and surroundings, but the total energy
of the system plus surroundings is constant.
• In open system: the change in energy ΔE of the system is
equal to the amount of energy that entered it( from the
surroundings) minus the energy that went out of it (into
the surroundings).
• In closed system:
• ΔE=q +W , q is the net heat transferred to the system
W is the net work done on the system (in)
ΔE equals the change in energy of the system
16
Additional terms can be added to the equation if there
are energy exchanges other than heat and work
between the system and surroundings or if the
system is open one.
ΔE= zero for an isolated system
• Because E is a property of the system, it is sometimes
called the internal energy of the system.
17
• Pressure P, volume V, and temperature T can
specify many other properties of liquid for
example, such as its density, surface tension,
refractive index, and so forth.
• All these properties of the system together
with P,V, and T are called variables of state.
• Work and heat depend on the path between
states
• Enthalpy H is a new variable of state
• H= E+PV
18
• The energy or enthalpy change when the teaspoon
of sugar is converted to CO2 and H2O is the same
whether sugar is burned in a reaction vessel or
metabolized in human body, as long as the final
states for the reaction are the same in the two cases.
• It does not matter whether the conversion involves a
direct reaction with O2 (combustion) or multiple
enzyme-catalyzed steps inside a human being
• Table A.6
table 2.3
• The bond dissociation energy is the enthalpy at 25oC
and 1 atm, for the reaction.
• A-B (g) →A (g) + B(g)
19
20
21
Ex.2.13 p54
• Calculate the heat of formation for gaseous cyclohexane using tble 2.3 and
comapre with the measured value in the appendix (table A.6).
• The rection for the formation of cyclohexane is
6C(graphite)+6H2(g) →C6H12(g)
• We can write it as a sum of bond-breaking and bond-forming reactions
• 16C(graphite)→6C(g)
ΔH1=6D(graphite) = 6x716.7=4300KJ
• This is the enthalpy required to remove 6 mol of carbon atoms from the
crystalline lattice of graphite, which is the standared state for elemental
carbon.
• 2-
6H2(g) →12H(g)
ΔH2=6D(H2 )=6x436 = 2616 KJ
• 3- 6C(g) + 12H(g) →{6(C-C)+12(C-H)}=C6H12(g)
ΔH3=-6D(C-C) -12D(C-H)= -6x344 -12x415
= -7044 KJ
Note that bond formation energies are just the negative
of bond dissociation energies
22
• ΔHf = ΔH1 + ΔH2 + ΔH3
= (4300+ 2616)- 7044= -128KJ
The value in table A.6 is -123.15KJ which is in
good agreement. (molecule with normal
bond)
23
Ex. 2.14
• Calculate the heat formation for gaseous benzene using table 2.3 and compare with
the measured value in table A.6 in the appendix.
• The reaction for benzene is
6C(graphite)+3H2(g) →C6H6(g)
• 16C(graphite)→6C(g)
ΔH1=6D(graphite) = 6x716.7=4300KJ
•
2-
•
3- 6C(g) + 6H(g) →{3(C-C)+3(C=C)+6(C-H)}=C6H6(g)
ΔH3= - 3D(C-C) -3D(C=C) - 6(C-H)
= -3x344 - 3x615 – 6x415
= -5367 KJ
•
ΔHf = ΔH1 + ΔH2 + ΔH3
= (4300+ 1308) - 5367= 241 KJ
3H2(g) →6H(g)
ΔH2=3D(H2 )=3x436 = 1308 KJ
The value in table A.6 is 82.93 i.e is about 158 KJ lower in enthalpy than would be
expected.
This energy is what we call the resonance energy.
24
Chapter 3. The second law
The entropy of the universe increases
•
•
The second law of thermodynamics can be phrased in several ways.
In term of macroscopic description of a system, it states that a quantity called the
entropy S tends to increase in all processes.
Macroscopic variable such as temperature, pressure, and volume.
•
At the microscopic level, entropy is closely related to the randomness or disorder of the
constituents; all systems tend toward states of greater disorder.
•
Example: every time we freeze an ice tray full of water in the freezer, we are increasing
the order the order in ice tray. However, the disorder caused by the heat released
outside the freezer compartment more than balances the order created in the ice.
•
The total disorder in the universe has increased; the total entropy of the universe has
increased
•
The greater the disorder the greater the entropy i.e. entropy is a quantitative measure
of disorder and it is not conserved.
Like the internal energy, the entropy of a system depends only on its state and not on
how that state is achieved.
•
25
Entropy
mol-1
H2O(s)
41
H2O(l)
63.2
188.3
H2O(g)
Entropy
mol-1
JK-1
JK-1
Carbon
(diamond)
2.4 JK-1 hard
JK-1
Carbon
(graphite)
5.7JK-1 soft
26
• All entropies increase as the temperature is
raised, because increasing molecular motion
increases disorder and thus increases the
entropy.
27
Gibbs free energy
• Gibbs free energy G, defined as the enthalpy H minus the product of
the absolute temperature T and the entropy S.
G= H-ST
• ΔG is -ve→ the process occurs spontaneously.
• ΔG is +ve→ the process can not occurs
spontaneously.
• ΔG = 0
→ the system is at equilibrium
• Thermodynamics allows us to decide which reactions are impossible
under given conditions and how the conditions can be changed to make
impossible reactions poprobable.
e.g.
graphite → diamonds ????
28
Noncovalent reactions p97
• If two points charge +e and -e are separated by a distance r, the dipole
moment= er
• Types of Interactions:
1- Ion dipole interactions
A charged ion and a neutral molecule with a dipole moment (such as water
molecule) are called ion dipole interactions.
2- charge-induced dipole moment
Ions can also interact with neutral molecule with zero dipole moment (such as
CCl4) causing the molecule to be polarized. We say that the molecule has
induced dipole moment and the interaction is called charge-induced dipole
moment.
3- London interaction (only attractive force)
induced dipole-induced dipole interaction:
Also exist because the fluctuations in the electronic distributions in the
molecules.
An induced dipole moment molecule can induce a dipole in the neighboring
molecule.
4- van der Waal interactions
Include permanent-dipole permanent dipole interactions.
29
Noncovalent reactions p97
The London-van der Waal forces can become specific when carful fitting of molecules
is involved.
Binding of a particular substrate to an enzyme, antigen-antibody binding, and the
function of specific membrane lipids may be dominated by The London-van der
Waal interactions.
5- The hydrogen bond
Is one of the important bonds that determines the three dimentional structure of
proteins and nucleic acids. O-H..O, N-H..N, N-H..O .
6- Hydrophobic interactions (fear of water)
It is important in aqueous solutions. Water molecules have a strong attraction for
each other (as a consequence of hydrogen-bond formation).
The oxygen atom of most molecules of liquid water is hydrogen-bonded to two
hydrogen atoms of two hydrogen atoms of two other water molecules and also
the hydrogen atoms.
Therefore, the molecules of liquid water form a mobile network. The network is not
a rigid one, and change in neighbors occurs rapidly because of thermal motions.
30
Noncovalent reactions
• Water-soluble proteins, polar lipid molecules form bilayer
sheets or membranes in water, in which the hydrocarbon
proteins are buried inside and the polar or charged proteins
are on the surface exposed to water. Such molecules are
called amphiphilic.
• Hydrophobic interactions are characterized by low enthalpy
changes and are entropy driven.
• We should note that hydrophobic interaction is a term that
we use to describe the combined effects of London, van der
Waals, and hydrogen-bonding interactions in certain
processes in aqueous solutions
31
32
Proteins and Nucleic Acids p101
• Proteins are polypeptides of 20 naturally occurring
amino acids.
• Amino acids are linked by amide bonds from the
carboxyl group of one amino acid to the amino group
of the next (fig. 3.4).
• The sequence of amino acid residues in a polypeptide
is called primary structure.
• The polypeptides fold into different secondary
structures held together by hydrogen bonds and
other non covalent interactions.
33
34
• The different folded conformations of a polypeptide
depend on rotation about the two single bonds
attached to the amide group, fig.3.4.
• α-helix is a common secondary structure element in
proteins.
• Nucleic acids are polynucleotides of four naturally
occurring nucleotides. The nucleotides are composed of
a sugar group connected to one of four bases and to a
phosphate group.
• Nucleotides are linked by phosphodiester bonds (fig.3.6
b). The sequence of the bases in the polynucleotide is
the primary structure.
• The stacking of the base pair, one above the
other, plus the hydrogen bonds between bases
provide the stabilizing enthalpy and free energy
of the helix
35
36
• Table 3.2 measured enthalpies for biochemical
reactions involving changes in shape (conformation)
of molecules.
• By changes in conformation, we mean changes in
the secondary structure of the molecule (the
primary structure involves the covalent bonds) e.g.
change in a polypeptide from a rigid helix to a
flexible coil.
• Denaturation of proteins involves this type of
change.
37
38
Chapter 4
Free energy and chemical equilibria
• When a chemical reaction occurs in a closed system,
the amounts of the reactants decrease, and the
amounts of the products increase, until an equilibrium
position is reached.
• At equilibrium, the reactant and products can
interconvert, but the composition of the system
remains unchanged.
• We learned in the preceding chapter that at constant
temperature and pressure, the change in the Gibbs free
energy G of a system undergoing a spontaneous
reaction must be -ve. If ΔG is +ve, only the reverse
reaction can spontaneously occur; if it is zero, the
system is at equilibrium.
39
Free energy and chemical equilibria
• The Gibbs free energy G of an open system is dependent on
the temperature, pressure, and the amounts of materials that
make up the system (concentration).
• When a very small amount of a substance is added to the
system at constant temperature and pressure without
changing any of the other composition variables, the change
in G per mole of the substance added is termed the partial
molar Gibbs free energy of the added substance.
• Thus, the partial molar Gibbs free energy of a substance
determines its chemical potential μ in a reaction at constant
temperature and pressure.
• Temperature, pressure, composition variables (partial
pressures for gases in a gaseous mixture and concentrations
for solutes in a solution) influence the chemical potential of a
substance.
40
Applications in biological systems
1- Metabolic reactions in which chemical bonds are
broken and new ones formed.
2- Dissociation of H+ from acidic compounds and
binding H + to bases.
3- Oxidation-reduction reactions in which electrons
transfer occurs.
4-Interactions involving the aqueous medium in which
metabolites and ionic species occurs in the
cytoplasm or other biological fluids.
5- The assembly and disassembly of membranes and
other multicomponent cellular structures.
41
Chapter 5
Free energy and physical equilibria
• Applications
• Membrane and transport
• Most biological membranes consist of a lipid bilayer that
contains proteins and other molecules that serve as
recognition sites, signal transmitters, or ports of entrance and
exit.
• Membranes are so thin that they are often considered to be
two-dimensional phases.
• The thermodynamic properties of the membrane are then
described in terms of surface properties, such as the surface
chemical potential and the surface tension or pressure.
42
• Membranes permit the controlled transport of
molecules and signals between the inside and
outside.
• Difference between the inside and outside of a cell
influence the exchange of metabolites and electrical
signals, the flow of heat, and changes in shape.
1- Temperature differences causes heat flow.
2- Pressure differences cause changes in shape.
3- Electrochemical potential differences cause
molecular transport and electrical signals.
43
Ligand binding
p188
• Noncovalent interactions that bind ligands like O2 to
hemoglobin, substrate to enzymes, and complementary
strands of DNA or RNA to one another underlie essential
dynamic processes in living cells.
• Equilibrium dialysis provides a method of exploring the
binding between macromolecules and small ligand
molecules.
• In equilibrium dialysis a semipermeable membrane allows a
ligand to reach equilibrium between two phases, one of which
contains a macromolecule. The difference in concentrations of
ligand on opposite sides of the membrane depends on the
interaction of ligands and macromolecule.
44
Colligative properties
• The chemical potential must be the same for each
component present in two or more phases at
equilibrium with one another.
• The component can be the solvent or each of the
solutes in a solution. The phases are solids, liquids,
gases, or solution compartments separated by a
semipermeable membrane.
• Any change in a property such as temperature,
pressure, or activity in one phase that results in a
change in chemical potential must be accompanied by
an equal change in chemical potential in the other
phase, for the for the system to remain in equilibrium.
45
• This fundamental fact allows us to explain the colligative
properties, such as
• 1- the freezing point lowering
• 2- the boiling-point elevation
• 3- the vapor-pressure lowering
• 4- the increase of osmotic pressure when a solute is
dissolved in a solvent.
• Colligative properties play essential roles in biological cells.
• Osmotic pressure that results from the activities of
components present in the cytoplasm needs to be balanced
by a suitable external pressure lest the cell rupture and burst.
• Colligative properties are used
• 1- To determine the concentrations and molecular weights of
solutes in solution
• 2- To measure association and dissociation equilibrium
constants of biopolymers.
46
•
•
•
•
•
Phase equilibria
The transfer of a chemical from one phase to another is
illustrated by :
1-the evaporation of liquid water into vapor phase
2- the heat removed from our bodies by evaporation of sweat
is essential to survival in hot climates.
3- the transport of ions from inside a cell to outside, which is
vital to nerve conduction.
(we can consider the inside and the outside of the cell as two
different phases).
47
• Equilibrium is a state where nothing seems to happen-nothing
apparently changes with time.
• For living system to exist, they must be out of equilibrium;
dynamic processes need to occur to maintain the living state.
• When an organism dies; it approaches closer to equilibrium.
• The usefulness of considering equilibrium in connection with
living organisms is that it helps define the direction of
dynamic processes.
• One of the consequences of the second law of
thermodynamics is that spontaneous processes result in the
system moving toward a state of equilibrium.
• For an open system, spontaneous processes are
accompanied by a decrease in chemical potential,
Δμ ≤ 0.
at equilibrium ΔμT,P =0
48
• Equilibrium dialysis
see p 197- p 200
• If we had to rely only on normal saline solution flowing in our
veins and arteries, the amount of O2 transferred from our lungs
to muscle cells would be far too little to support life as we know
it.
• The dissolved oxygen concentration is too low, even if we
breath pure O2.
• Red blood cells (erythrocytes) solve this problem for us by
packaging hemoglobin (Hb) molecules, which are proteins
containing a heme that binds O2 strongly. Muscle cells contain a
related protein, myoglobin (Mb), that binds O2 and stores it
until needed.
• Red blood cells are packed full of Hb and contained by a plasma
membrane boundary.
• The plasma membrane is freely permeable to small, neutral
molecules like O2 but is impermeable to large protein
molecules like Hb and to many charged ions.
49
Equilibrium Dialysis
• The operation of the red blood cell is illustrative of a technique called
equilibrium dialysis that is a laboratory method of studying the binding
of a ligand (small molecule like O2) by a macromolecule (protein, nucleic
acid, etc.)
• Fig 5.4 p 197
• 1- Control, where no macromolecule inside the dialysis bag
• 2- Another control, where albumin protein is inside (it does not bind to
O2).
• 3- If a protein like myoglobin is in the bag, then the total concentration of
O2 (in mol/L) inside will be significantly larger than the concentration of O2
ouside, where myoglobin is absent.
• The presence of the Mb inside serves to concentrate the O2 by binding it.
• By series of quantitative measurements, it is possible to determine both
the binding equilibrium constant K and the number of ligand binding sites
per macromolecule.
50
51
• M+A ↔M.A ,M macromolecule
•
A single binding site for ligand A
•
•
•
•
•
•
•
K=[M.A] / [M][A] , K equilibrium constant
To relate these concentrations to the measurable quantities,
CM = [M.A]+[M]
cA(outside)=[A]
cA(inside)=[A]+[M.A]
cA(bound)=[M.A]
At equilibrium the activity of A inside is the same inside.
K=cA(bound)/ {cM - cA(bound)} cA(outside)
52
The Scatchard equation
• The equation of K can be simplified
• The average number of ligand molecules bound per macromolecule at
equilibrium =γ
γ = cA(bound)/ cM
, cA(bound)=concentration of A bound
cM concentration of macromolecule
K= γ / (1- γ)[A]
→ γ / [A] = K (1- γ)
The equilibrium constant was written with the assumption that only one molecule
of a was bound per macromolecule; i.e. Γ can vary only from 0(no ligand) to 1
(each macromolecule has bound an A).
However, many macromolecules have more than one binding site for ligand. (Hb
for example has four binding sites for O2).
53
Now γ can vary from 0 to N, the number of binding sites on
each macromolecule.
γ / [A] = K (N- γ)
The Scatchard equation
see Fig. 5.5
The slope = -K intersect the y-axis at NK
and x-axis at N
If there are N identical and independent binding sites per
macromolecule, this means that the N sites have the same
binding equilibrium constant K and that binding at one site
does not change the binding at another site.
54
• The Scatchard equation is often used to study binding to macromolecule.
• The value of [A] (free cA), is the concentration on the solvent side of the
dialysis membrane at equilibrium.
• The value of γ = cA(bound)/ cM is the concentration of A on the
macromolecule side at equilibrium.
• If a Scatchard plot does not give a straight line, this indicates
that the binding sites are not identical or not independent.
•
•
•
•
•
(The four binding sites for O2 in Hb are neither identical nor independent).
A macromolecule is made of monomer units, such as the peptide units in
a protein. A DNA molecule is a polynucleotide consisting of nucleotides as
its monomer building blocks.
Sometimes it is more convenient to define the binding parameters on a
per monomer unit basis.
r= number of bound A per monomer unit of the macromolecule
n=number of binding sites per monomer unit of the macromolecule
r / [A] = K (n- r)
The Scatchard equation
55