[jwhalen]

Greetings. I was wondering if someone might be able and willing to help me with a particular problem.

It's from the third chapter of Organic Chemistry as a Second Language: First Semester Topics by David Klein. A little context: the purpose of the question is to identify which hydrogen is more likely to be donated (more acidic), using one of the four factors:
(i) Atom
(ii) Resonance
(iii) Induction
(iv) Orbital

I have ruled out (i) because both protons come from Carbon, and (iv) because they are both sp3 hybridized.

For factor (ii), I drew resonance structures but I can only come up with two for each, so I'm not quite sure if one connjugate base is more stable than the other.

I'm a little uncertain about (iii) because one proton is between two oxygens and the other proton is between an oxygen and a carbon.

The other questions I got wrong I was able to work through and figure out where I went wrong, but I can't figure this one out so I would be incredibly appreciative if someone would be able to help guide me to the answer. Thank you in advance!

[Babcock_Hall]

Can you show us what your resonance structures look like?

[jwhalen]

Can you show us what your resonance structures look like?

Absolutely, but please don't judge. 

The structures on the left pertain to the top carbon's proton (between the two Oxygen bonds), and the structures on the right pertain to the other proton. (FYI: The numbers within the ring are the #hydrogens, just for my own clarity since I'm fairly new at this.)

Since you brought up observing my structures, I just realized that the structure on the left could have another structure that is mirrored (i.e - either breaking the double bond of the left Oxygen or right Oxygen). So therefore the proton attached to the carbon between the two oxygens could have a total of 3 resonance structures, whereas the other option would only have the two that I've drawn. Correct? Horrendously and unforgivably erroneous?

[Babcock_Hall]

There are three resonance structures for the left-hand anion.
EDT
The final paragraph you wrote in the previous response is correct.

[jwhalen]

There are three resonance structures for the left-hand anion.

Right, that's what I deduced once you requested seeing my structures, as I outlined above. Herego: more structures = increased stability = more acidic, therefore the left anion is the correct answer.

Thank you very much for your help.