Reasonings on the pH of calcium carbonate in ammonium chloride solution

Consider calcium carbonate saturated in $1.0\:\mathrm{M}$ ammonium chloride solution. I have calculated the $\mathrm{pH}$ of this solution analytically (with mass and charge balance) to be $6.92$.

Now, how would the actual solution $\mathrm{pH}$ compare to the theoretical, calculated $\mathrm{pH}$ - in a general sense?

Would one expect the actual solution $\mathrm{pH}$ to be higher or lower than $6.92$?

I know that there are going to be a host of solute-solute interactions in this system that are more than likely to cause deviations from ideal solute behavior. Here's a list of species in the system:

1. $\ce{Ca^2+}$ and its respective hydrates
2. $\ce{CO_3^2-}$ and its respective protonation products (i.e. bicarb and carbonic acid)
3. $\ce{H_4N+}$ and its respective deprotonation products (i.e. ammonia)
4. $\ce{Cl-}$ and perhaps (unlikely) a bit of its protonation product - hydrochloric acid.
5. $\ce{H_3O+}$
6. $\ce{HO-}$

Now, the question I'm fundamentally getting at is how would all these solutes interact with each other. I understand that the calcium ion and the carbonate ion with their +2 charge magnitudes is likely going to cause this solution to deviate significantly from ideal behavior. A quick leafing through of an analytical text lead me to this hypothesis. However, is it possible to actually predict the direction, so to speak, of $\mathrm{pH}$ deviation? Can we model this system with a computer program?

Also, I plan on actually taking $\mathrm{pH}$ measurements on this system. Here is a general outline of the things I plan to do; is there anything else that I need to take into account?

1. Use of triple distilled water. Our laboratory's "deionized" water runs strongly basic. Water will be distilled with a high partial pressure of nitrogen gas as to prevent carbon dioxide from dissolving in water.
2. Should we measure $\mathrm{pH}$ in a sealed vessel? I don't want any carbon dioxide to be dissolving into the system, again. Also, I don't want any ammonia gassing off from the system (since ammonia is a possible product upon saturating ammonium chloride solution with calcium carbonate). How would measuring $\mathrm{pH}$ in a sealed vessel work?
3. Any other lab practical tips/suggestions?