When do I use the hydronium ion in an acid-base equation? I have a question about when to use H3O+ and when to use the actual compound. I'm not really sure how to word this question so I'll show you an example of what I mean. 



Example of using H3O:

"A titration for a sample of 25mL of 0.1 M NH3 by 0.1M HCl is conducted. Calculate the pH after the addition of 12 mL of 0.1M HCl"

$\ce{NH3 + H3O -&gt; NH3 + H2O} $
(etc)



Example using the compound: 

"Calculate the pH of 75 mL of 0.1M HC2H3O2 and .2M of NaC2H3O2 to which 9.5mL of 0.1M HCL is added"

$\ce{C2H3O2- + HCl -&gt; HC2H3O2 + Cl-}$
(etc)



My question is, when are we supposed to use HCl in the equation and when are we supposed to use H3O+? Is it only when you are using a buffer that you are to use HCl? If so, why is this?
In both your cases, only H+ actually participates in the reaction. Remember that HCl is a strong acid, and dissociates completely into H+ and Cl-. For example, consider the net ionic form of your second equation:

$\ce{C2H3O2- + HCL -&gt; HC2H3O2 + Cl-}$

$\ce{C2H3O2- + (H+) + Cl- -&gt; HC2H3O2 + Cl-}$

$\ce{C2H3O2- + H+ -&gt; HC2H3O2}$

For your first equation, also note that, similarly, although the entire H30+ molecule participates in the reaction, only the H+ is transferred. (Also, I think you meant NH4+ instead of NH3 as a product.) So:

$\ce{NH3 + (H3O)+ -&gt; NH4+ H2O}$ 

$\ce{NH3 + H+ -&gt; NH4+}$

So basically, they both use the same compound (H+). Usually water is the main producer of H+ (through self-ionization). You just need to consider factors such as the common ion effect that would make other compounds such as HCl the main producer of H+ instead of water.