Numerical simulation and calculations of pH a. Reaction of $\ce{CO2}$ addition in water is as follows: 

$\ce{CO2}$ + $\ce{H2O}$ $\ce{-&gt;}$ $\ce{H2CO3}$

b. Then, pH of $\ce{H2CO3}$ solution is increased to 12 by addition of 1M $\ce{NaOH}$.

So, the reaction would be:

$\ce{2NaOH(aq)}$ + $\ce{H2CO3(aq)}$ $\ce{-&gt;}$ $\ce{Na2CO3(aq)}$ + $\ce{2H2O}$

c. This new solution at pH 12 is added to $\ce{CaCl2}$ solution; the final reaction of the system would be:

(  $\ce{Na2CO3(aq)}$ + $\ce{2H+}$ + $\ce{2OH-}$  ) + $\ce{CaCl2}$ $\ce{-&gt;}$ $\ce{CaCO3(s)}$ + $\ce{2 NaCl}$ + $\ce{2H2O}$

My questions are:

1. Is the final chemical reaction correct?

2. By setting the pH of step c equal to 12, which is ( $\ce{Na2CO3(aq)}$ + $\ce{2H+}$ + $\ce{2OH-}$ ), and addition of 50 ml of that to $\ce{CaCl2}$ solution, is it possible to make some sort of pH calculations?

$\ce{[H+]} = 10^{-12} M$

$\ce{[OH-]} = 10^{-2} M$

$\ce{[CO3]}$ = assuming 0.05 M in 50 ml

3. Overall, is it possible to do a numerical simulation (e.g., MATLAB) of change in the overall solution pH? OR, predict the final pH by calculations?

Thanks and Best Regards,
As an answer to your overall question: it is indeed possible to do numerical simulations of pH in different solutions or mixtures, and there is a number of programs or spreadsheets available if ou search the net. My personal favorite is Curtipot made by Prof. Gutz: http://www.iq.usp.br/gutz/Curtipot_.html