Download Physical Chemistry for the Biosciences I (Ch 416 )

Physical Chemistry for the Biosciences I (Ch 416 )
Shankar B Rananavare
Email: [email protected]
Phone: 503-725-8511
Office: Science Bldg. II Rm. 358
Office Hours: MWF 1-3pm
Text
Physical Chemistry: Principles and Applications in Biological Sciences
Tinoco.Saur.Wang.Pulglisi
Supplementary Text
Physical Chemistry
P. W. Atkins
Course Description
Intended primarily for students in the biological sciences and allied medical
health fields. The emphasis is on the application of modern physical chemistry to
problems of biological interest. Ch 416 includes the study of heat, work, energy,
entropy, vapor pressure, chemical equilibrium, and transport phenomena. These
fundamental concepts find applications in variety of biological phenomena
ranging from bioenergetics to electrical nerve signal transmission. The course will
cover Chapters 1-6 during the fall quarter. Emerging new biotechnological
applications involving gene/protein biochips will be also presented.
Prerequisite: Ch 223 or 203 and Ch 229, Ch 320, 321, a year of general physics, and two
terms of calculus
General Issues
Grading
o 30% Homework
o Discussion group meeting once a week for 1 hour
o 30% Midterm
o 50% Final
Lectures Notes Available by email
Name
Math/phys
Email
Tentative Schedule
Tuesday
1 Oct: #1 Introduction Preliminaries
Thermodynamic concepts (chapter2)
8 Oct: #3: Heat of formation of
molecules (Chapter 2)
15 Oct: #5 Measurement of Entropy
and Third law of thermodynamics
(Chapter 3)
22 Oct: #7 Free energy: Chemical
Potentials, activity coefficients,
equilibrium constants (Chapter 4)
29 Oct: #9 Biochemical Redox
Reactions (Chapter 4)
5 Nov: #11 Membrane Transport,
Ligand Binding, Colligative properties
(Chapter 5)
12 Nov: #13: Membrane Transport,
Active vs. Passive; Surface tension
(Chapter 5)
19 Nov: #15 Kinetic theory,
Molecular Collisions (Chapter 6)
26 Nov: #17 Continuation
3 Dec: # 18 Electrophoresis (Chapter
6)
10 Dec: Final
Thursday
3 Oct. #2: First Law of thermodynamics:
Equation of State(chapter 2)
10 Oct #4: Second Law of
thermodynamics: Notion of entropy
Chapter(3)
17 Oct #6: Gibbs and Helmholtz Free
Energies. (Chapter3)
24 Oct #8: Electrochemistry: Galvanic
Cells Biochemical applications (Chapter
4)
31 Oct. #10 Midterm
7 Nov #12: Phase Equilibrium (Chapter
5)
14 Nov #14: Continuation
21 Nov #16 Diffusion, Sedimentation
and Viscosity (Chapter 6)
28 Nov (Thanks giving Holiday)
No lecture
5 Dec #19 Emerging applications
November 11 Veteran’s Day observed – University closed
November 28-29 Thanksgiving Holiday – University closed
December 9-14 Final Examinations for Fall Quarter (last day of classes, Dec. 6)
Lecture 1
o
o
Energy and it’s inter-conversion key concepts
o Heat
o Work
Thermodynamics and notion of Equilibrium
o
o
o
Laws of thermodynamics strength and weakness
Application to biological Problems
 The First law
 The Second Law
 The Third Law
A quantitative picture
o
Notion of system: Open, Closed, Isolated
o
Concept of Work (sign convention)
 Mechanical
 Electrical
 Gravitational
 Frictional
o
Concept of heat
 Heat capacity
 Heat Transfer
o
First law of thermodynamics
Problem Set Assignment
Energy
There are many forms of energy that we use in daily life.
They may include:
o
o
o
o
Chemical, (gasoline for car for example)
Electrical (lighting bulb)
Thermal (heating house)
Mechanical (Lifting weight)
Take the case of gasoline. We know it is flammable and
explosive. We make use of the latter property to
controllably burn it in car to provide mechanical energy to
drive the car. The process can be thought of as follows.
Locomotion
Gasoline
(tank)
Engine:
Combustion
/explosion
Charge
Battery
Sound
Light
Key idea: energy can be inter-converted from one form to
another.
Thermodynamics concerns with this problem of interconversion of energy.
Laws of Thermodynamics
1. First law: Total Energy is conserved
2. Second Law: Efficiency of the inter-conversion is
not 100%; Criteria for spontaneous process
3.
Third Law: At absolute zero temperature there is a
perfect order
The first two laws were discovered in 19th century and the
third in 20th. These are very few laws of nature that are
assured to survive in that they define as much of science as
its philosophy.
For if they were not true we would have:
1. Perpetual machine
2. Immortality
These laws are triumph of experimental science. But as
chemist we must keep in mind their existence does not
depend on whether the matter composed of atoms or
molecules or some other structure. This is also their
weakness in terms of how we can apply them to
chemical/biochemical problems. More precisely they
apply to the systems at equilibrium. Dynamics or
kinetics of system cannot be predicted based on these
laws. Nevertheless these laws are foundation of natural
science.
How do we apply these abstract laws to real systems?
Key to application of these laws is the notion of a system.
System is part of universe we choose to focus. There are
boundaries between the system and rest of the
surroundings. Depending on the nature boundaries we
define different types of systems.
Thermos Bottle
Isolated
Closed flask
Closed
Beaker of boiling water
Open
o Isolated system: Neither mass nor energy flows in or
out of the system.
o Closed System: Energy can flow but not mass.
o Open System: Both energy and Mass can flow in or
out of the system.
This classification of the system is an example of idealized
way of representing reality. In practice, no system is
perfectly isolated; more importantly the biological systems
are open type. However it is common to use this type of
classification.
Work
We all know what work means in everyday life. In science,
we define work as follows.
W  External Force.  Displaceme nt
 F .d
Force could be any force we can identify e.g. electrical,
gravitational, mechanical etc. Displacement does not have
to be a physical distance; it can be an angle for example,
But in thermodynamic context, we have to define work bit
more precisely. Note the force is the external force,
meaning force exerted by the surrounding on the system. If
there is no external force then there is no work done by the
system. This ushers in the sign convention. The sign of
work in thermodynamics is positive if surrounding does the
work on the system, that is, the direction of displacement is
in same direction as the external force. If the direction of
displacement is in the opposite direction to that of the
external force then sign of work is negative, meaning that
the system does work on the surroundings.
Consider a rechargeable battery as an example of system.
When battery is discharging it is converting electrical
energy, by sending current to outside surrounding, to
perform useful work. In this instance, the work is done on
the surrounding so its sign is negative. While in charging
the battery, we are sending current into the battery from the
charger. So work is done on the battery by the surrounding,
hence the sign work in this instance is positive
Work done in lifting weight.
Consider a system made up weight of mass m. If the weight
is lifted to height h, we are doing work against gravitational
force, mg. Mathematically we write:
mg  FExternal   Fgravitational
W  Fexternal .displaceme nt  mgh
Since the movement of the weight is in the direction of
applied lifting force, its sign is same as the applied force
the work is done by the surrounding on the system of
weight. Therefore, the sign of work is positive. This is
particularly simple case of work, in that we have assumed
that the gravitational acceleration, g is independent of
displacement.
How do we treat the case if the force depends on the
displacement?
The problem can be resolved easily if we think of work as
an area under the force versus displacement curve. The area
under such curve can be calculated using the following:
W  Fexternal .displacement
W   FExtenal ( x).dx
Let us consider a simple example, where the force depends
on displacement.
Work done in stretching a spring
Consider a system made up of a spring. Hooks law from
freshman physics tells us that force needed to stretch or
compress a spring is proportional to the extent of extension
or compression. Mathematically we write:
FSpring  kx   FExternal
Where k is the spring constant, larger the k stiffer the
spring. x is the change in the length of the spring, i.e.
displacement from equilibrium. Note the external force is
opposite direction to that exerted by spring. This is
Newton’s third law! Now if we stretch or compress the
spring we are performing work on the spring. This can be
calculated easily applying the definition of work.
W  Fexternal .displacement
W   FExtenal ( x).dx
x
x
x
 
1
W   kx.dx  k  x.dx  k x 2
2
o
0
Units for work!
1 joule ≡ 1N-m ≡ 1kg m s-2
1 erg=10-7 J
1 cal=4.184J
This can also be demonstrated graphically.
0
1
 kx2
2
Hooks Law
2.0
Force(N)
1.5
1.0
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.8
1.0
Displacement(x)
Work involved in stretching
1.0
0.8
Work
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Displacement(x)
Note since the work depends on x2
This means whether we compress (-x) or stretch (+x)
through distance x, we perform identical amount of work.
Work done in stretching DNA
Coiled
Normal Transition
Irreversible
Work required to stretch from r=1 to 1.6?
1.6
W   f ex dl   fd (l0 r )  l0  f ex dr
1
 15  10 6 m  (26  15)10 12 N  6.15  10 18 N m
 6.15  10 18 J
Very small energy indeed! But compared to thermal energy
at body temperature: kT=1.38x10-23J/K x(273.15+37.4)K
=4.3x10-21J, it is thousand times larger, so DNA should not
be affected by body temperature.
p-V work
Consider following system where a mass-less piston is
resting on certain volume of gas trapped in cylinder. Now
to have equilibrium, pressure exerted by the surroundings
must equal pressure inside. If we apply excess pressure on
the contained gas by applying external
force, the volume of the gas will
decrease. In this instance, surroundings
have done work on the system of
trapped gas; so the sign of work is
positive. If, on the other hand, we
decrease the external pressure, to
maintain equilibrium the gas will expand
and it’s volume will increase. In this
case, system does the work on surrounding hence the sign
of work is negative.
These facts can be stated as:
FExtenal ( x)
W   FExtenal ( x).dx  
. Adx
A
F
W    PExtenal .dV  P 
and dV  Adx
A
Note the negative sign, if the volume decrease surrounding
does work on system.
Please read and work through problems in book 2.1-2.8.
Next we consider the connection of work to heat.
Heat
When we lift weights or exercise a common sensation
is that we feel warm. This sensation of warmth or heat is
measured by temperature.
Hot coffee becomes lukewarm if we do not drink it
quickly. More succinctly we can say that when two bodies
at different temperature when brought in contact will
develop identical temperature through exchange of heat.
How do we quantify heat? A common observation is that it
takes lot more heat to warm water than corresponding
volume of air (Think about heating water versus air with a
hair dryer). Thus, we measure heat by defining a special
quantity, heat capacity. Heat capacity of an object is the
amount of heat needed to raise it’s temperature by 1 degree.
dq q
C

dT T
Where C is heat capacity, and q, T are heat and
temperature. Since we can only measure temperature we
can rewrite:
q   C.dT  C (T2  T1 )
Generally C does not vary much with temperature except
near phase transition. T2 and T1 are the final and initial
temperatures. So if system cools then the sign of q is
negative since it looses heat to surrounding and vice versa.
Units of C are J/K. Similarly we can define specific molar
heat capacities depending on whether it is measured under
conditions of constant pressure or volume.
Relation between Work and Heat
The first law of thermodynamics.
In 1840, Joule performed pioneering set of experiments to
show:
W  Jq
Where a direct proportionality between work and heat was
established. The conversion factor J, is 4.18Joules/calorie
in honor of Joule.
Some of his experiments were very simple. He let
fixed weight to rotate paddle in water and measured the rise
in temperature. Similarly he passed current through resistor
and measured the rise in temperature.
Now we know that in a closed system, energy can
flow in either as work done on the system or as heat flow.
If the energy flows into the system it must be provided by
surroundings. Otherwise we will have invented a perpetual
motion machine. Although different forms energy may be
inter-converted, the first law states that the total energy of
system and surroundings is conserved. For a closed system
we may therefore write:
E  q  W
H. Von Helmhotz stated this in 1847. For isolated
system ΔE=0. What about an open system?