I understand that all strong acids have weak bases and strong bases have weak acid conjugates therefore the conjugate base of HCl with the conjugate acid of NaOH for example (NaCl) does not effect the pH. So when you pair a strong acid conjugate to a strong base conjugate it is neutral. When you pair a strong acid conjugate to a weak base conjugate it is acidic? When you pair a weak acid conjugate to a strong base conjugate it is basic? Anyone wish to clarify please....
First, the difference between a strong acid/base and a weak acid/base is that the strong completely dissociates while the weak exists in an equilibrium. The conjugate of a weak base is a weak acid, however there does not exist an acid/base conjugate for strong acid and bases.
For the HCl + NaOH situation, as long as moles = moles, yes they will "cancel out". When you start titration and mixing weak acids/bases things get a little more shaky. Especially when you throw in polyprotic acid combinations.
Know that the reverse reaction the K is 1/K for the constant given. Also Kb (of the conjugate) is equal to Kw/Kb (because KaKb = Kw) and when you add chemical equations you multiply the constants
But to calculate the pH in your example you would have to take into consideration the following:
CO3 2- (reacting with NH4+, H20, H2CO3, H3O+)
HCO3- (reacting with H20, NH3, NH4+, OH-, H3O+)
NH4+ (reacting with CO3 2-, HCO3-, H20, OH-)
etc etc for NH3, H3CO3...
There's just too many components and reactions to follow, and while its possible (thanks analytical chem!), you're probably not going to have something so complicated on the MCAT
It you're mixing monoprotic/basic components it's a lot easier to calculate pH