[alexofordummies]

The original question I was answering was: Draw the structure of benzoic acid in ether and 5% aq NaOH. After a week/weekend of looking over it, I realize that I really don't know as much about chemistry as I thought I did. Could anyone look at the (perhaps excessive) train of thought I used, and the questions that came up? Be as anal and critical as you can, I have a lot to learn.

I understand that solids form due to the intermolecular forces holding the individual models together, so for something like benzoic acid I'd imagine there'd be hydrogen bonding between the double bonded O and O-H.

Benzoic acid is soluble in hot water (25C), which must mean in combonation, the heat of the solution and polarity of H2O is enough to break and replace the hydrogen bonding between the benzoic acid molecules. If 25C is just enough to break the intermolecular forces, i don`t think the intramolecular forces can be broken (I`m assuming the intramolecular forces are significantly stronger than the intermolecular forces), and so the benzoic acid molecule does not lose a proton off of it`s O-H.

When benzoic acid is dissolved in NaOH, the negative pull of OH- is enough to pull the proton off benzoic acid and the Na+ takes it place creating an ionic bond.

Now when benzoic acid is mixed with diethyl ether, it has a much easier time dissolving than it did with water, I read this is because of the general trend "like dissolves like". Trying to picture this in my head, the oxygen has two bonds in diethyl ether just as it does in water, so the negative intermolecular pull from diethyl ether should be about the same as it is from water? Which must mean it's the size of diethyl ether that makes the difference, which I sort of have a difficult time visualizing; how does the size in this case really make that much of a difference?

If my logic is correct, then benzoic acid has more than one form it can dissolve into (this is new to me), one that perserves it's structure entirely, and another where it turns into a benzoate ion. My main concern is then how do I go about (theoretically) telling whether a compound (benzoic acid in this case) is just dissolving, or is actually losing protons in a particular solvent. Is there some sort of electronegativity calculation I can do? Or is it a more qualitative knowledge that I need to become familiar with? If I where given this assignment again for a different compound and I didn't have google, what would be the approach to take answering it?

[Yggdrasil]

When benzoic acid is dissolved in NaOH, the negative pull of OH- is enough to pull the proton off benzoic acid and the Na+ takes it place creating an ionic bond.

Correct.  The ionic bond probably won't be very stable in water.  However, water has an easy time dissolving ions, so the benzoate ion will be pretty soluble in water.

Now when benzoic acid is mixed with diethyl ether, it has a much easier time dissolving than it did with water, I read this is because of the general trend "like dissolves like".

Correct.

Trying to picture this in my head, the oxygen has two bonds in diethyl ether just as it does in water, so the negative intermolecular pull from diethyl ether should be about the same as it is from water? Which must mean it's the size of diethyl ether that makes the difference, which I sort of have a difficult time visualizing; how does the size in this case really make that much of a difference?

The difference isn't so much in size, but it's that the dipole moment of diethyl ether is much smaller than the dipole moment of water (e.g. compare the dielectric constants of the two solvents).  In water, water-water interactions are very strong and they tend to exclude benzoic acid molecules (benzoate-water interactions are favorable enough so that benzoate ions are not excluded from the solution, however).  Because diethyl ether much less polar than water, ether-ether interactions aren't strong enough to disfavor ether-benzoic acid interactions, so benzoic acid is able to dissolve in ether.

Benzoic acid does have a polar region (the carboxylic acid portion), however.  In some non-polar solvents, benzoic acid and other organic acids will often form a hydrogen-bonded dimer (as you mentioned in the beginning of your post) and this dimer will the be unit that has dissolved in the solvent.  I'm not sure if benzoic acid forms a dimer in ether.

If my logic is correct, then benzoic acid has more than one form it can dissolve into (this is new to me), one that perserves it's structure entirely, and another where it turns into a benzoate ion.

Absolutely correct.  I'm glad the question helped you learn something.

My main concern is then how do I go about (theoretically) telling whether a compound (benzoic acid in this case) is just dissolving, or is actually losing protons in a particular solvent. Is there some sort of electronegativity calculation I can do? Or is it a more qualitative knowledge that I need to become familiar with? If I where given this assignment again for a different compound and I didn't have google, what would be the approach to take answering it?

In most of the cases where dissolving a compound leads to ionization, there is an acid/base reaction involved.  Therefore, you just need to be able to recognize acidic/basic groups in organic compounds (e.g. carboxylic acids, amines, phenols, etc.).