The dissociation of formic acid ($\ce{HCOOH}$) is: $$ \ce{HCOOH -> H+ + COOH-} $$
Why is there a charge on $\ce{COOH^{-1}}$ though? Is it achieved through: $$1\times(\ce{C^{4+}}) + 2\times(\ce{O^{2-}}) + 1\times(\ce{H-})?$$
Does carbon exist as a 4+ ion?
Also, as a somewhat unrelated question, can an acid donate multiple $\ce{H+}$ ions (or can a base receive multiple $\ce{H+}$ ions)?
Thanks in advance!
Not all bonds are ionic bonds. While saying that "Carbon is 4+ valency and is a $\ce{C^{4+}}$ ion" works for carbides like $\ce{Be2C}$, it will not work for a covalent compound like $\ce{HCOOH}$.
Instead of ionic bonds, here we have covalent bonds. Whereas in an ionic bond one atom donates an electron to the other, in a covalent bond, two atoms each contribute some electrons and share them.
For example, with $\ce{O2}$, each atom shares two electrons with the other. Neither "give up" any electrons, they are just shared and contribute to the octets of both atoms:
The formate ($\ce{HCOO-}$) ion is like this:
The central carbon shares one electron with a hydrogen, and two electrons with an oxygen. It also shares one electron with a negatively charged oxygen. This completes the octets (or doublets in the case of hydrogen) of all four atoms.
With electrons drawn on:
Note that while the charges are not of the $1\times(\ce{C^{4+}}) + 2\times(\ce{O^{2-}}) + 1\times(\ce{H-})$ form, the oxidation numbers are.
You have convoluted a simple chemical into a ponderous problem. The formula as written [H-CO-OH] implies that is there is a H attached to carbon and a H attached to oxygen. The conjugate base as written [COOH-] implies that the H attached to carbon was removed without its electron leaving a negative charge on the COOH that resides on the carbon. Whether this was intentional to confuse or simply an inanity is hard to tell, but it does make it hard to assign oxidation numbers, but I can try: O is -2, the first O is double bonded to the carbon sharing 4 electrons so its ox no. is -4. The second O is single bonded and shares 2 electrons so is -2; total negative is -6 from the O's. We supposedly know that the total charge on the ion is -1 so must come up with 5 +charges; so C+4 and H+1 fill the bill. [Another way to look at a carbonyl, C=O, is to hydrate it making C[OH]2.] Alternatively let the oxygens be -2, then the remaining H is +1 and the Carbon is +2. This is in line with the hydrated structure H-C[OH]3: 3 O's = -6, 4 H's = +4, C = +2. This is in agreement with a +2 oxidation number for the carbon in carbon monoxide, CO, which happens to be the anhydride of formic acid. My advice is to not get involved with oxidation numbers with organic compounds.
Now some chemistry! formic acid HCO2H is a weak acid with a proton attached to carbon and a proton attached to one of the oxygens. The hydrogen attached to oxygen is MUCH more acidic and the reaction is H-COO-H +:B = H-CO-O- + H:B+. Now you see where the electrons are [if you were interested, at least you will be less enticed to make H -1 when attached to O.]
