Physical Chemistry for the Biosciences I (Ch 416 )



|Physical Chemistry for the Biosciences I (Ch 416 ) |

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|Shankar B Rananavare |

|Email: Rananavares@pdx.edu |

|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 |

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|Supplementary Text |

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|Physical Chemistry |

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|P. W. Atkins |

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|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. |

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|Prerequisite: Ch 223 or 203 and Ch 229, Ch 320, 321, a year of general physics, and two terms of calculus |

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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

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Tentative Schedule

|Tuesday |Thursday |

|1 Oct: #1 Introduction Preliminaries |3 Oct. #2: First Law of thermodynamics: Equation of |

|Thermodynamic concepts (chapter2) |State(chapter 2) |

|8 Oct: #3: Heat of formation of molecules (Chapter 2) |10 Oct #4: Second Law of thermodynamics: Notion of entropy |

| |Chapter(3) |

|15 Oct: #5 Measurement of Entropy and Third law of |17 Oct #6: Gibbs and Helmholtz Free Energies. (Chapter3) |

|thermodynamics (Chapter 3) | |

|22 Oct: #7 Free energy: Chemical Potentials, activity |24 Oct #8: Electrochemistry: Galvanic Cells Biochemical |

|coefficients, equilibrium constants (Chapter 4) |applications (Chapter 4) |

|29 Oct: #9 Biochemical Redox Reactions (Chapter 4) |31 Oct. #10 Midterm |

|5 Nov: #11 Membrane Transport, Ligand Binding, Colligative|7 Nov #12: Phase Equilibrium (Chapter 5) |

|properties (Chapter 5) | |

|12 Nov: #13: Membrane Transport, Active vs. Passive; |14 Nov #14: Continuation |

|Surface tension (Chapter 5) | |

|19 Nov: #15 Kinetic theory, Molecular Collisions (Chapter |21 Nov #16 Diffusion, Sedimentation and Viscosity (Chapter 6) |

|6) | |

|26 Nov: #17 Continuation |28 Nov (Thanks giving Holiday) |

| |No lecture |

|3 Dec: # 18 Electrophoresis (Chapter 6) |5 Dec #19 Emerging applications |

|10 Dec: Final | |

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 Energy and it’s inter-conversion key concepts

o Heat

o Work

o Thermodynamics and notion of Equilibrium

o Laws of thermodynamics strength and weakness

o Application to biological Problems

▪ The First law

▪ The Second Law

▪ The Third Law

o 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 Chemical, (gasoline for car for example)

o Electrical (lighting bulb)

o Thermal (heating house)

o 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.

Key idea: energy can be inter-converted from one form to another.

Thermodynamics concerns with this problem of inter-conversion of energy.

Laws of Thermodynamics

3 First law: Total Energy is conserved

1. Second Law: Efficiency of the inter-conversion is not 100%; Criteria for spontaneous process

2. 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 Closed flask Beaker of boiling water

[pic] [pic] [pic]

Isolated Closed 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.

[pic]

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:

[pic]

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:

[pic]

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:

[pic]

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.

[pic]

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.

[pic]

[pic]

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

[pic]

Coiled Normal Transition Irreversible

Work required to stretch from r=1 to 1.6?

[pic]

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:

[pic]

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.

[pic]

Where C is heat capacity, and q, T are heat and temperature. Since we can only measure temperature we can rewrite:

[pic]

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:

[pic]

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:

[pic]

H. Von Helmhotz stated this in 1847. For isolated system ΔE=0. What about an open system?

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Gasoline

(tank)

Engine: Combustion/explosion

Locomotion

Charge Battery

Sound

Light

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