It is always possible to postulate a kinetic rate law and test it. The chemical reaction in this case is
$$ \ce{CaCO3(s) + 2H+(aq) -> Ca^{2+}(aq) + H2O(l) + CO2(g)} \tag{1} $$
and the statement of mass conservation is
\begin{equation}
\frac{\mathrm{d}c_\ce{H+}}{\mathrm{d}t} = -2r_\ce{H+} \tag{2}
\end{equation}
Eq. (2) assumes that there are no spatial variations of the concentration along the volume, which is ensured with a sufficiently high stirring rate. The only thing you have to do, is propose a function for $r_\ce{H^+}$.
What you can always do is apply finite differences with Eq. (2), so that
\begin{equation}
r_\ce{H+} \approx -\frac{1}{2}
\left(\frac{\Delta c_\ce{H+}}{\Delta t}\right) \tag{3}
\end{equation}
which is what you stated in the post that you are going to do.
Fusi et al. have studied this particular reaction. Since this is a heterogeneous system, the reaction takes place at the solid/aqueous interface between the calcium carbonate and hydrogen ions. The authors wrote the RHS of Eq. (2) in the next form
$$ r = kS^*(c^* - c_0^*)^\gamma \tag{4} $$
If you take a look at the results, they obtained an excellent agreement with experimental data. Thus, the mathematical model of the authors postulate that:
- The kinetics are directly proportional to the surface available of reaction. This surface changes with time, and is a function of a particular geometry shape of the solid, which must be decided.
- It is proportional to the concentration difference between the hydrogen ions $c^*$ and some threshold concentration $c_0^*$ for which the reaction stops, at a certain power $\gamma$.
As a result, the mathematical model has three unknowns: the rate constant $k^*$, the threshold concentration $c_0^*$, and the power $\gamma$.
You can do exactly the same, propose a function and see the goodness in the fit.
References
The paper can be downloaded for free in here:
- Fusi, L. & Monti, Alessandro & Primicerio, Mario. (2012). Determining calcium carbonate neutralization kinetics from experimental laboratory data. Journal of Mathematical Chemistry. 50. 10.1007/s10910-012-0045-3.
