Here we will go through a few examples on how we choose primary and secondary species using the tableau method. Details are referred to in chapter 2, Morel and Hering, 1993.
How do we categorize the primary and secondary species of the system? Here we go through several steps for the choice of primary and secondary species.
We have 3 fast aqueous reactions, which means that we have 3 laws of mass action, as shown in three expressions defining the equilibrium constant for each reaction.
Species | H+ | CO32- | (H2O) |
---|---|---|---|
H+ | 1< | 0 | 0 |
OH- | -1 | 0 | 1 |
H2CO30 | 2 | 1 | >0 |
HCO3- | 1 | 1 | 0 |
CO32- | 0 | 1 | 0 |
We can write all species in terms of H+ and CO32-:
$$\begin{array}{l}
\mathrm{H}^{+}=\mathrm{H}^{+} \\
\mathrm{CO}_{3}^{2-}=\mathrm{CO}_{3}^{2-} \\
\mathrm{OH}^{-}=\left(\mathrm{H}_{2} \mathrm{O}\right)-\mathrm{H}^{+} \\
\mathrm{H}_{2} \mathrm{CO}_{3}=2 \mathrm{H}^{+}+\mathrm{CO}_{3}^{2-} \\
\mathrm{HCO}_{3}^{-}=\mathrm{H}^{+}+\mathrm{CO}_{3}^{2-}
\end{array}$$
Here ${OH}^{-}$, $\mathrm{H}_{2} \mathrm{CO}_{3}{}^{0}$, and ${HCO}_{3}^{-}$ are secondary species.
Species | OH- | HCO3- | (H2O) |
---|---|---|---|
H+ | -1 | 0 | 1 |
OH- | 1 | 0 | 0 |
H2CO3 | -1 | 1 | 1 |
HCO3- | 0 | 1 | 0 |
CO32- | 1 | 1 | -1 |
We can then write all species in terms of primary species:
$$\begin{array}{l} \mathrm{H}^{+}=\left(\mathrm{H}_{2} \mathrm{O}\right)-\mathrm{OH}^{-} \\ \mathrm{OH}^{-}=\mathrm{OH}^{-} \\ \mathrm{H}_{2} \mathrm{CO}_{3}=\mathrm{HCO}_{3}^{-}+\mathrm{H}_{2} \mathrm{O}-\mathrm{OH}^{-} \\ \mathrm{HCO}_{3}^{-}=\mathrm{HCO}_{3}^{-} \\ \mathrm{CO}_{3}{ }^{2-}=\mathrm{HCO}_{3}^{-}-\mathrm{H}_{2} \mathrm{O}+\mathrm{OH}^{-} \end{array}$$Similarly, (H+, HCO3-), (H+, H2CO3), (OH-, CO32-) are also legitimate choices for primary species. However (H2CO3, CO32-), (HCO3-, CO32-), are not. You can practice using these species to write the expression of secondary species.
If we impose the charge balance condition in example 1, we will then an additional algebraic relationship: $$\mathrm{H}^{+}=\mathrm{OH}^{-}+\mathrm{HCO}_{3}^{-}+2 \mathrm{CO}_{3}^{2-}$$ In this case how many primary species will we have? How many secondary species? What are they?
If we add an additional species Ca2+ in the closed carbonate system in example 1, we then have the following reactions in addition to those in Example 1:
$$\begin{array}{l}
\mathrm{CaCO}_{3}^{0} \Leftrightarrow \mathrm{Ca}^{2+}+\mathrm{CO}_{3}^{2-} \\
\mathrm{CaHCO}_{3}^{+} \Leftrightarrow \mathrm{Ca}^{2+}+\mathrm{HCO}_{3}^{-} \\
\mathrm{CaOH}^{+} \Leftrightarrow \mathrm{Ca}^{2+}+\mathrm{OH}^{-}
\end{array}$$