Re: is there a difference between these voltage definitions (see below)?

Chris,
In both chemistry and physics, the volt is defined as the difference in 
potential required to impart 1 Joule of energy to a charge of 1 coulomb:
1V = 1J/1C. The working definitions you ask about are related to the 
source of the electric potential--you know that there is only one type of 
voltmeter that measures the potential difference, no matter what the 
source of that difference may be. The potential difference may come from 
rotating a coil of wire in a magnetic field (like in a generator) or from 
an electrochemical cell (like a battery). Therefore, the answer to your 
first question is that the two working definitions (specialized 
definitions rather than the overall definition of voltage) will give the 
same result when measured by a voltmeter. (Source: Chapter 20, Section 
20.4 Cell EMF, "Chemistry the Central Science, 8th Edition", Brown, 
LeMay, and Bursten, Prentice Hall, New Jersey, 2000 ISBN 0-13-084090-4. 
Or any of the first 10 hits on a search for "voltage definition" at 
www.google.com)

Now for the Chemistry: "Why exactly does one substance have a stronger 
attraction for electrons than another..." You mention electronegativity, 
but to fully understand why one substance has a stronger attraction for 
electrons, we need to understand the atomic structure of atoms, and how 
the electrons are arranged around the nucleus of the atom. If an atom is 
completely isolated, it will have a number of protons with a charge of +1 
in the nucleus (along with neutrons and other subatomic particles) and 
the exact same number of electrons with a charge of -1 arranged in a 
specific pattern around the nucleus. 

The pattern of the electrons is determined by quantum theory. As protons 
and electrons are added to make different elements (the number of protons 
is called the atomic number, and defines an element--eg. 1 = hydrogen, 8 
= oxygen, 50 = tin, and 82 = lead). Quantum theory describes how the 
electrons are placed in atomic orbitals, and how many electrons can be in 
each orbital. This theory is observed in the Periodic Chart of the 
Elements. The most stable atomic structures are the Noble Gases (Group(or 
vertical column) 8A containing He = Atomic Number 2, Ne = 10, Ar = 18, Kr 
= 36, Xe = 54, and Rn = 86). Notice that these gases are at the right end 
of each period (row). These atomic numbers represent a completely filled 
quantum shell (each succeeding period is the next shell). This imparts 
high stability to that electronic structure. One measure of the stability 
of the electron cloud is the amount of energy required to take an 
electron away from the atom--the ionization energy. 

If we bring an electric field near the atom, how much energy (kJ/mole) 
must be provided to take an electron away? Figure 7.6 of Brown et al., 
shows the trend of the ionization energies of the elements (for the first 
electron). There are peaks at 
He (appx 2400 kJ/mole) followed by a drop to Li (appx 500 kJ/mole), 
a gradual climb to Ne (appx 2050 kJ/mole) followed by a drop to Na (appx 
500 kJ/mole),
a gradual climb to Ar (appx 1500 kJ/mole followed by a drop to K (appx 
480 kJ/mole),
a gradual climb to Kr (appx 1350 kJ/mole followed by a drop to Rb (appx 
450 kJ/mole) 
This pattern continues for Xe and Rn. The decrease in energy required to 
remove the first electron from Kr is less than that required for Ar 
because there are more electrons between the nucleus and the last 
electron, and that last electron if farther away from the nucleus; both 
those factors reduce the effective positive charge from the nucleus on 
the last electron making it easier to remove.      

Each element, starting at the left end of a row, is formed by adding one 
proton and electron to the preceeding element. 

The elements at the left side of the Periodic Table have one electron 
beyond the "magic number" of the noble gases. This electron is easily 
removed to leave the electron structure of a noble gas (the sodium ion 
Na+ has the same electronic structure as Ne). The energy required to 
remove that electron is much less than that required to remove an 
electron from a noble gas. That accounts for the drop in ionization 
energy after each noble gas. 

The elements at the right of the Periodic Table next to the Noble Gases, 
Group 7A, called the halogens--F, Cl, Br, I, and At, are one electron 
short of noble gas electronic structure. Therefore, this group has a very 
high electron affinity (leading to a high electronegativity value). The F-
ion has the same electronic structure as Ne. 

The details of Quantum Theory (given in Brown et al. Chapter 6 Electronic 
Structure of Atoms) show how the electron configuration for every element 
is determined, but using the Periodic Table, we can now answer the second 
question.

If we bring an electric field near an atom (or a molecule, or an ionized 
species such as Carbonate, CO3-), we can increase that field until there 
is enough energy available to take one electron away from the atom--that 
is changing the ionization energy into the potential that will give 
sufficient energy to cause ionization.

To give a uniform scale so that experimenters can share information, the 
reaction for the oxidation of the hydrogen atom to H+ and the reduction 
of the H+ to H is defined as 0 volts on the electrochemical scale. The 
common scale in use today is the Standard Reduction Potentials in Water 
at 25 degrees Celsius. A small table is given in Appendix E of Brown, et 
al. Others are available on the internet (search: Standard Reduction 
Potentials). We see that F2 (gaseous) + 2 electrons yielding 2F- 
(aqueous) has a Standard Reduction Potential of +2.87 volts. This 
indicates a very strong electron attraction. Whereas the reaction Li+ 
(aq) + an electron going to Li(solid) has a Standard Reduction Potential 
of -3.05 volts--indicating a very low electron attraction (equivalently, 
it takes a lot of work to add an electron to Li+). 

If we make an electrochemical cell with Li(s) and F2(gas), the cell will 
have an electrochemical potential of 5.92 volts with the Li the anode and 
the F the cathode (an ox and a red cat is a helpful mnemonic--anode is 
where oxidation takes place and reduction occurs at the cathode). 

To make an electrochemical cell, the constituents must be separated so 
that the electrons are forced into an external circuit where they can do 
work. Just mixing the two constituents will result in a reaction that 
does not do any external work. That is the main problem in making a LiF 
battery.

Now we can say that the exact answer to your question is that 
the "something to do with the potential energy of the electrons" is the 
Quantum Theory of the Electronic Structure of the Elements.