What is the balanced equation for the reaction of a strong acid, using
say XCOOH to represent a strong acid, with NaHCO3. Would the rxn be
XCOOH + NaHCO3 goes to XCOO- + Na+ + CO2 + H2O?

What about the balanced equation for the reaction of a weak acid,
using ArOH to represent weak acid, with NaOH?

Hello,
-----------
I tried to address all possibilities in crafting my answer. If you
want a concise answer, simply read the sections with a star or
asterisk (*).
-----------

Almost all carboxylic acids (-COOH) are weak. Thus, I will present two
scenarios for acid + sodium bicarbonate.

Strong acid + sodium bicarbonate
HX + NaHCO3 --> H2CO3 + NaX
H2CO3 --> H20 + CO2 (decomposition of carbonic acid)
N.B. The first line can be written as: HX + NaHCO3 --> H2CO3 + Na+ + X-

example:
HCl + NaHCO3 --> H2CO3 + NaCl
H2CO3 --> H2O + CO2

* Weak acid (-COOH) + sodium bicarbonate
RCOOH + NaHCO3 --> RCOONa + H2CO3
H2CO3 --> H2O + CO2
N.B. Convention has it that R- is used to represent alkyl groups with
a carboxylic acid group. X can be substituted and the above reaction
would make sense; however, in general, X denotes a halogen (chlorine,
fluorine, etc.)
* N.B.2 The first line can be written as: RCOOH + NaHCO3 --> RCOO- +
Na+ + H2CO3. So yes, you are correct. (You simply combined the
neutralisation and the decomposition of carbonic acid into one
equation, which is correct.)

example:
CH3COOH (acetic acid, vinegar) + NaHCO3 --> CH3COONa (sodium acetate) + H2CO3
H2CO3 --> H2O + CO2


As for a weak acid and sodium hydroxide -
You mention that you want ArOH to denote the acid. This corresponds
with an alcohol group or a hydroxide group. Hydroxide groups, as an
ion, do not donate protons and cannot act as acids, since O(-2)
(single doubly-negative oxygen) never forms. Thus, I will assume you
want the reaction between an alcohol and a base. (It must be noted
that alcohols are extremely weak acids.)

For a general alcohol -
R-OH + NaOH --> R-O-Na + H2O
N.B. Can be written as ROH + NaOH --> RO- + Na+ + H2O

* Ar may denote a benzene (aromatic) ring. ArOH would then be phenol,
and the following reaction applies:
ArOH + NaOH --> Ar-O-Na + H2O
N.B. Also can be written as C6H5OH + NaOH --> C6H5O-Na + H2O ... since
a phenyl (aromatic ring) is C6H5.

If you used Ar to denote argon, then it is wrong; there is no such
thing as argon hydroxide (ArOH).

If you have questions about any part of this answer, please use the
"Clarify Answer" function.

Thanks!

- supermacman-ga

Reference
J McMurry, Organic Chemistry, 6th edition, United States of America,
Thomson-Brooks/Cole, 2004.

thank you for the very detailed explanation! That will help me
understand future equations too!

Also note that when using weak acids, an equilibrium is involved. 
Just Trying to help.

Regards,
webdesignerservr-ga

Hello shadowrider-ga:

I'm glad my detail helped you. Sometimes I think I write too much, but
in this case detail was a plus!