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HyperPhysics - Electric Potential Energy

PY106 Notes - Electric energy and potential
Well-expressed and illustrated introduction to these crucial concepts. Includes an illustration of the concept of electric potential energy in the context of the ionization energy of an atom.



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Special points of emphasis

Work, Energy, and Power

Electricity

The general concepts of Work, Energy, & Power we discussed earlier are a framework to apply in interpreting the changes undergone by electrostatic systems. As you move through electrostatics, keep yourself fresh on the fundamentals of Work, Power, & Energy, because so much of the conceptual challenge is to understand what is happening with energy.

The work required to shift a system of charges from one arrangement to another represents the change in potential energy of the system. Keep it simple. Two like charges store energy as they are moved together. With unlike charges, energy is stored as they are moved apart. Imagine yourself physically pulling and pushing charges in space to understand potential energy changes in a concrete way.

When you have a good sense of the work involved in changing the relative positions of static charges, you can interpret the formula for the electrostatic potential energy in a common-sense way.





Gravitation

Electricity

Let us repeat this one more time. The potential energy changes in a system of two masses are analogous to the changes occurring within a system of unlike charges.

Both systems are composed of mutually attracting components. Work is required to separate the components (mutually attracting masses or mutually attracting charges) and as they are moved further apart, the system gains potential energy equal to the work performed in moving the components of the system from the initial to the final position.

We are repeating this basic statement fifty times because it really is important. If I had not worked with a large number of premedical students, I might think this is enough, but I know you need to hear it.

Think of two masses attracted by gravity or two unlike charges attracted by electric force as having potential energy down below zero, a negative number.

How far below zero is the potential energy? That tells you how much work needs to be done to completely seperate the components of the system, the binding energy.




Work, Energy, and Power

Electricity

Atomic Theory

The Chemical Bond

Intermolecular Forces

Thermochemistry

Chemical Thermodynamics and the Equilibrium State

When conceptually interpreting the internal energy change involved in a chemical process, the first step is to judge the electrostatic potential energy changes that occur with the realignment of the charged particles between the initial and final states. What are the changes in the relative position of charge densities (electrons and protons) at the atomic level. What has changed at the the molecular level or intermolecular molecular level? This can often lead directly to predicting the internal energy changes that occur through a chemical reaction or other type of chemical transformation such as a phase change or solution process.

Note that along with the collective electrical potential energy of the charged particles, the kinetic energy, which they possess through their motion, is the other major form of chemical internal energy. Kinetic energy is distributed in partitions or modes of translational, rotational and vibrational motion.

Although you must always keep in mind that the interactions are governed by quantum mechanics, for most purposes a basic view of electrostatic potential energy change is often sufficient to predict whether or not a system has gained or lost energy through a particular transformation.

Often the next step in chemical analysis is to move from the particle level approach to internal energy to the macrostate perspective of thermochemistry and ask how the internal energy changes we have analyzed will translate into heat flow and work between the system and its surroundings. From thermochemistry, then you move on to chemical thermodynamics, in which the heat flow, or enthalpy change, is a primary conceptual operator, along with the entropy change of the system, to determine which direction the reaction will proceed on its way toward the equilibrium state. The combination of enthalpy change and entropy change in determining the direction of spontaneity is embodied in the thermodynamic quantity - the free energy of the system.

This line of reasoning, as an imaginative conceptual skill rather than a specific type of quantitative problem solving, to move in the conceptual imagination from the consideration of electrostatic potential energy changes at the particle level to internal energy change of the system to heat flow and work between the system and its surroundings, then bringing entropy into the discussion and, deriving, finally, an understanding of the free energy change and, thus, spontaneity, really is of central importance to understanding chemical change. It is one of the primary conceptual arcs in physical science.




Electricity

Thermochemistry

Chemical Thermodynamics and the Equilibrium State

Acids and Bases

Organic Acids and Bases

Before beginning the discussion below, get a sheet of scratch paper and draw out the molecular structures of ethanol, ethoxide anion, acetic acid, acetate anion, fluoroacetic acid, and fluoroacetate anion.

Although molecules are quantum electrodynamic systems, classical electrostatics provides an extremely helpful 'rule of thumb' framework for interpreting potential energy changes at the molecular level. At heart, the discussion which follows involves comparative analysis of the molecular forms at hand in the light of the following basic formula for electrostatic potential energy:



Let us develop an example to show how a basic understanding of electrostatics can help interpret a chemical equilibrium problem, let us take an example from acid-base chemistry. Why is acetic acid a stronger acid than ethanol, and why is trifluoroacetic acid a stronger acid than acetic acid? In other words, let us examine the strength of these three acids, from weakest to strongest: ethanol, acetic acid, and trifluoroacetic acid.

To begin, part of any examination of the strength of an acid is an investigation of the stability of the conjugate base. Typically, the ionization of an acids yields an anionic conjugate base. As a general rule, the lower the internal energy of this negatively charged product, generally, the more thermodynamically favored will be ionization, and therefore, the stronger the acid. In other words, something that causes the energy of the negatively charged conjugate base to be lower is going to tend to increase the acidity.

For example, increasing acidity in the progression from ethanol to acetic acid to fluoroacetic acid can be interpreted in terms of the decreased electrostatic potential energy of the negatively charged product. First, compare the conjugate base of ethanol (ethoxide) to the conjugate base of acetic acid (acetate). The big difference is that acetate is a resonant form, while ethoxide is not. Although the details are a bit more complicated, resonance allows the electron charge to spread out. With resonance stabilization, the acetate anion has lower energy vis--vis acetic acid than ethoxide does vis--vis ethanol. This lower electrostatic potential energy encourages spontaneous formation.

Moving from acetic acid to the even stronger acid, trifluoroacetic acid, we see further stabilization by induction in the trifluoroacetate anion. Induction enables opposite charges to draw closer together, the negative electrons being pulled inward by the powerful fluorine nucleus represents a different kind of decrease in electrostatic potential energy (electrostatic potential energy can decrease when like charges spread apart and when unlike charges move together).

In summary, a basic understanding of electrostatic potential energy is extremely helpful to understanding why acetic acid is a stronger acid than ethanol, and why trifluoroacetic acid is a stronger acid than acetic acid.








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