# Hydrate decomposition equation steps

When a hydrate decomposes it loses water molecules in steps. Does each step have a chemical equation?

If so is the following equations for decomposition of cupric sulfate hydrate correct? \begin{align} \ce{CuSO4 * 5 H2O &→ CuSO4 * 4 H2O + H2O}\\ \ce{CuSO4 * 4 H2O &→ CuSO4 * 3 H2O + H2O}\\ \ce{CuSO4 * 3 H2O &→ CuSO4 * 2 H2O + H2O}\\ \ce{CuSO4 * 2 H2O &→ CuSO4 * H2O + H2O}\\ \ce{CuSO4 * H2O &→ CuSO4 + H2O} \end{align}

One can rarely tell a priori what the steps are, and the results obtained experimentally may seem not intuitive at all if one tries to deduce the dehydration steps solely from the crystal structure (e.g. from the arrangement of the aqua ligands and water molecules trapped within the crystal lattice).¹

TG-DTG-DTA techniques, often coupled with powder XRD, are commonly used to determine the exact process behind each step interpreting mass change over time. Alternatively, you can deduce the possible steps from the initial structure, but this approach is less accurate.

So, for the classical textbook example of thermal decomposition of copper(II) sulfate pentahydrate the following steps of dehydration (1–2) and calcination (3–4) can be distinguished [1]:

\begin{align} \ce{CuSO4 * 5 H2O &→ CuSO4 * H2O + 4 H2O}\tag{1}\\ \ce{CuSO4 * H2O &→ CuSO4 + H2O}\tag{2}\\ \ce{2 CuSO4 &→ CuO * CuSO4 + SO3}\tag{3}\\ \ce{CuO * CuSO4 &→ 2 CuO + SO3}\tag{4} \end{align}

You could also assume the loss of four water molecules as a single step since in the crystal structure copper(II) atom has octahedral environment with four $$\ce{H2O}$$ and two $$\ce{SO4^2-}$$ ligands. Writing chemical equation for each act of the water molecule loss is not a sin, but it makes little practical sense as the intermediate crystallohydrates are unstable and rapidly undergo further dehydration.

### Notes

¹ From the crystal structure one may assume that during the first step only one water molecule is eliminated from the lattice (Figure 2a) since copper(II) is coordinated octahedrally by four water molecules in equatorial area and has two sulfate ligands in apical positions (Figure 2b).

Figure 2. Crystal structure of $$\ce{CuSO4 * 5 H2O}$$, data from CIF for Chalcanthite. Color scheme: $$\color{#EEEEEE}{\Large\bullet}~\ce{H}$$; $$\color{#FF0D0D}{\Large\bullet}~\ce{O}$$; $$\color{#FFFF30}{\Large\bullet}~\ce{S}$$; $$\color{#C88033}{\Large\bullet}~\ce{Cu}$$. a: Unit cell content. b: Coordination environment and nearest neighboring water molecules of the copper(II) center.

However, this is not the case even though lattice water molecules are kept in place via H-bonds and should posses seemingly weaker interaction with the cationic part. In reality many assumptions suitable for estimation of melting points of molecular crystals, e.g. regarding the number of bonds and their types don't work well for ionic crystals and so the dehydration patterns can only be established exactly experimentally.

### References

1. Gadalla, A. M. Kinetics of Thermal Decomposition of $$\ce{CuSO4 · 5H2O}$$ to $$\ce{CuO}$$. International Journal of Chemical Kinetics 1984, 16 (6), 655–668. https://doi.org/10.1002/kin.550160604.